Finite Group Databasebeta

← #32883699

Subgroups — #32883699

Order 18176.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602648C211yesmaximal, characteristic, complemented
2#22602009C211yesmaximal, characteristic, complemented
3#22600492C211yesmaximal, characteristic, complemented
4#22600365C211yesmaximal, characteristic, complemented
5#22600342C211yesmaximal, characteristic, complemented
6#22600335C211yesmaximal, characteristic, complemented
7#22600286C211yesmaximal, characteristic, complemented
8#22600231C211yesmaximal, characteristic, complemented
9#22600191C211yesmaximal, characteristic, complemented
10#22600146C211yesmaximal, characteristic, complemented
11#22600094C211yesmaximal, characteristic, complemented
12#22600040C211yesmaximal, characteristic, complemented
13#22600019C211yesmaximal, characteristic, complemented
14#22600010C211yesmaximal, characteristic, complemented
15#22599880C211yesmaximal, characteristic, complemented
16#22599880C211yesmaximal, characteristic, complemented
17#22599828C211yesmaximal, characteristic, complemented
18#22599824C211yesmaximal, characteristic, complemented
19#22599440C211yesmaximal, characteristic, complemented
20#22599388C211yesmaximal, characteristic, complemented
21#22599241C211yesmaximal, characteristic, complemented
22#22599189C211yesmaximal, characteristic, complemented
23#22599101C211yesmaximal, characteristic, complemented
24#22599091C211yesmaximal, characteristic, complemented
25#22598603C211yesmaximal, characteristic, complemented
26#22598532C211yesmaximal, characteristic, complemented
27#22597648C211yesmaximal, characteristic, complemented
28#22597605C211yesmaximal, characteristic, complemented
29C2×#17986144C211yesmaximal, characteristic, complemented
30#22597394C211yesmaximal, characteristic, complemented
31C71×#3002C211yesmaximal, characteristic, complemented
32C2×#14556174C2211yescharacteristic, complemented
33C2×#14556155C2211yescharacteristic, complemented
34C2×#14556155C2211yescharacteristic, complemented
35C2×#14556151C2211yescharacteristic, complemented
36C22×#11765852C2211yescharacteristic, complemented
37C22×#11765850C2211yescharacteristic, complemented
38C2×D8×D71C2211yescharacteristic, complemented
39#17986746—21no—
40#17986739—21no—
41#17986712C2211yescharacteristic, complemented
42#17986693C2211yescharacteristic, complemented
43#17986691C2211yescharacteristic, complemented
44#17986678—21no—
45#17986668C2211yescharacteristic, complemented
46#17986668C2211yescharacteristic, complemented
47#17986668C2211yescharacteristic, complemented
48#17986660C2211yescharacteristic
49#17986660C2211yescharacteristic, complemented
50#17986649C2211yescharacteristic, complemented
51#17986644—21no—
52#17986640C2211yescharacteristic, complemented
53#17986637—21no—
54#17986637—21no—
55#17986637C2211yescharacteristic, complemented
56#17986637C2211yescharacteristic, complemented
57#17986637C2211yescharacteristic, complemented
58#17986633C2211yescharacteristic, complemented
59D4×C22⋊D71—21no—
60D4×C22⋊D71—21no—
61D4×C22⋊D71C2211yescharacteristic
62D4×C22⋊D71C2211yescharacteristic, complemented
63#17986622C2211yescharacteristic, complemented
64#17986602C2211yescharacteristic, complemented
65#17986600—21no—
66#17986582—21no—
67#17986579C2211yescharacteristic, complemented
68#17986577—21no—
69#17986577C2211yescharacteristic, complemented
70#17986565C2211yescharacteristic, complemented
71#17986564—21no—
72#17986563—21no—
73#17986563C2211yescharacteristic, complemented
74#17986559—21no—
75#17986510—21no—
76#17986510C2211yescharacteristic
77C2×#14556102—21no—
78C2×#14556102C2211yescharacteristic, complemented
79C2×#14556102C2211yescharacteristic, complemented
80#17986482C2211yescharacteristic, complemented
81#17986385C2211yescharacteristic, complemented
82#17986385C2211yescharacteristic, complemented
83#17986384C2211yescharacteristic, complemented
84#17986374C2211yescharacteristic, complemented
85#17986362C2211yescharacteristic, complemented
86#17986360C2211yescharacteristic, complemented
87#17986355C2211yescharacteristic, complemented
88#17986344C2211yescharacteristic, complemented
89#17986339C2211yescharacteristic, complemented
90#17986333C2211yescharacteristic, complemented
91#17986332C2211yescharacteristic, complemented
92#17986323C2211yescharacteristic, complemented
93#17986323C2211yescharacteristic, complemented
94#17986321C2211yescharacteristic, complemented
95#17986315C2211yescharacteristic, complemented
96#17986313C2211yescharacteristic, complemented
97#17986313C2211yescharacteristic, complemented
98#17986313C2211yescharacteristic, complemented
99#17986313C2211yescharacteristic, complemented
100#17986311C2211yescharacteristic, complemented
101#17986308C2211yescharacteristic, complemented
102#17986297C2211yescharacteristic, complemented
103#17986292C2211yescharacteristic, complemented
104#17986277C2211yescharacteristic, complemented
105#17986251C2211yescharacteristic, complemented
106#17986248C2211yescharacteristic, complemented
107#17986242C2211yescharacteristic, complemented
108#17986242C2211yescharacteristic, complemented
109#17986237C2211yescharacteristic, complemented
110#17986235C2211yescharacteristic, complemented
111#17986235C2211yescharacteristic, complemented
112#17986235C2211yescharacteristic, complemented
113#17986235C2211yescharacteristic, complemented
114#17986234C2211yescharacteristic, complemented
115#17986233C2211yescharacteristic, complemented
116#17986233C2211yescharacteristic, complemented
117#17986232C2211yescharacteristic, complemented
118#17986231C2211yescharacteristic, complemented
119#17986230C2211yescharacteristic, complemented
120#17986230C2211yescharacteristic, complemented
121#17986223C2211yescharacteristic, complemented
122#17986223C2211yescharacteristic, complemented
123#17986217C2211yescharacteristic, complemented
124#17986217C2211yescharacteristic, complemented
125#17986216C2211yescharacteristic, complemented
126#17986216C2211yescharacteristic, complemented
127#17986197C2211yescharacteristic, complemented
128#17986197C2211yescharacteristic, complemented
129#17986193C2211yescharacteristic, complemented
130#17986193C2211yescharacteristic, complemented
131#17986192C2211yescharacteristic, complemented
132#17986192C2211yescharacteristic, complemented
133#17986160C2211yescharacteristic, complemented
134#17986160C2211yescharacteristic, complemented
135#17986149C2211yescharacteristic, complemented
136#17986148C2211yescharacteristic, complemented
137#17986148C2211yescharacteristic, complemented
