Finite Group Databasebeta

← #32876401

Subgroups — #32876401

Order 18176.

1884 conjugacy classes of subgroups.

The subgroup lattice has 1732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602074C211yesmaximal, characteristic, complemented
2#22602068C211yesmaximal, characteristic, complemented
3#22600846C211yesmaximal, characteristic, complemented
4#22600842C211yesmaximal, characteristic, complemented
5#22600836C211yesmaximal, characteristic, complemented
6#22600815C211yesmaximal, characteristic, complemented
7#22600811C211yesmaximal, characteristic, complemented
8#22600809C211yesmaximal, characteristic, complemented
9#22600805C211yesmaximal, characteristic, complemented
10#22600758C211yesmaximal, characteristic, complemented
11#22600757C211yesmaximal, characteristic, complemented
12#22600739C211yesmaximal, characteristic, complemented
13#22600736C211yesmaximal, characteristic, complemented
14#22600735C211yesmaximal, characteristic, complemented
15#22600735C211yesmaximal, characteristic, complemented
16#22600686C211yesmaximal, characteristic, complemented
17#22600682C211yesmaximal, characteristic, complemented
18#22598875C211yesmaximal, characteristic, complemented
19#22598295C211yesmaximal, characteristic, complemented
20#22598291C211yesmaximal, characteristic, complemented
21#22598279C211yesmaximal, characteristic, complemented
22#22598279C211yesmaximal, characteristic, complemented
23#22598168C211yesmaximal, characteristic, complemented
24#22598164C211yesmaximal, characteristic, complemented
25#22597986C211yesmaximal, characteristic, complemented
26#466×D71C211yesmaximal, characteristic, complemented
27#22597189C211yesmaximal, characteristic, complemented
28#22597031C211yesmaximal, characteristic, complemented
29#22596939C211yesmaximal, characteristic, complemented
30#427×D71C211yesmaximal, characteristic, complemented
31C71×#3347C211yesmaximal, characteristic, complemented
32C2×D8×D71C2211yescharacteristic
33C2×#14556136C2211yescharacteristic
34C22×C8×D71C2211yescharacteristic
35#17986714C2211yescharacteristic, complemented
36#17986713C2211yescharacteristic, complemented
37#17986712C2211yescharacteristic, complemented
38#17986702C2211yescharacteristic, complemented
39#17986699C2211yescharacteristic, complemented
40#17986696C2211yescharacteristic, complemented
41#17986696C2211yescharacteristic, complemented
42#17986695C2211yescharacteristic, complemented
43#17986693C2211yescharacteristic, complemented
44#17986693C2211yescharacteristic, complemented
45#17986679—21no—
46#17986678—21no—
47#17986674—21no—
48#17986673—21no—
49#17986654C2211yescharacteristic, complemented
50#17986652C2211yescharacteristic, complemented
51#17986650C2211yescharacteristic, complemented
52#17986649C2211yescharacteristic, complemented
53#17986646—21no—
54#17986642—21no—
55#17986641—21no—
56#17986638—21no—
57#17986629C2211yescharacteristic
58#17986626C2211yescharacteristic
59#17986617—21no—
60#17986613—21no—
61#17986599—21no—
62#17986599—21no—
63#17986565C2211yescharacteristic
64#17986565C2211yescharacteristic
65#17986548—21no—
66#17986546—21no—
67#17986532—21no—
68#17986527—21no—
69#17986508C2211yescharacteristic
70#121×D71C2211yescharacteristic
71#121×D71C2211yescharacteristic
72#17986480C2211yescharacteristic
73#17986479C2211yescharacteristic
74#17986471C2211yescharacteristic
75#17986471C2211yescharacteristic
76#117×D71C2211yescharacteristic
77#117×D71C2211yescharacteristic