138#17986147C2211yescharacteristic, complemented
139#17986147C2211yescharacteristic, complemented
140#17986144C2211yescharacteristic
141#17986144C2211yescharacteristic, complemented
142#17986144C2211yescharacteristic, complemented
143#17986144C2211yescharacteristic, complemented
144#17986144C2211yescharacteristic, complemented
145#17986144C2211yescharacteristic, complemented
146#17986144C2211yescharacteristic, complemented
147#17986144C2211yescharacteristic, complemented
148#17986144C2211yescharacteristic, complemented
149#17986144C2211yescharacteristic, complemented
150#17986143C2211yescharacteristic, complemented
151#17986143C2211yescharacteristic, complemented
152#17986135C2211yescharacteristic, complemented
153#17986135C2211yescharacteristic, complemented
154#17986135C2211yescharacteristic, complemented
155#17986135C2211yescharacteristic, complemented
156#17986134C2211yescharacteristic, complemented
157#17986134C2211yescharacteristic, complemented
158#17986132C2211yescharacteristic, complemented
159#17986131C2211yescharacteristic, complemented
160#17986131C2211yescharacteristic, complemented
161#17986108C2211yescharacteristic, complemented
162#17986102C2211yescharacteristic, complemented
163#17986100C2211yescharacteristic, complemented
164#17986100C2211yescharacteristic, complemented
165Q16×Dic71C2211yescharacteristic, complemented
166#17986084C2211yescharacteristic, complemented
167D8×Dic71C2211yescharacteristic, complemented
168#17986079C2211yescharacteristic, complemented
169#17986070C2211yescharacteristic, complemented
170#17986070C2211yescharacteristic, complemented
171#17986067C2211yescharacteristic, complemented
172#17986067C2211yescharacteristic, complemented
173C8×C22⋊D71C2211yescharacteristic, complemented
174C8×C22⋊D71C2211yescharacteristic, complemented
175(C22⋊D71)⋊C8C2211yescharacteristic, complemented
176(C22⋊D71)⋊C8C2211yescharacteristic, complemented
177#17986057C2211yescharacteristic, complemented
178#17986057C2211yescharacteristic, complemented
179#17986002C2211yescharacteristic, complemented
180#17985999C2211yescharacteristic, complemented
181#17985994C2211yescharacteristic, complemented
182C2×#14556052C2211yescharacteristic, complemented
183C2×#14556049C2211yescharacteristic, complemented
184#102×D71C2211yescharacteristic, complemented
185#17985964C2211yescharacteristic, complemented
186#17985964C2211yescharacteristic, complemented
187C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
188C22×#41×C71C2211yescharacteristic, complemented
189C2×#135×C71C2211yescharacteristic, complemented
190C2×#135×C71C2211yescharacteristic, complemented
191#525×C71C2211yescharacteristic, complemented
192#452×C71C2211yescharacteristic, complemented
193#452×C71C2211yescharacteristic, complemented
194#451×C71C2211yescharacteristic, complemented
195#450×C71C2211yescharacteristic, complemented
196#449×C71C2211yescharacteristic, complemented
197#449×C71C2211yescharacteristic, complemented
198#448×C71C2211yescharacteristic, complemented
199#447×C71C2211yescharacteristic, complemented
200#416×C71C2211yescharacteristic, complemented
201#416×C71C2211yescharacteristic, complemented
202C2×C22⋊C8×C71C2211yescharacteristic, complemented
203#14556174—42no—
204#14556174—42no—
205C2×#11765866C2311yescharacteristic
206C2×#11765866C2311yescharacteristic
207C2×#11765866C2311yescharacteristic
208C2×#11765865—21no—
209C2×#11765865C2311yescharacteristic
210C2×#11765864—21no—
211C22×D284—21no—
212C22×D284C2311yescharacteristic
213C22×D284C2311yescharacteristic
214C22×C22⋊D71—21no—
215C22×C22⋊D71—21no—
216C22×C22⋊D71—21no—
217C22×C22⋊D71—21no—
218C2×D4×D71—21no—
219C2×D4×D71—21no—
220C2×D4×D71—21no—
221C2×D4×D71C2311yescharacteristic
222C2×D4×D71C2311yescharacteristic
223C2×D4×D71C2311yescharacteristic
224#14556155—42no—
225#14556155—42no—
226#14556151—42no—
227C2×#11765852—42no—
228C2×#11765852C2311yescharacteristic
229C2×#11765852C2311yescharacteristic
230C2×#11765852C2311yescharacteristic
231C2×#11765852C2311yescharacteristic
232C2×#11765852C2311yescharacteristic
233C2×#11765852C2311yescharacteristic
234C2×D568C2311yescharacteristic
235C2×D568C2311yescharacteristic
236C2×D568C2311yescharacteristic
237C2×D568C2311yescharacteristic
238C2×#11765850—42no—
239C2×#11765850C2311yescharacteristic
240C2×#11765850C2311yescharacteristic
241C2×#11765850C2311yescharacteristic
242C2×#11765850C2311yescharacteristic
243C2×#11765850C2311yescharacteristic
244C2×#11765850C2311yescharacteristic
245D8×D71—42no—
246C2×#11765848C2311yescharacteristic
247C2×#11765848C2311yescharacteristic
248C22×C71⋊C8C2311yescharacteristic
249C22×C71⋊C8C2311yescharacteristic
250C2×C8×D71C2311yescharacteristic
251C2×C8×D71C2311yescharacteristic
252#14556127C2311yescharacteristic
253#14556124—21no—
254#14556124—21no—
255#14556124—21no—
256#14556124—21no—
257#14556124C2311yescharacteristic
258#14556124C2311yescharacteristic
259#14556124C2311yescharacteristic
260#14556123—21no—
261#14556123—21no—
262#14556122—21no—
263#14556119—21no—
264#14556119C2311yescharacteristic
265#14556117—21no—
266#14556117—21no—
267#14556117C2311yescharacteristic
268#14556117C2311yescharacteristic
269#14556117C2311yescharacteristic
270#14556116—21no—
271#14556114—21no—
272#14556114—21no—
273#14556114—21no—
274#14556113—21no—
275#14556112—21no—
276#14556112—21no—
277#14556111—21no—
278#14556111—21no—
279#14556111—21no—
280#14556111D411yescharacteristic
281#14556111D411yescharacteristic
282#14556110—21no—
283#14556110—21no—
284#14556110—21no—
285#14556110—21no—
286#14556109—21no—
287#14556108—21no—
288#14556107—21no—
289#14556107D411yescharacteristic
290#14556107D411yescharacteristic
291#14556106—21no—
292#14556105—21no—
293#14556104—21no—
294#14556104—21no—
295#14556104C2311yescharacteristic
296#14556104C2311yescharacteristic
297#14556104C2311yescharacteristic
298#14556103—21no—
299#14556103—21no—
300#14556103C2311yescharacteristic
301#14556103C2311yescharacteristic
302#14556102—21no—
303#14556102—21no—
304#14556102—21no—
305#14556102—21no—
306#14556102—21no—
307#14556102—21no—
308#14556102—21no—
309#14556102—21no—
310#14556102—21no—
311#14556102—21no—
312#14556102—21no—
313#14556102—21no—
314#14556102D411yescharacteristic
315#14556102D411yescharacteristic
316#14556102C2311yescharacteristic
317#14556102C2311yescharacteristic
318#14556102C2311yescharacteristic
319#14556102C2311yescharacteristic
320#14556102C2311yescharacteristic
321#14556102C2311yescharacteristic
322#14556102C2311yescharacteristic
323#14556102C2311yescharacteristic
324#14556101—21no—
325#14556101—21no—
326#14556101—21no—
327#14556101—21no—
328#14556101—21no—
329#14556100—21no—
330#14556100—21no—
331#14556100—21no—
332#14556100—21no—
333#14556100—21no—
334#14556100—21no—
335#14556100—21no—
336#14556100—21no—
337#14556099—21no—
338#14556099—21no—
339#14556099—21no—
340#14556099—21no—
341#14556099C2311yescharacteristic
342#14556099C2311yescharacteristic
343#14556099C2311yescharacteristic
344#14556098—21no—
345#14556098—21no—
346#14556098—21no—
347#14556097—21no—
348#14556097—21no—
349#14556097D411yescharacteristic
350#14556097D411yescharacteristic
351#14556096—21no—
352#14556096—21no—
353#14556096—21no—
354#14556096—21no—
355#14556096—21no—
356#14556096—21no—
357#14556096—21no—
358#14556096—21no—
359#14556096—21no—
360Q8×Dic71C2311yescharacteristic
361Q8×Dic71C2311yescharacteristic
362Q8×Dic71C2311yescharacteristic
363C4×D284—21no—
364D4×Dic71—21no—
365D4×Dic71—21no—
366D4×Dic71C2311yescharacteristic
367D4×Dic71C2311yescharacteristic
368D4×Dic71C2311yescharacteristic
369#14556090C2311yescharacteristic
370#14556090C2311yescharacteristic
371C4×C22⋊D71—21no—
372C4×C22⋊D71—21no—
373C4×C22⋊D71—21no—
374C4×C22⋊D71—21no—
375C4×C22⋊D71—21no—
376C4×C22⋊D71C2311yescharacteristic
377C4×C22⋊D71C2311yescharacteristic
378C4×C22⋊D71C2311yescharacteristic
379C4×C22⋊D71C2311yescharacteristic
380#14556087—21no—
381#14556087C2311yescharacteristic
382#14556086C2311yescharacteristic
383#14556085—21no—
384#14556084—21no—
385C2×C4⋊Dic71—21no—
386C2×C4⋊Dic71C2311yescharacteristic
387C2×C4⋊Dic71C2311yescharacteristic
388C4⋊C4×D71C2311yescharacteristic
389C2×(C2×D71)⋊C4—21no—
390C2×(C2×D71)⋊C4—21no—
391C2×(C2×D71)⋊C4—21no—
392C2×(C2×D71)⋊C4—21no—
393C2×(C2×D71)⋊C4—21no—
394C22⋊C4×D71—21no—
395#14556062C2311yescharacteristic
396#14556062C2311yescharacteristic
397#14556062C2311yescharacteristic
398#14556062C2311yescharacteristic
399#14556061C2311yescharacteristic
400#14556061C2311yescharacteristic
401#14556059C2311yescharacteristic
402#14556059C2311yescharacteristic
403Dic71⋊C8C2311yescharacteristic
404Dic71⋊C8C2311yescharacteristic
405Dic71⋊C8C2311yescharacteristic
406Dic71⋊C8C2311yescharacteristic
407#14556052C2311yescharacteristic
408#14556052C2311yescharacteristic
409#14556052C2311yescharacteristic
410#14556052C2311yescharacteristic
411#14556052C2311yescharacteristic
412#14556052C2311yescharacteristic
413#14556050C2311yescharacteristic
414#14556050C2311yescharacteristic
415#14556050C2311yescharacteristic
416#14556050C2311yescharacteristic
417#14556050C2311yescharacteristic
418#14556050C2311yescharacteristic
419#14556050C2311yescharacteristic
420#14556050C2311yescharacteristic
421#14556049C2311yescharacteristic
422#14556049C2311yescharacteristic
423#14556049C2311yescharacteristic
424#14556049C2311yescharacteristic
425#14556049C2311yescharacteristic
426#14556049C2311yescharacteristic
427#14556048C2311yescharacteristic
428#14556048C2311yescharacteristic
429#14556048C2311yescharacteristic
430#14556048C2311yescharacteristic
431C22⋊(C71⋊C8)C2311yescharacteristic
432C22⋊(C71⋊C8)C2311yescharacteristic
433C22⋊(C71⋊C8)C2311yescharacteristic
434C22⋊(C71⋊C8)C2311yescharacteristic
435(C2×D71)⋊C8C2311yescharacteristic
436(C2×D71)⋊C8C2311yescharacteristic
437(C2×D71)⋊C8C2311yescharacteristic
438(C2×D71)⋊C8C2311yescharacteristic
439#14556038C2311yescharacteristic
440#14556038C2311yescharacteristic
441C8×Dic71C2311yescharacteristic
442C8×Dic71C2311yescharacteristic
443C2×#41×C71—21no—
444C2×#41×C71—21no—
445C2×#41×C71—42no—
446C2×#41×C71—42no—
447C2×#41×C71C2311yescharacteristic
448C2×#41×C71C2311yescharacteristic
449C2×#41×C71C2311yescharacteristic
450C2×#41×C71C2311yescharacteristic
451C2×#41×C71C2311yescharacteristic
452C22×Q8×C71C2311yescharacteristic
453C22×D4×C71—21no—
454C22×D4×C71C2311yescharacteristic
455C23×C4×C71—21no—
456C23×C4×C71C2311yescharacteristic
457#135×C71—42no—
458#135×C71—42no—
459C2×Q16×C71C2311yescharacteristic
460C2×Q16×C71C2311yescharacteristic
461C2×SD16×C71C2311yescharacteristic
462C2×SD16×C71C2311yescharacteristic
463C2×SD16×C71C2311yescharacteristic
464C2×SD16×C71C2311yescharacteristic
465C2×D8×C71C2311yescharacteristic
466C2×D8×C71C2311yescharacteristic
467C22×C8×C71C2311yescharacteristic
468C22×C8×C71C2311yescharacteristic
469#123×C71—21no—
470C22⋊Q8×C71C2311yescharacteristic
471C22⋊Q8×C71C2311yescharacteristic
472#121×C71C2311yescharacteristic
473#121×C71C2311yescharacteristic
474#120×C71—21no—
475C4×D4×C71—21no—
476C4×D4×C71—21no—
477#117×C71C2311yescharacteristic
478#103×C71C2311yescharacteristic
479#103×C71C2311yescharacteristic
480#103×C71C2311yescharacteristic
481#103×C71C2311yescharacteristic
482#102×C71C2311yescharacteristic
483#102×C71C2311yescharacteristic
484#102×C71C2311yescharacteristic
485#102×C71C2311yescharacteristic
486C22⋊C8×C71C2311yescharacteristic
487C22⋊C8×C71C2311yescharacteristic
488C22⋊C8×C71C2311yescharacteristic
489C22⋊C8×C71C2311yescharacteristic
490C23×D71—21no—
491C23×D71—21no—
492C23×D71—21no—
493C23×D71—21no—
494C23×D71—21no—
495#11765866—22no—
496#11765866—22no—
497#11765866—41no—
498#11765866—41no—
499#11765866—41no—
500#11765866—41no—
501#11765865—41no—
502#11765865—41no—
503#11765865—44no—
504#11765864—82no—
505C2×Dic142—21no—
506C2×Dic142C2×D411yescharacteristic
507C2×D284—21no—
508C2×D284—21no—
509C2×D284—21no—
510C2×D284—21no—
511C2×D284—21no—
512C2×D284—21no—
513C2×D284—21no—
514C2×D284—41no—
515C2×D284—41no—
516C2×D284—41no—
517C2×D284—41no—
518C2×D284—44no—
519C2×D284C2×D411yescharacteristic
520C2×D284C2411yescharacteristic
521C2×D284C2411yescharacteristic
522C2×D284C2411yescharacteristic
523C2×D284C2411yescharacteristic
524C2×C22⋊D71—21no—
525C2×C22⋊D71—21no—
526C2×C22⋊D71—21no—
527C2×C22⋊D71—21no—
528C2×C22⋊D71—21no—
529C2×C22⋊D71—21no—
530C2×C22⋊D71—21no—
531C2×C22⋊D71—21no—
532C2×C22⋊D71—21no—
533C2×C22⋊D71—21no—
534C2×C22⋊D71—21no—
535C2×C22⋊D71—21no—
536C2×C22⋊D71—21no—
537C2×C22⋊D71—21no—
538C2×C22⋊D71—21no—
539C2×C22⋊D71—21no—
540C2×C22⋊D71—21no—
541C2×C22⋊D71—21no—
542C2×C22⋊D71—21no—
543C2×C22⋊D71—21no—
544C2×C22⋊D71—82no—
545C2×C22⋊D71—82no—
546C2×C22⋊D71—82no—
547C2×C22⋊D71—82no—
548C2×C22⋊D71C2×D411yescharacteristic
549C2×C22⋊D71C2×D411yescharacteristic
550C2×C22⋊D71C2×D411yescharacteristic
551C2×C22⋊D71C2×D411yescharacteristic
552C2×C22⋊D71C2×D411yescharacteristic
553C2×C22⋊D71C2×D411yescharacteristic
554D4×D71—22no—
555D4×D71—22no—
556D4×D71—41no—
557D4×D71—41no—
558D4×D71—41no—
559D4×D71—41no—
560D4×D71—44no—
561D4×D71—44no—
562D4×D71—82no—
563C22×Dic71—21no—
564C22×Dic71—21no—
565C22×Dic71—21no—
566C22×Dic71—21no—
567C22×Dic71—21no—