78#17986408C2211yescharacteristic, complemented
79#17986407C2211yescharacteristic, complemented
80#17986406C2211yescharacteristic, complemented
81#17986403C2211yescharacteristic, complemented
82#17986402C2211yescharacteristic, complemented
83#17986399C2211yescharacteristic, complemented
84#17986398C2211yescharacteristic, complemented
85#17986326C2211yescharacteristic, complemented
86#17986326C2211yescharacteristic, complemented
87#17986324C2211yescharacteristic, complemented
88#17986324C2211yescharacteristic, complemented
89#17986324C2211yescharacteristic, complemented
90#17986323C2211yescharacteristic, complemented
91#17986323C2211yescharacteristic, complemented
92#17986323C2211yescharacteristic, complemented
93#17986321C2211yescharacteristic, complemented
94#17986321C2211yescharacteristic, complemented
95#17986320C2211yescharacteristic, complemented
96#17986320C2211yescharacteristic, complemented
97#17986320C2211yescharacteristic, complemented
98#17986319C2211yescharacteristic, complemented
99#17986319C2211yescharacteristic, complemented
100#17986319C2211yescharacteristic, complemented
101#17986317C2211yescharacteristic, complemented
102#17986316C2211yescharacteristic, complemented
103#17986316C2211yescharacteristic, complemented
104#17986316C2211yescharacteristic, complemented
105#17986315C2211yescharacteristic, complemented
106#17986314C2211yescharacteristic, complemented
107#17986314C2211yescharacteristic, complemented
108#17986314C2211yescharacteristic, complemented
109#17986313C2211yescharacteristic, complemented
110#17986311C2211yescharacteristic, complemented
111#17986311C2211yescharacteristic, complemented
112#17986311C2211yescharacteristic, complemented
113#17986302C2211yescharacteristic, complemented
114#17986302C2211yescharacteristic, complemented
115#17986300C2211yescharacteristic, complemented
116#17986299C2211yescharacteristic, complemented
117#17986297C2211yescharacteristic, complemented
118#17986297C2211yescharacteristic, complemented
119#17986296C2211yescharacteristic, complemented
120#17986289C2211yescharacteristic, complemented
121#17986288C2211yescharacteristic, complemented
122#17986287C2211yescharacteristic, complemented
123#17986286C2211yescharacteristic, complemented
124#17986280C2211yescharacteristic, complemented
125#17986278C2211yescharacteristic, complemented
126#17986277C2211yescharacteristic, complemented
127#17986253C2211yescharacteristic, complemented
128#17986252C2211yescharacteristic, complemented
129#17986249C2211yescharacteristic, complemented
130#17986236C2211yescharacteristic
131#17986235C2211yescharacteristic
132#17986234C2211yescharacteristic
133#17986234C2211yescharacteristic
134#17986234C2211yescharacteristic, complemented
135#17986234C2211yescharacteristic, complemented
136#17986233C2211yescharacteristic
137#17986233C2211yescharacteristic
138#17986233C2211yescharacteristic, complemented
139#17986233C2211yescharacteristic, complemented
140#17986232C2211yescharacteristic
141#17986112C2211yescharacteristic, complemented
142#17986111C2211yescharacteristic, complemented
143#17986110C2211yescharacteristic, complemented
144C4×#11765850C2211yescharacteristic, complemented
145C4×#11765850C2211yescharacteristic, complemented
146#17986079C2211yescharacteristic, complemented
147#17986079C2211yescharacteristic, complemented
148#17986072C2211yescharacteristic, complemented
149#17986070C2211yescharacteristic, complemented
150#17986068C2211yescharacteristic, complemented
151D4×C71⋊C8C2211yescharacteristic, complemented
152#17986064C2211yescharacteristic, complemented
153(C22⋊D71)⋊C8C2211yescharacteristic, complemented
154(C22⋊D71)⋊C8C2211yescharacteristic, complemented
155#17986041C2211yescharacteristic, complemented
156#17986040C2211yescharacteristic
157#17986040C2211yescharacteristic
158#17986040C2211yescharacteristic, complemented
159#17986038C2211yescharacteristic
160#17986038C2211yescharacteristic
161#17986038C2211yescharacteristic, complemented
162#17986037C2211yescharacteristic, complemented
163#17986036C2211yescharacteristic
164#17986036C2211yescharacteristic
165#17986035C2211yescharacteristic, complemented
166#17986035C2211yescharacteristic, complemented
167#17986035C2211yescharacteristic, complemented
168#17986034C2211yescharacteristic
169#17986034C2211yescharacteristic
170#17986034C2211yescharacteristic, complemented
171C2×#14556061C2211yescharacteristic, complemented
172#107×D71C2211yescharacteristic
173#107×D71C2211yescharacteristic, complemented
174#107×D71C2211yescharacteristic, complemented
175#107×D71C2211yescharacteristic, complemented
176#106×D71C2211yescharacteristic, complemented
177#106×D71C2211yescharacteristic, complemented
178#17986024C2211yescharacteristic
179#17986002C2211yescharacteristic
180#17986002C2211yescharacteristic
181#17986002C2211yescharacteristic
182#17986002C2211yescharacteristic
183#102×D71C2211yescharacteristic
184#102×D71C2211yescharacteristic
185#17985964C2211yescharacteristic
186#17985961C2211yescharacteristic
187#17985956C2211yescharacteristic
188#555×C71C2211yescharacteristic, complemented
189#553×C71C2211yescharacteristic, complemented
190#501×C71C2211yescharacteristic, complemented
191#482×C71C2211yescharacteristic, complemented
192#482×C71C2211yescharacteristic, complemented
193#482×C71C2211yescharacteristic, complemented
194#480×C71C2211yescharacteristic, complemented
195#478×C71C2211yescharacteristic, complemented
196#474×C71C2211yescharacteristic, complemented
197#469×C71C2211yescharacteristic, complemented
198#466×C71C2211yescharacteristic
199#442×C71C2211yescharacteristic, complemented
200#435×C71C2211yescharacteristic, complemented
201#428×C71C2211yescharacteristic, complemented
202#427×C71C2211yescharacteristic, complemented
203C2×#11765866—21no—
204C2×#11765865—21no—
205C2×#11765865—21no—
206C2×#11765865C2311yescharacteristic
207C2×#11765864—21no—
208C2×D4×D71—21no—
209C2×D4×D71—21no—
210C2×D4×D71C2311yescharacteristic
211C2×D4×D71C2311yescharacteristic
212C22×C4×D71C2311yescharacteristic
213C2×D568C2311yescharacteristic
214C2×#11765850C2311yescharacteristic
215C2×#11765850C2311yescharacteristic
216D8×D71—24no—
217#14556136—24no—
218C2×#11765848C2311yescharacteristic
219C2×#11765848C2311yescharacteristic
220C2×#11765848C2311yescharacteristic
221C22×C71⋊C8C2311yescharacteristic
222C22×C71⋊C8C2311yescharacteristic
223C2×C8×D71—24no—
224C2×C8×D71C2311yescharacteristic
225C2×C8×D71C2311yescharacteristic
226C2×C8×D71C2311yescharacteristic
227C2×C8×D71C2311yescharacteristic
228C2×C8×D71C2311yescharacteristic
229#14556128C2311yescharacteristic
230#14556127—21no—
231#14556127C2311yescharacteristic
232#14556127C2311yescharacteristic
233#14556126—21no—
234#14556124—21no—
235#14556124—21no—
236#14556123—21no—
237#14556123—21no—
238#14556122—21no—
239#14556122—21no—
240#14556121—21no—
241#14556121—21no—
242#14556121—21no—
243#14556120C2311yescharacteristic
244#14556119C2311yescharacteristic