568C2×C4×D71—21no—
569C2×C4×D71—21no—
570C2×C4×D71—21no—
571C2×C4×D71—21no—
572C2×C4×D71—21no—
573C2×C4×D71—21no—
574C2×C4×D71C2411yescharacteristic
575C2×C4×D71C2411yescharacteristic
576#11765852—22no—
577#11765852—22no—
578#11765852—41no—
579#11765852—41no—
580#11765852—41no—
581#11765852—41no—
582D568—41no—
583D568—41no—
584D568—41no—
585D568—41no—
586#11765850—22no—
587#11765850—22no—
588#11765850—41no—
589#11765850—41no—
590#11765850—41no—
591#11765850—41no—
592#11765848—41no—
593#11765848—41no—
594C2×C71⋊C8—41no—
595C2×C71⋊C8—41no—
596C2×C71⋊C8C2411yescharacteristic
597C2×C71⋊C8C2411yescharacteristic
598C2×C71⋊C8C2411yescharacteristic
599C2×C71⋊C8C2411yescharacteristic
600C8×D71—41no—
601C8×D71—41no—
602C4⋊Dic71—21no—
603C4⋊Dic71—21no—
604C4⋊Dic71—21no—
605C4⋊Dic71—21no—
606C4⋊Dic71—21no—
607C4⋊Dic71—21no—
608C4⋊Dic71C2×D411yescharacteristic
609C4⋊Dic71C2×D411yescharacteristic
610C4⋊Dic71C2411yescharacteristic
611C4⋊Dic71C2411yescharacteristic
612C4⋊Dic71C2411yescharacteristic
613C4⋊Dic71C2411yescharacteristic
614Dic71⋊C4—21no—
615Dic71⋊C4—21no—
616Dic71⋊C4—21no—
617Dic71⋊C4—21no—
618Dic71⋊C4—21no—
619Dic71⋊C4—21no—
620Dic71⋊C4C2×D411yescharacteristic
621Dic71⋊C4C2×D411yescharacteristic
622Dic71⋊C4C2×D411yescharacteristic
623Dic71⋊C4C2×D411yescharacteristic
624C22⋊Dic71—21no—
625C22⋊Dic71—21no—
626C22⋊Dic71—21no—
627C22⋊Dic71—21no—
628C22⋊Dic71—21no—
629C22⋊Dic71—21no—
630C22⋊Dic71C2×D411yescharacteristic
631C22⋊Dic71C2×D411yescharacteristic
632C22⋊Dic71C2×D411yescharacteristic
633C22⋊Dic71C2×D411yescharacteristic
634C22⋊Dic71C2×D411yescharacteristic
635C22⋊Dic71C2×D411yescharacteristic
636(C2×D71)⋊C4—21no—
637(C2×D71)⋊C4—21no—
638(C2×D71)⋊C4—21no—
639(C2×D71)⋊C4—21no—
640(C2×D71)⋊C4—21no—
641(C2×D71)⋊C4—21no—
642(C2×D71)⋊C4—21no—
643(C2×D71)⋊C4—21no—
644(C2×D71)⋊C4—21no—
645(C2×D71)⋊C4—21no—
646(C2×D71)⋊C4—21no—
647(C2×D71)⋊C4—21no—
648(C2×D71)⋊C4—21no—
649(C2×D71)⋊C4—21no—
650(C2×D71)⋊C4—21no—
651(C2×D71)⋊C4—21no—
652(C2×D71)⋊C4—21no—
653(C2×D71)⋊C4—21no—
654(C2×D71)⋊C4—21no—
655(C2×D71)⋊C4—21no—
656(C2×D71)⋊C4—21no—
657(C2×D71)⋊C4—21no—
658(C2×D71)⋊C4C2×D411yescharacteristic
659(C2×D71)⋊C4C2×D411yescharacteristic
660(C2×D71)⋊C4C2×D411yescharacteristic
661(C2×D71)⋊C4C2×D411yescharacteristic
662C4×Dic71—21no—
663C4×Dic71—21no—
664C4×Dic71—21no—
665C4×Dic71—21no—
666C4×Dic71C2411yescharacteristic
667C4×Dic71C2411yescharacteristic
668C24×C71—21no—
669C24×C71C2×D411yescharacteristic
670#41×C71—22no—
671#41×C71—22no—
672#41×C71—22no—
673#41×C71—22no—
674#41×C71—41no—
675#41×C71—41no—
676#41×C71—41no—
677#41×C71—41no—
678#41×C71—44no—
679#41×C71—41no—
680#41×C71—41no—
681#41×C71—44no—
682C2×Q8×C71—21no—
683C2×Q8×C71—22no—
684C2×Q8×C71—41no—
685C2×Q8×C71C2411yescharacteristic
686C2×Q8×C71C2411yescharacteristic
687C2×Q8×C71C2411yescharacteristic
688C2×D4×C71—21no—
689C2×D4×C71—22no—
690C2×D4×C71—21no—
691C2×D4×C71—21no—
692C2×D4×C71—21no—
693C2×D4×C71—21no—
694C2×D4×C71—21no—
695C2×D4×C71—21no—
696C2×D4×C71—21no—
697C2×D4×C71—41no—
698C2×D4×C71—44no—
699C2×D4×C71C2411yescharacteristic
700C2×D4×C71C2411yescharacteristic
701C2×D4×C71C2411yescharacteristic
702C22×C4×C71—21no—
703C22×C4×C71—21no—
704C22×C4×C71—21no—
705C22×C4×C71—21no—
706C22×C4×C71—21no—
707C22×C4×C71—21no—
708C22×C4×C71—41no—
709C22×C4×C71—41no—
710C22×C4×C71—44no—
711C22×C4×C71C2×D411yescharacteristic
712C22×C4×C71C2×D411yescharacteristic
713C22×C4×C71C2×D411yescharacteristic
714C22×C4×C71C2411yescharacteristic
715C22×C4×C71C2411yescharacteristic
716C22×C4×C71C2411yescharacteristic
717Q16×C71—22no—
718Q16×C71—41no—
719SD16×C71—22no—
720SD16×C71—22no—
721SD16×C71—41no—
722SD16×C71—41no—
723D8×C71—22no—
724D8×C71—41no—
725C2×C8×C71—41no—
726C2×C8×C71—41no—
727C2×C8×C71C2411yescharacteristic
728C2×C8×C71C2411yescharacteristic
729C2×C8×C71C2411yescharacteristic
730C2×C8×C71C2411yescharacteristic
731C4⋊C4×C71—21no—
732C4⋊C4×C71—21no—
733C4⋊C4×C71C2411yescharacteristic
734C4⋊C4×C71C2411yescharacteristic
735C22⋊C4×C71—21no—
736C22⋊C4×C71—21no—
737C22⋊C4×C71—21no—
738C22⋊C4×C71—21no—
739C22⋊C4×C71—21no—
740C42×C71—21no—
741C23×C71—21no—
742C23×C71—22no—
743C23×C71—21no—
744C23×C71—21no—
745C23×C71—41no—
746C23×C71—41no—
747C23×C71—42no—
748C23×C71—42no—
749C23×C71—81no—
750C23×C71C22×D411yescharacteristic
751C23×C71C22×D411yescharacteristic
752C23×C71C22×D411yescharacteristic
753C22×D71—21no—
754C22×D71—21no—
755C22×D71—21no—
756C22×D71—21no—
757C22×D71—42no—
758C22×D71—42no—
759C22×D71—42no—
760C22×D71—42no—
761C22×D71—81no—
762C22×D71—81no—
763C22×D71—81no—
764C22×D71—81no—
765C22×D71—81no—
766C22×D71—81no—
767C22×D71—81no—
768C22×D71—81no—
769C22×D71—81no—
770C22×D71—81no—
771C22×D71—81no—
772C22×D71C22×D411yescharacteristic
773C22×D71C22×D411yescharacteristic
774Q8×C71—21no—
775Q8×C71—21no—
776Q8×C71—21no—
777Q8×C71—21no—
778Q8×C71—21no—
779Q8×C71—42no—
780Q8×C71H(5,𝔽2)12yes—
781D4×C71—24no—
782D4×C71—21no—
783D4×C71—21no—
784D4×C71—21no—
785D4×C71—21no—
786D4×C71—21no—
787D4×C71—42no—
788D4×C71—42no—
789D4×C71—42no—
790D4×C71—42no—
791D4×C71—42no—
792D4×C71—81no—
793D4×C71—81no—
794D4×C71H(5,𝔽2)12yes—
795C2×C4×C71—24no—
796C2×C4×C71—21no—
797C2×C4×C71—21no—
798C2×C4×C71—21no—
799C2×C4×C71—21no—
800C2×C4×C71—21no—
801C2×C4×C71—21no—
802C2×C4×C71—21no—
803C2×C4×C71—21no—
804C2×C4×C71—21no—
805C2×C4×C71—21no—
806C2×C4×C71—21no—
807C2×C4×C71—41no—
808C2×C4×C71—41no—
809C2×C4×C71—41no—
810C2×C4×C71—42no—
811C2×C4×C71—42no—
812C2×C4×C71—42no—
813C2×C4×C71—42no—
814C2×C4×C71—81no—
815C2×C4×C71C22×D411yescharacteristic
816C2×C4×C71C22×D411yescharacteristic
817C2×C4×C71C22×D411yescharacteristic
818C2×C4×C71C2511yescharacteristic
819C22⋊D71—22no—
820C22⋊D71—22no—
821C22⋊D71—41no—
822C22⋊D71—41no—
823C22⋊D71—41no—
824C22⋊D71—41no—
825C22⋊D71—42no—
826C22⋊D71—42no—
827C22⋊D71—42no—
828C22⋊D71—42no—
829C22⋊D71—81no—
830C22⋊D71—81no—
831C22⋊D71—81no—
832C22⋊D71—81no—
833C22⋊D71—81no—
834C22⋊D71—81no—
835C22⋊D71—81no—
836C22⋊D71—81no—
837C22⋊D71—81no—
838C22⋊D71—81no—
839C22⋊D71—81no—
840C22⋊D71—81no—
841C22⋊D71—81no—
842C22⋊D71—81no—
843C22⋊D71—81no—
844C22⋊D71—81no—
845C2×Dic71—21no—
846C2×Dic71—21no—
847C2×Dic71—21no—
848C2×Dic71—21no—
849C2×Dic71—42no—
850C2×Dic71—81no—
851C2×Dic71—81no—
852C2×Dic71—81no—
853C2×Dic71—81no—
854C2×Dic71C22×D411yescharacteristic
855C2×Dic71C22×D411yescharacteristic
856C2×Dic71C22×D411yescharacteristic
857C2×Dic71C22×D411yescharacteristic
858C2×Dic71C22×D411yescharacteristic
859C2×Dic71C22×D411yescharacteristic
860D284—21no—
861D284—21no—
862D284—21no—
863D284—21no—
864D284—21no—
865D284—21no—
866D284—21no—
867D284—21no—
868D284—41no—
869D284—42no—
870D284—42no—
871D284—42no—
872D284—81no—
873D284—81no—
874D284—81no—
875D284—81no—
876C4×D71—21no—
877C4×D71—21no—
878C4×D71—21no—
879C4×D71—21no—
880C4×D71—42no—
881C4×D71—42no—
882C4×D71—81no—
883C4×D71—81no—
884C4×D71—81no—
885C4×D71—81no—
886Dic142—41no—
887Dic142—81no—
888C8×C71—21no—
889C8×C71—21no—
890C8×C71—21no—
891C8×C71—21no—
892C71⋊C8—21no—
893C71⋊C8—21no—
894C71⋊C8—21no—
895C71⋊C8—21no—
896C22×C71—21no—
897C22×C71—21no—
898C22×C71—21no—
899C22×C71—21no—
900C22×C71—21no—
901C22×C71—22no—
902C22×C71—21no—
903C22×C71—21no—
904C22×C71—21no—
905C22×C71—41no—
906C22×C71—41no—
907C22×C71—41no—
908C22×C71—41no—
909C22×C71—41no—
910C22×C71—41no—
911C22×C71—41no—
912C22×C71—41no—
913C22×C71—82no—
914C22×C71—84no—
915C22×C71#57612yes—
916C22×C71C23×D411yescharacteristic
917C2×D71—21no—
918C2×D71—21no—
919C2×D71—21no—
920C2×D71—21no—
921C2×D71—21no—
922C2×D71—21no—
923C2×D71—41no—
924C2×D71—41no—
925C2×D71—41no—
926C2×D71—41no—
927C2×D71—41no—
928C2×D71—41no—
929C2×D71—41no—
930C2×D71—41no—
931C2×D71—41no—
932C2×D71—41no—
933C2×D71—41no—
934C2×D71—41no—
935C2×D71—162no—
936C2×D71—162no—
937C2×D71—162no—
938C2×D71—162no—
939C2×D71—162no—
940C4×C71—21no—
941C4×C71—22no—
942C4×C71—21no—
943C4×C71—21no—
944C4×C71—41no—
945C4×C71—41no—
946C4×C71—41no—
947C4×C71—41no—
948C4×C71C2×H(5,𝔽2)11yescharacteristic
949C4×C71C2×H(5,𝔽2)11yescharacteristic
950Dic71—21no—
951Dic71—21no—
952Dic71—21no—
953Dic71—21no—
954Dic71—21no—
955Dic71—21no—
956Dic71—41no—
957Dic71—41no—
958Dic71—41no—
959Dic71—41no—
960#61639—711nomaximal, Sylow
961C2×C71—22no—
962C2×C71—41no—
963C2×C71—42no—
964C2×C71—41no—
965C2×C71—81no—
966C2×C71—81no—
967C2×C71#348411yescharacteristic
968C2×C71C2×#57611yescharacteristic
969C2×C71#358411yescharacteristic
970D71—41no—
971D71—41no—
972D71—81no—
973D71—81no—
974D71—81no—
975D71—81no—
976#3542—711no—
977#3488—711no—
978#3319—711no—
979#3310—711no—
980#3309—711no—
981#3308—711no—
982#3305—711no—
983#3300—711no—
984#3297—711no—
985#3294—711no—
986#3287—711no—
987#3282—711no—
988#3280—711no—
989D4×D8—711no—
990#3268—711no—
991#3268—711no—
992#3265—711no—
993#3264—711no—
994#3224—711no—
995#3220—711no—
996#3203—711no—
997#3198—711no—
998#3188—711no—
999#3186—711no—
1000#3124—711no—
1001#3119—711no—
1002#3012—711no—
1003#3008—711no—
1004#3002D7111yescharacteristic, complemented
1005C2×#449—711no—
1006#2977—711no—
1007C71#6163911yescharacteristic, complemented, Sylow
1008C2×H(5,𝔽2)—711no—
1009C22×#41C2×D7111yescharacteristic, complemented
1010C2×AGL(1,ℤ/8)—711no—
1011C2×AGL(1,ℤ/8)—711no—
1012C2×#135—711no—
1013C2×#135C2×D7111yescharacteristic, complemented
1014C2×#135C2×D7111yescharacteristic, complemented
1015C22×SD16—711no—
1016C22×D8—711no—
1017C22×D8—711no—
1018#562—1421no—
1019#560—1421no—
1020#555—711no—
1021#553—711no—
1022#552—711no—
1023#551—1421no—
1024#550—711no—
1025#550—711no—
1026#550—711no—
1027#548—711no—
1028#548—711no—
1029#547—711no—
1030#546—711no—
1031#546—711no—
1032#546—711no—
1033#546—711no—
1034#546—1421no—
1035#546—1421no—
1036#546—1421no—
1037D42—711no—
1038D42—711no—
1039D42—711no—
1040D42—1421no—
1041D42—1421no—
1042#542—711no—
1043#540—711no—
1044#540—1421no—
1045#538—1421no—
1046#537—711no—
1047#537—711no—
1048#537—1421no—
1049#535—711no—
1050#535—711no—
1051#535—1421no—
1052#535—1421no—
1053#534—1421no—
1054#525—711no—
1055#525—1421no—
1056#525C2×D7111yescharacteristic, complemented
1057C2×#121—711no—
1058C2×#121—711no—
1059C2×#121—1421no—
1060#520—711no—
1061#496—711no—
1062#496—711no—
1063#495—711no—
1064#493—711no—
1065#490—711no—
1066#489—711no—
1067#488—711no—
1068#486—711no—
1069#485—711no—
1070#484—711no—
1071#484—711no—
1072#482—711no—
1073#482—711no—
1074#482—711no—
1075#481—711no—
1076#480—711no—
1077#480—711no—
1078#480—711no—
1079#480—711no—
1080#480—711no—
1081#479—711no—
1082#478—711no—
1083#477—711no—
1084#474—711no—
1085#469—711no—
1086#468—711no—
1087#468—711no—
1088#468—711no—
1089#467—711no—
1090#466—711no—
1091#466—711no—
1092#466—711no—
1093#466—711no—
1094#466—711no—
1095#466—711no—
1096#466—711no—
1097#466—711no—
1098#465—711no—
1099#465—711no—
1100#465—711no—
1101#464—711no—
1102#464—711no—
1103#463—711no—
1104#463—711no—
1105#463—711no—
1106#463—711no—
1107#460—711no—
1108#460—711no—
1109#459—711no—
1110#459—711no—
1111#459—711no—
1112#459—711no—
1113#452—711no—
1114#452—711no—
1115#452C2×D7111yescharacteristic, complemented
1116#452C2×D7111yescharacteristic, complemented
1117#451C2×D7111yescharacteristic, complemented
1118#450—711no—
1119#450—711no—
1120#450—711no—
1121#450C2×D7111yescharacteristic, complemented
1122#449—711no—
1123#449—711no—
1124#449—711no—
1125#449—711no—
1126#449—711no—
1127#449—711no—
1128#449—711no—
1129#449—711no—
1130#449—711no—
1131#449—711no—
1132#449—711no—
1133#449—711no—
1134#449—711no—
1135#449—711no—
1136#449C2×D7111yescharacteristic, complemented
1137#449C2×D7111yescharacteristic, complemented
1138#448C2×D7111yescharacteristic, complemented
1139#447—711no—
1140#447—711no—
1141#447—711no—
1142#447—711no—
1143#447—711no—
1144#447—711no—
1145#447—711no—
1146#447—711no—
1147#447—711no—
1148#447C2×D7111yescharacteristic, complemented
1149#442—711no—
1150#440—711no—
1151#440—711no—
1152#440—711no—
1153C4×Q16—711no—
1154C4×SD16—711no—
1155C4×D8—711no—
1156C4×D8—711no—
1157#435—711no—
1158#435—711no—
1159#435—711no—
1160#435—711no—
1161C8×D4—711no—
1162C8×D4—711no—
1163C8×D4—711no—
1164C8×D4—711no—
1165#433—711no—
1166#433—711no—
1167#418—711no—
1168#417—711no—
1169#416—711no—
1170#416C2×D7111yescharacteristic, complemented
1171#416C2×D7111yescharacteristic, complemented
1172C2×#103—711no—
1173C2×#102—711no—
1174C2×#102—711no—
1175#408—711no—
1176#408—711no—
1177C2×C22⋊C8—711no—
1178C2×C22⋊C8C2×D7111yescharacteristic, complemented
1179H(5,𝔽2)—2842no—
1180H(5,𝔽2)—2842no—
1181C2×#41—21no—
1182C2×#41—21no—
1183C2×#41—42no—
1184C2×#41—42no—
1185C2×#41—711no—
1186C2×#41—711no—
1187C2×#41—711no—
1188C2×#41—711no—
1189C2×#41—1421no—
1190C2×#41—1421no—
1191C2×#41C22×D7111yescharacteristic
1192C2×#41C22×D7111yescharacteristic
1193C2×#41C22×D7111yescharacteristic
1194C2×#41C22×D7111yescharacteristic
1195C2×#41C22×D7111yescharacteristic
1196C22×Q8C22×D7111yescharacteristic
1197C22×D4—21no—
1198C22×D4—711no—
1199C22×D4—711no—
1200C22×D4—711no—
1201C22×D4—711no—
1202C22×D4—711no—
1203C22×D4—1421no—
1204C22×D4—1421no—
1205C22×D4—1421no—
1206C22×D4—1421no—
1207C22×D4—1421no—
1208C22×D4—1421no—
1209C22×D4—1421no—
1210C22×D4—1421no—
1211C22×D4C22×D7111yescharacteristic