245#14556119C2311yescharacteristic
246#14556118—21no—
247#14556118—21no—
248#14556116—21no—
249#14556115—21no—
250#14556114—21no—
251#14556114—21no—
252#14556114—21no—
253#14556114—21no—
254#14556114—21no—
255#14556114—21no—
256#14556113—21no—
257#14556113—21no—
258#14556113—21no—
259#14556113—21no—
260#14556113D411yescharacteristic
261#14556111—21no—
262#14556111—21no—
263#14556110—21no—
264#14556110—21no—
265#14556110—21no—
266#14556110—21no—
267#14556110—21no—
268#14556110—21no—
269#14556110D411yescharacteristic
270#14556109—21no—
271#14556109—21no—
272#14556109—21no—
273#14556108—21no—
274#14556107—21no—
275#14556106—21no—
276#14556106—21no—
277#14556106—21no—
278#14556106D411yescharacteristic
279#14556105—21no—
280#14556105D411yescharacteristic
281#14556104—21no—
282#14556104—21no—
283#14556103—21no—
284#14556103C2311yescharacteristic
285#14556103C2311yescharacteristic
286#14556103C2311yescharacteristic
287#14556103C2311yescharacteristic
288#14556102C2311yescharacteristic
289#14556102C2311yescharacteristic
290#14556102C2311yescharacteristic
291#14556102C2311yescharacteristic
292#14556101—21no—
293#14556101—21no—
294#14556101—21no—
295#14556101—21no—
296#14556101—21no—
297#14556101—21no—
298#14556101D411yescharacteristic
299#14556100—21no—
300#14556100—21no—
301#14556100—21no—
302#14556100—21no—
303#14556100D411yescharacteristic
304#14556099—21no—
305#14556099—21no—
306#14556099—21no—
307#14556099C2311yescharacteristic
308#14556099C2311yescharacteristic
309#14556099C2311yescharacteristic
310#14556099C2311yescharacteristic
311#14556098—21no—
312#14556098—21no—
313#14556098D411yescharacteristic
314#14556096—21no—
315#14556096—21no—
316#14556096D411yescharacteristic
317C4×Dic142—21no—
318#14556093—21no—
319C4×D284—21no—
320C4×D284—21no—
321C4×D284—21no—
322C4×D284C2311yescharacteristic
323C4×D284C2311yescharacteristic
324C4×D284C2311yescharacteristic
325D4×Dic71C2311yescharacteristic
326D4×Dic71C2311yescharacteristic
327#14556090—21no—
328#14556090—21no—
329#14556090C2311yescharacteristic
330#14556090C2311yescharacteristic
331C4×C22⋊D71—21no—
332C4×C22⋊D71—21no—
333C4×C22⋊D71—21no—
334C4×C22⋊D71—21no—
335C4×C22⋊D71—21no—
336C4×C22⋊D71C2311yescharacteristic
337C4×C22⋊D71C2311yescharacteristic
338(C22⋊D71)⋊C4—21no—
339(C22⋊D71)⋊C4—21no—
340(C22⋊D71)⋊C4—21no—
341(C22⋊D71)⋊C4—21no—
342(C22⋊D71)⋊C4—21no—
343(C22⋊D71)⋊C4—21no—
344(C22⋊D71)⋊C4—21no—
345#14556087C2311yescharacteristic
346#14556087C2311yescharacteristic
347#14556087C2311yescharacteristic
348#14556086—21no—
349#14556086C2311yescharacteristic
350#14556086C2311yescharacteristic
351#14556086C2311yescharacteristic
352#14556086C2311yescharacteristic
353#14556086C2311yescharacteristic
354#14556086C2311yescharacteristic
355#14556085—21no—
356#14556085—21no—
357#14556085—21no—
358#14556085C2311yescharacteristic
359#14556084—21no—
360#14556084—21no—
361#14556084—21no—
362C2×C4⋊Dic71C2311yescharacteristic
363C4⋊C4×D71C2311yescharacteristic
364C4⋊C4×D71C2311yescharacteristic
365C4⋊C4×D71C2311yescharacteristic
366C4⋊C4×D71C2311yescharacteristic
367C4⋊C4×D71C2311yescharacteristic
368C4⋊C4×D71C2311yescharacteristic
369C4⋊C4×D71C2311yescharacteristic
370C4⋊C4×D71C2311yescharacteristic
371C2×(C2×D71)⋊C4—21no—
372C2×(C2×D71)⋊C4—21no—
373C22⋊C4×D71—21no—
374C22⋊C4×D71—21no—
375C22⋊C4×D71—21no—
376C22⋊C4×D71—21no—
377C22⋊C4×D71—21no—
378C22⋊C4×D71—21no—
379C42×D71—21no—
380C42×D71—21no—
381#14556062C2311yescharacteristic
382#14556062C2311yescharacteristic