1212C23×C4—21no—
1213C23×C4C22×D7111yescharacteristic
1214AGL(1,ℤ/8)—2842no—
1215AGL(1,ℤ/8)—2842no—
1216#135—42no—
1217#135—42no—
1218#135—2842no—
1219C2×Q16C22×D7111yescharacteristic
1220C2×Q16C22×D7111yescharacteristic
1221C2×SD16—2842no—
1222C2×SD16—711no—
1223C2×SD16—711no—
1224C2×SD16—711no—
1225C2×SD16—711no—
1226C2×SD16—711no—
1227C2×SD16—711no—
1228C2×SD16C22×D7111yescharacteristic
1229C2×SD16C22×D7111yescharacteristic
1230C2×SD16C22×D7111yescharacteristic
1231C2×SD16C22×D7111yescharacteristic
1232C2×D8—2842no—
1233C2×D8—2842no—
1234C2×D8—711no—
1235C2×D8—711no—
1236C2×D8—711no—
1237C2×D8—711no—
1238C2×D8—711no—
1239C2×D8—711no—
1240C2×D8—711no—
1241C2×D8—711no—
1242C2×D8—711no—
1243C2×D8—711no—
1244C2×D8C22×D7111yescharacteristic
1245C2×D8C22×D7111yescharacteristic
1246C2×M16—711no—
1247C2×M16—711no—
1248C22×C8—711no—
1249C22×C8—711no—
1250C22×C8—711no—
1251C22×C8—711no—
1252C22×C8C22×D7111yescharacteristic
1253C22×C8C22×D7111yescharacteristic
1254C4⋊Q8—711no—
1255#127—711no—
1256#127—711no—
1257#127—711no—
1258#127—1421no—
1259#127—1421no—
1260#127—1421no—
1261#127—1421no—
1262#126—1421no—
1263#126—1421no—
1264#126—1421no—
1265#125—711no—
1266#125—1421no—
1267#124—711no—
1268#124—711no—
1269#124—711no—
1270#124—1421no—
1271#124—1421no—
1272#124—1421no—
1273#124—1421no—
1274#124—1421no—
1275#124—1421no—
1276#123—21no—
1277#123—711no—
1278#123—711no—
1279#123—1421no—
1280#123—1421no—
1281#123—1421no—
1282#123—1421no—
1283#123—1421no—
1284#123—1421no—
1285#123—1421no—
1286#123—1421no—
1287#123—1421no—
1288#123—1421no—
1289#123—1421no—
1290C22⋊Q8—711no—
1291C22⋊Q8—711no—
1292C22⋊Q8—711no—
1293C22⋊Q8—711no—
1294C22⋊Q8—711no—
1295C22⋊Q8—1421no—
1296C22⋊Q8—1421no—
1297C22⋊Q8—1421no—
1298C22⋊Q8—1421no—
1299C22⋊Q8—1421no—
1300C22⋊Q8—1421no—
1301C22⋊Q8C22×D7111yescharacteristic
1302C22⋊Q8C22×D7111yescharacteristic
1303#121—711no—
1304#121—711no—
1305#121—711no—
1306#121—711no—
1307#121—711no—
1308#121—711no—
1309#121—711no—
1310#121—711no—
1311#121—711no—
1312#121—711no—
1313#121—711no—
1314#121—711no—
1315#121—711no—
1316#121—711no—
1317#121—711no—
1318#121—1421no—
1319#121—1421no—
1320#121—1421no—
1321#121—1421no—
1322#121—1421no—
1323#121—1421no—
1324#121—1421no—
1325#121—1421no—
1326#121—1421no—
1327#121—1421no—
1328#121—1421no—
1329#121—1421no—
1330#121—1421no—
1331#121—1421no—
1332#121—1421no—
1333#121—1421no—
1334#121—1421no—
1335#121—1421no—
1336#121—1421no—
1337#121—1421no—
1338#121—1421no—
1339#121—1421no—
1340#121—1421no—
1341#121—1421no—
1342#121—1421no—
1343#121—1421no—
1344#121—1421no—
1345#121—1421no—
1346#121—1421no—
1347#121—1421no—
1348#121—1421no—
1349#121C22×D7111yescharacteristic
1350#121C22×D7111yescharacteristic
1351#120—21no—
1352#120—711no—
1353#120—711no—
1354#120—1421no—
1355#120—1421no—
1356#120—1421no—
1357#120—1421no—
1358#120—1421no—
1359#120—1421no—
1360#120—1421no—
1361#120—1421no—
1362#120—1421no—
1363#120—1421no—
1364#120—1421no—
1365#120—1421no—
1366#120—1421no—
1367#120—1421no—
1368C4×Q8—711no—
1369C4×Q8—711no—
1370C4×Q8—711no—
1371C4×D4—21no—
1372C4×D4—21no—
1373C4×D4—711no—
1374C4×D4—711no—
1375C4×D4—711no—
1376C4×D4—711no—
1377C4×D4—711no—
1378C4×D4—711no—
1379C4×D4—711no—
1380C4×D4—711no—
1381C4×D4—711no—
1382C4×D4—1421no—
1383C4×D4—1421no—
1384C4×D4—1421no—
1385C4×D4—1421no—
1386C4×D4—1421no—
1387C4×D4—1421no—
1388C4×D4—1421no—
1389C4×D4—1421no—
1390#117—711no—
1391#117—711no—
1392#117—1421no—
1393#117—1421no—
1394#117—1421no—
1395#117C22×D7111yescharacteristic
1396C2×C4⋊C4—711no—
1397C2×C4⋊C4—711no—
1398C2×C4⋊C4—711no—
1399C2×C4⋊C4—1421no—
1400C2×C22⋊C4—1421no—
1401C2×C22⋊C4—1421no—
1402C2×C22⋊C4—1421no—
1403C2×C22⋊C4—1421no—
1404C2×C22⋊C4—1421no—
1405C2×C22⋊C4—1421no—
1406#107—711no—
1407#107—711no—
1408#107—711no—
1409#107—711no—
1410#107—711no—
1411#107—711no—
1412#106—711no—
1413#106—711no—
1414C4⋊C8—711no—
1415C4⋊C8—711no—
1416C4⋊C8—711no—
1417C4⋊C8—711no—
1418#103—711no—
1419#103—711no—
1420#103—711no—
1421#103—711no—
1422#103—711no—
1423#103—711no—
1424#103C22×D7111yescharacteristic
1425#103C22×D7111yescharacteristic
1426#103C22×D7111yescharacteristic
1427#103C22×D7111yescharacteristic
1428#102—711no—
1429#102—711no—
1430#102—711no—
1431#102—711no—
1432#102—711no—
1433#102—711no—
1434#102—711no—
1435#102—711no—
1436#102—711no—
1437#102—711no—
1438#102—711no—
1439#102—711no—
1440#102—711no—
1441#102—711no—
1442#102—711no—
1443#102—711no—
1444#102—711no—
1445#102—711no—
1446#102C22×D7111yescharacteristic
1447#102C22×D7111yescharacteristic
1448#102C22×D7111yescharacteristic
1449#102C22×D7111yescharacteristic
1450C22⋊C8—711no—
1451C22⋊C8—711no—
1452C22⋊C8—711no—
1453C22⋊C8—711no—
1454C22⋊C8—711no—
1455C22⋊C8—711no—
1456C22⋊C8—711no—
1457C22⋊C8—711no—
1458C22⋊C8C22×D7111yescharacteristic
1459C22⋊C8C22×D7111yescharacteristic
1460C22⋊C8C22×D7111yescharacteristic
1461C22⋊C8C22×D7111yescharacteristic
1462#97—711no—
1463#97—711no—
1464C4×C8—711no—
1465C4×C8—711no—
1466C24—21no—
1467C24—1421no—
1468C24—1421no—
1469C24—1421no—
1470C24—1421no—
1471C24—1421no—
1472C24D4×D7111yescharacteristic
1473#41—22no—
1474#41—22no—
1475#41—22no—
1476#41—22no—
1477#41—41no—
1478#41—41no—
1479#41—41no—
1480#41—41no—
1481#41—44no—
1482#41—41no—
1483#41—41no—
1484#41—44no—
1485#41—2844no—
1486#41—2841no—
1487#41—2841no—
1488#41—2841no—
1489#41—2841no—
1490#41—2841no—
1491#41—2841no—
1492#41—5682no—
1493#41—1422no—
1494#41—1422no—
1495C2×Q8—21no—
1496C2×Q8—22no—
1497C2×Q8—41no—
1498C2×Q8—711no—
1499C2×Q8—1421no—
1500C2×Q8C23×D7111yescharacteristic
1501C2×Q8C23×D7111yescharacteristic
1502C2×Q8C23×D7111yescharacteristic
1503C2×D4—21no—
1504C2×D4—22no—
1505C2×D4—21no—
1506C2×D4—21no—
1507C2×D4—21no—
1508C2×D4—21no—
1509C2×D4—21no—
1510C2×D4—21no—
1511C2×D4—21no—
1512C2×D4—41no—
1513C2×D4—44no—
1514C2×D4—2844no—
1515C2×D4—2841no—
1516C2×D4—2841no—
1517C2×D4—2841no—
1518C2×D4—2841no—
1519C2×D4—2844no—
1520C2×D4—2844no—
1521C2×D4—2841no—
1522C2×D4—2841no—
1523C2×D4—2841no—
1524C2×D4—2841no—
1525C2×D4—5682no—
1526C2×D4—5682no—
1527C2×D4—5682no—
1528C2×D4—5682no—
1529C2×D4—5682no—
1530C2×D4—711no—
1531C2×D4—711no—
1532C2×D4—711no—
1533C2×D4—711no—
1534C2×D4—711no—
1535C2×D4—711no—
1536C2×D4—711no—
1537C2×D4—711no—
1538C2×D4—711no—
1539C2×D4—711no—
1540C2×D4—711no—
1541C2×D4—1421no—
1542C2×D4—1421no—
1543C2×D4—1421no—
1544C2×D4—1421no—
1545C2×D4—1421no—
1546C2×D4—1421no—
1547C2×D4—1421no—
1548C2×D4—1421no—
1549C2×D4—1421no—
1550C2×D4—1421no—
1551C2×D4—1421no—
1552C2×D4—1421no—
1553C2×D4—1421no—
1554C2×D4—1421no—
1555C2×D4—1421no—
1556C2×D4—1421no—
1557C2×D4—1422no—
1558C2×D4—1422no—
1559C2×D4—1421no—
1560C2×D4—1421no—
1561C2×D4—1421no—
1562C2×D4—1421no—
1563C2×D4—1421no—
1564C2×D4—1421no—
1565C2×D4—1421no—
1566C2×D4—1421no—
1567C2×D4—1421no—
1568C2×D4—1421no—
1569C2×D4—1421no—
1570C2×D4C23×D7111yescharacteristic
1571C2×D4C23×D7111yescharacteristic
1572C2×D4C23×D7111yescharacteristic
1573C22×C4—21no—
1574C22×C4—21no—
1575C22×C4—21no—
1576C22×C4—21no—
1577C22×C4—21no—
1578C22×C4—21no—
1579C22×C4—41no—
1580C22×C4—41no—
1581C22×C4—44no—
1582C22×C4—711no—
1583C22×C4—711no—
1584C22×C4—1421no—
1585C22×C4—1421no—
1586C22×C4—1421no—
1587C22×C4—1421no—
1588C22×C4—1421no—
1589C22×C4—1421no—
1590C22×C4—1421no—
1591C22×C4—1421no—
1592C22×C4—1421no—
1593C22×C4—1421no—
1594C22×C4—1421no—
1595C22×C4D4×D7111yescharacteristic
1596C22×C4D4×D7111yescharacteristic
1597C22×C4D4×D7111yescharacteristic
1598C22×C4C23×D7111yescharacteristic
1599C22×C4C23×D7111yescharacteristic
1600C22×C4C23×D7111yescharacteristic
1601Q16—22no—
1602Q16—41no—
1603SD16—22no—
1604SD16—22no—
1605SD16—41no—
1606SD16—41no—
1607SD16—2841no—
1608SD16—2841no—
1609SD16—2841no—
1610SD16—2841no—
1611SD16—1422no—
1612SD16—1422no—
1613D8—22no—
1614D8—41no—
1615D8—2841no—
1616D8—2841no—
1617D8—2841no—
1618D8—2841no—
1619D8—2841no—
1620D8—2841no—
1621D8—2841no—
1622D8—2841no—
1623D8—1422no—
1624D8—1422no—
1625M16—2841no—
1626M16—2841no—
1627C2×C8—41no—
1628C2×C8—41no—
1629C2×C8—2841no—
1630C2×C8—2841no—
1631C2×C8—2841no—
1632C2×C8—2841no—
1633C2×C8—711no—
1634C2×C8—711no—
1635C2×C8—711no—
1636C2×C8—711no—
1637C2×C8C23×D7111yescharacteristic
1638C2×C8C23×D7111yescharacteristic
1639C2×C8C23×D7111yescharacteristic
1640C2×C8C23×D7111yescharacteristic
1641C4⋊C4—21no—
1642C4⋊C4—21no—
1643C4⋊C4—711no—
1644C4⋊C4—711no—
1645C4⋊C4—711no—
1646C4⋊C4—711no—
1647C4⋊C4—711no—
1648C4⋊C4—711no—
1649C4⋊C4—711no—
1650C4⋊C4—711no—
1651C4⋊C4—711no—
1652C4⋊C4—711no—
1653C4⋊C4—1421no—
1654C4⋊C4—1421no—
1655C4⋊C4—1421no—
1656C4⋊C4—1421no—
1657C4⋊C4—1421no—
1658C4⋊C4—1421no—
1659C4⋊C4—1421no—
1660C4⋊C4—1421no—
1661C4⋊C4—1421no—
1662C4⋊C4—1421no—
1663C4⋊C4—1421no—
1664C4⋊C4—1421no—
1665C4⋊C4C23×D7111yescharacteristic
1666C4⋊C4C23×D7111yescharacteristic
1667C22⋊C4—21no—
1668C22⋊C4—21no—
1669C22⋊C4—21no—
1670C22⋊C4—21no—
1671C22⋊C4—21no—
1672C22⋊C4—711no—
1673C22⋊C4—711no—
1674C22⋊C4—711no—
1675C22⋊C4—711no—
1676C22⋊C4—711no—
1677C22⋊C4—711no—
1678C22⋊C4—711no—
1679C22⋊C4—711no—
1680C22⋊C4—711no—
1681C22⋊C4—711no—
1682C22⋊C4—1421no—
1683C22⋊C4—1421no—
1684C22⋊C4—1421no—
1685C22⋊C4—1421no—
1686C22⋊C4—1421no—
1687C22⋊C4—1421no—
1688C22⋊C4—1421no—
1689C22⋊C4—1421no—
1690C22⋊C4—1421no—
1691C22⋊C4—1421no—
1692C22⋊C4—1421no—
1693C22⋊C4—1421no—
1694C22⋊C4—1421no—
1695C22⋊C4—1421no—
1696C22⋊C4—1421no—
1697C22⋊C4—1421no—
1698C22⋊C4—1421no—
1699C22⋊C4—1421no—
1700C22⋊C4—1421no—
1701C22⋊C4—1421no—
1702C22⋊C4—1421no—
1703C22⋊C4—1421no—
1704C22⋊C4—1421no—
1705C22⋊C4—1421no—
1706C22⋊C4—1421no—
1707C22⋊C4—1421no—
1708C22⋊C4—1421no—
1709C22⋊C4—1421no—
1710C42—21no—
1711C42—711no—
1712C42—711no—
1713C42—1421no—
1714C42—1421no—
1715C42—1421no—
1716C42—1421no—
1717C23—21no—
1718C23—22no—
1719C23—21no—
1720C23—21no—
1721C23—41no—
1722C23—41no—
1723C23—42no—
1724C23—42no—
1725C23—81no—
1726C23—2842no—
1727C23—2842no—
1728C23—2842no—
1729C23—2842no—
1730C23—5681no—
1731C23—5681no—
1732C23—5681no—
1733C23—5681no—
1734C23—5681no—
1735C23—5681no—
1736C23—5681no—
1737C23—5681no—
1738C23—5681no—
1739C23—5681no—
1740C23—5681no—
1741C23—711no—
1742C23—711no—
1743C23—1421no—
1744C23—1421no—
1745C23—1421no—
1746C23—1421no—
1747C23C2×D4×D7111yescharacteristic
1748C23C2×D4×D7111yescharacteristic
1749C23C2×D4×D7111yescharacteristic
1750Q8—21no—
1751Q8—21no—
1752Q8—21no—
1753Q8—21no—
1754Q8—21no—
1755Q8—42no—
1756Q8—2841no—
1757Q8—5681no—
1758Q8#1455617312yes—
1759D4—24no—
1760D4—21no—
1761D4—21no—
1762D4—21no—
1763D4—21no—
1764D4—21no—
1765D4—42no—
1766D4—42no—
1767D4—42no—
1768D4—42no—
1769D4—42no—
1770D4—81no—
1771D4—81no—
1772D4—2842no—
1773D4—2842no—
1774D4—2842no—
1775D4—2841no—
1776D4—2842no—
1777D4—2842no—
1778D4—2842no—
1779D4—2842no—
1780D4—2841no—
1781D4—2841no—
1782D4—2841no—
1783D4—2841no—
1784D4—5681no—
1785D4—5681no—
1786D4—5681no—
1787D4—5681no—
1788D4—5681no—
1789D4—5681no—
1790D4—5681no—
1791D4—5681no—
1792D4—5681no—
1793D4—5681no—
1794D4—5681no—
1795D4—5681no—
1796D4—5681no—
1797D4—5681no—
1798D4—5681no—
1799D4—5681no—
1800D4—5681no—
1801D4—5681no—
1802D4—5681no—
1803D4—5681no—
1804D4—1422no—
1805D4—1422no—
1806D4—1421no—
1807D4—1421no—
1808D4—1421no—
1809D4—1421no—
1810D4—1421no—
1811D4—1421no—
1812D4—1421no—
1813D4—1421no—
1814D4#1455617312yes—
1815C2×C4—24no—
1816C2×C4—21no—
1817C2×C4—21no—
1818C2×C4—21no—
1819C2×C4—21no—
1820C2×C4—21no—
1821C2×C4—21no—
1822C2×C4—21no—
1823C2×C4—21no—
1824C2×C4—21no—
1825C2×C4—21no—
1826C2×C4—21no—
1827C2×C4—41no—
1828C2×C4—41no—
1829C2×C4—41no—
1830C2×C4—42no—
1831C2×C4—42no—
1832C2×C4—42no—
1833C2×C4—42no—
1834C2×C4—81no—
1835C2×C4—2842no—
1836C2×C4—2842no—
1837C2×C4—2842no—
1838C2×C4—5681no—
1839C2×C4—5681no—
1840C2×C4—5681no—
1841C2×C4—5681no—
1842C2×C4—5681no—
1843C2×C4—5681no—
1844C2×C4—5681no—
1845C2×C4—5681no—
1846C2×C4—711no—
1847C2×C4—711no—
1848C2×C4—711no—
1849C2×C4—711no—
1850C2×C4—711no—
1851C2×C4—711no—
1852C2×C4—1421no—
1853C2×C4—1421no—
1854C2×C4—1421no—
1855C2×C4—1421no—
1856C2×C4—1421no—
1857C2×C4—1421no—
1858C2×C4—1421no—
1859C2×C4—1421no—
1860C2×C4C2×D4×D7111yescharacteristic
1861C2×C4C2×D4×D7111yescharacteristic
1862C2×C4C2×D4×D7111yescharacteristic
1863C2×C4C24×D7111yescharacteristic
1864C8—21no—
1865C8—21no—
1866C8—21no—
1867C8—21no—
1868C8—1421no—
1869C8—1421no—
1870C8—1421no—
1871C8—1421no—
1872C22—21no—
1873C22—21no—
1874C22—21no—
1875C22—21no—
1876C22—21no—
1877C22—21no—
1878C22—21no—
1879C22—22no—
1880C22—21no—
1881C22—41no—
1882C22—41no—
1883C22—41no—
1884C22—41no—
1885C22—41no—
1886C22—41no—
1887C22—41no—
1888C22—41no—
1889C22—82no—
1890C22—84no—
1891C22—2841no—
1892C22—2841no—
1893C22—2841no—
1894C22—2841no—
1895C22—2841no—
1896C22—2841no—
1897C22—2841no—
1898C22—2841no—
1899C22—2841no—
1900C22—2841no—
1901C22—2841no—
1902C22—2841no—
1903C22—11362no—
1904C22—11362no—
1905C22—11362no—
1906C22—11362no—
1907C22—11362no—
1908C22—1421no—
1909C22—1421no—
1910C22—1421no—
1911C22—1421no—
1912C22—1421no—
1913C22—1421no—
1914C22#1798680112yes—
1915C22C22×D4×D7111yescharacteristic
1916C4—21no—
1917C4—22no—
1918C4—21no—
1919C4—21no—
1920C4—41no—
1921C4—41no—
1922C4—41no—
1923C4—41no—
1924C4—2841no—
1925C4—2841no—
1926C4—2841no—
1927C4—2841no—
1928C4—1421no—
1929C4—1421no—
1930C4—1421no—
1931C4—1421no—
1932C4—1421no—
1933C4—1421no—
1934C4C2×#1455617311yescharacteristic
1935C4C2×#1455617311yescharacteristic
1936C2—22no—
1937C2—41no—
1938C2—41no—
1939C2—42no—
1940C2—81no—
1941C2—81no—
1942C2—2841no—
1943C2—2841no—
1944C2—5681no—
1945C2—5681no—
1946C2—5681no—
1947C2—5681no—
1948C2#2260196911yescharacteristic
1949C2C2×#1798680111yescharacteristic
1950C2#2260311311yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3002C2
socleC22×C71C23×D4
hypercenter#3002D71
hypocenterC71#61639
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3002

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22602648C2semidirect
2. #22602009C2semidirect
3. #22600492C2semidirect
4. #22600365C2semidirect
5. #22600342C2semidirect
6. #22600335C2semidirect
7. #22600286C2semidirect
8. #22600231C2semidirect
9. #22600191C2semidirect
10. #22600146C2semidirect
11. #22600094C2semidirect
12. #22600040C2semidirect
13. #22600019C2semidirect
14. #22600010C2semidirect
15. #22599880C2semidirect
16. #22599880C2semidirect
17. #22599828C2semidirect
18. #22599824C2semidirect
19. #22599440C2semidirect
20. #22599388C2semidirect
21. #22599241C2semidirect
22. #22599189C2semidirect
23. #22599101C2semidirect
24. #22599091C2semidirect
25. #22598603C2semidirect
26. #22598532C2semidirect
27. #22597648C2semidirect
28. #22597605C2semidirect
29. C2×#17986144C2semidirect
30. #22597394C2semidirect
31. C71×#3002C2semidirect
32. C2×#14556174C22semidirect
33. C2×#14556155C22semidirect
34. C2×#14556155C22semidirect
35. C2×#14556151C22semidirect
36. C22×#11765852C22semidirect
37. C22×#11765850C22semidirect
38. C2×D8×D71C22semidirect
41. #17986712C22semidirect
42. #17986693C22semidirect
43. #17986691C22semidirect
45. #17986668C22semidirect
46. #17986668C22semidirect
47. #17986668C22semidirect
49. #17986660C22semidirect
50. #17986649C22semidirect
52. #17986640C22semidirect
55. #17986637C22semidirect
56. #17986637C22semidirect
57. #17986637C22semidirect
58. #17986633C22semidirect
62. D4×C22⋊D71C22semidirect
63. #17986622C22semidirect
64. #17986602C22semidirect
67. #17986579C22semidirect
69. #17986577C22semidirect
70. #17986565C22semidirect
73. #17986563C22semidirect
78. C2×#14556102C22semidirect
79. C2×#14556102C22semidirect
80. #17986482C22semidirect
81. #17986385C22semidirect
82. #17986385C22semidirect
83. #17986384C22semidirect
84. #17986374C22semidirect
85. #17986362C22semidirect
86. #17986360C22semidirect
87. #17986355C22semidirect
88. #17986344C22semidirect
89. #17986339C22semidirect
90. #17986333C22semidirect
91. #17986332C22semidirect
92. #17986323C22semidirect
93. #17986323C22semidirect
94. #17986321C22semidirect
95. #17986315C22semidirect
96. #17986313C22semidirect
97. #17986313C22semidirect
98. #17986313C22semidirect
99. #17986313C22semidirect
100. #17986311C22semidirect
101. #17986308C22semidirect
102. #17986297C22semidirect
103. #17986292C22semidirect
104. #17986277C22semidirect
105. #17986251C22semidirect
106. #17986248C22semidirect
107. #17986242C22semidirect
108. #17986242C22semidirect
109. #17986237C22semidirect
110. #17986235C22semidirect
111. #17986235C22semidirect
112. #17986235C22semidirect
113. #17986235C22semidirect
114. #17986234C22semidirect
115. #17986233C22semidirect
116. #17986233C22semidirect
117. #17986232C22semidirect
118. #17986231C22semidirect
119. #17986230C22semidirect
120. #17986230C22semidirect
121. #17986223C22semidirect
122. #17986223C22semidirect
123. #17986217C22semidirect
124. #17986217C22semidirect
125. #17986216C22semidirect
126. #17986216C22semidirect
127. #17986197C22semidirect
128. #17986197C22semidirect
129. #17986193C22semidirect
130. #17986193C22semidirect
131. #17986192C22semidirect
132. #17986192C22semidirect
133. #17986160C22semidirect
134. #17986160C22semidirect
135. #17986149C22semidirect
136. #17986148C22semidirect
137. #17986148C22semidirect
138. #17986147C22semidirect
139. #17986147C22semidirect
141. #17986144C22semidirect
142. #17986144C22semidirect
143. #17986144C22semidirect
144. #17986144C22semidirect
145. #17986144C22semidirect
146. #17986144C22semidirect
147. #17986144C22semidirect
148. #17986144C22semidirect
149. #17986144C22semidirect
150. #17986143C22semidirect
151. #17986143C22semidirect
152. #17986135C22semidirect
153. #17986135C22semidirect
154. #17986135C22semidirect
155. #17986135C22semidirect
156. #17986134C22semidirect
157. #17986134C22semidirect
158. #17986132C22semidirect
159. #17986131C22semidirect
160. #17986131C22semidirect
161. #17986108C22semidirect
162. #17986102C22semidirect
163. #17986100C22semidirect
164. #17986100C22semidirect
165. Q16×Dic71C22semidirect
166. #17986084C22semidirect
167. D8×Dic71C22semidirect
168. #17986079C22semidirect
169. #17986070C22semidirect
170. #17986070C22semidirect
171. #17986067C22semidirect
172. #17986067C22semidirect
173. C8×C22⋊D71C22semidirect
174. C8×C22⋊D71C22semidirect
175. (C22⋊D71)⋊C8C22semidirect
176. (C22⋊D71)⋊C8C22semidirect
177. #17986057C22semidirect
178. #17986057C22semidirect
179. #17986002C22semidirect
180. #17985999C22semidirect
181. #17985994C22semidirect
182. C2×#14556052C22semidirect
183. C2×#14556049C22semidirect
184. #102×D71C22semidirect
185. #17985964C22semidirect
186. #17985964C22semidirect
187. C2×C22⋊(C71⋊C8)C22semidirect
188. C22×#41×C71C22semidirect
189. C2×#135×C71C22semidirect
190. C2×#135×C71C22semidirect
191. #525×C71C22semidirect
192. #452×C71C22semidirect
193. #452×C71C22semidirect
194. #451×C71C22semidirect
195. #450×C71C22semidirect
196. #449×C71C22semidirect
197. #449×C71C22semidirect
198. #448×C71C22semidirect
199. #447×C71C22semidirect
200. #416×C71C22semidirect
201. #416×C71C22semidirect
202. C2×C22⋊C8×C71C22semidirect
1004. #3002D71semidirect
1007. C71#61639semidirect
1009. C22×#41C2×D71semidirect
1013. C2×#135C2×D71semidirect
1014. C2×#135C2×D71semidirect
1056. #525C2×D71semidirect
1115. #452C2×D71semidirect
1116. #452C2×D71semidirect
1117. #451C2×D71semidirect
1121. #450C2×D71semidirect
1136. #449C2×D71semidirect
1137. #449C2×D71semidirect
1138. #448C2×D71semidirect
1148. #447C2×D71semidirect
1170. #416C2×D71semidirect
1171. #416C2×D71semidirect
1178. C2×C22⋊C8C2×D71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226026482
#226020092
#226004922
#226003652
#226003422
#226003352
#226002862
#226002312
#226001912
#226001462
#226000942
#226000402
#226000192
#226000102
#225998802
#225998282
#225998242
#225994402
#225993882
#225992412
#225991892
#225991012
#225990912
#225986032
#225985322
#225976482
#225976052
C2×#179861442
#225973942
C71×#30022
#6163971