383#14556062C2311yescharacteristic
384#14556062C2311yescharacteristic
385#14556062C2311yescharacteristic
386#14556061C2311yescharacteristic
387#14556061C2311yescharacteristic
388#14556061C2311yescharacteristic
389#14556061C2311yescharacteristic
390#14556061C2311yescharacteristic
391#14556061C2311yescharacteristic
392#14556061C2311yescharacteristic
393#14556061C2311yescharacteristic
394#14556061C2311yescharacteristic
395#14556061C2311yescharacteristic
396#14556060C2311yescharacteristic
397#14556060C2311yescharacteristic
398#14556060C2311yescharacteristic
399#14556060C2311yescharacteristic
400#14556059C2311yescharacteristic
401#14556059C2311yescharacteristic
402#14556059C2311yescharacteristic
403#14556059C2311yescharacteristic
404#14556059C2311yescharacteristic
405#14556059C2311yescharacteristic
406#14556059C2311yescharacteristic
407#14556059C2311yescharacteristic
408C4⋊(C71⋊C8)C2311yescharacteristic
409Dic71⋊C8C2311yescharacteristic
410Dic71⋊C8C2311yescharacteristic
411#14556050C2311yescharacteristic
412#14556050C2311yescharacteristic
413#14556050C2311yescharacteristic
414#14556050C2311yescharacteristic
415#14556050C2311yescharacteristic
416#14556050C2311yescharacteristic
417#14556049C2311yescharacteristic
418#14556049C2311yescharacteristic
419#14556049C2311yescharacteristic
420#14556049C2311yescharacteristic
421#14556049C2311yescharacteristic
422#14556049C2311yescharacteristic
423#14556048C2311yescharacteristic
424#14556048C2311yescharacteristic
425#14556048C2311yescharacteristic
426#14556048C2311yescharacteristic
427#14556048C2311yescharacteristic
428#14556048C2311yescharacteristic
429C22⋊(C71⋊C8)C2311yescharacteristic
430C22⋊(C71⋊C8)C2311yescharacteristic
431(C2×D71)⋊C8C2311yescharacteristic
432(C2×D71)⋊C8C2311yescharacteristic
433(C2×D71)⋊C8C2311yescharacteristic
434(C2×D71)⋊C8C2311yescharacteristic
435#14556038C2311yescharacteristic
436C4×C71⋊C8C2311yescharacteristic
437C8×Dic71C2311yescharacteristic
438C2×D8×C71C2311yescharacteristic
439C2×M16×C71C2311yescharacteristic
440C22×C8×C71C2311yescharacteristic
441C4⋊Q8×C71C2311yescharacteristic
442#126×C71—21no—
443#125×C71C2311yescharacteristic
444#124×C71—21no—
445#124×C71—21no—
446#123×C71—21no—
447#121×C71—21no—
448#121×C71—21no—
449#121×C71C2311yescharacteristic
450#121×C71C2311yescharacteristic
451#121×C71C2311yescharacteristic
452#121×C71C2311yescharacteristic
453C4×D4×C71—21no—
454C4×D4×C71C2311yescharacteristic
455C4×D4×C71C2311yescharacteristic
456C4×D4×C71C2311yescharacteristic
457#117×C71—21no—
458#117×C71C2311yescharacteristic
459#117×C71C2311yescharacteristic
460#117×C71C2311yescharacteristic
461C2×C4⋊C4×C71C2311yescharacteristic
462#107×C71C2311yescharacteristic
463#107×C71C2311yescharacteristic
464#107×C71C2311yescharacteristic
465#107×C71C2311yescharacteristic
466#107×C71C2311yescharacteristic
467#106×C71C2311yescharacteristic
468#106×C71C2311yescharacteristic
469#106×C71C2311yescharacteristic
470#106×C71C2311yescharacteristic
471C4⋊C8×C71C2311yescharacteristic
472#102×C71C2311yescharacteristic
473#102×C71C2311yescharacteristic
474#102×C71C2311yescharacteristic
475#102×C71C2311yescharacteristic
476#102×C71C2311yescharacteristic
477#102×C71C2311yescharacteristic
478C22⋊C8×C71C2311yescharacteristic
479C22⋊C8×C71C2311yescharacteristic
480#97×C71C2311yescharacteristic
481C23×D71—21no—
482C23×D71—21no—
483C23×D71C2×D411yescharacteristic
484#11765866—82no—
485#11765865—22no—
486#11765865—22no—
487#11765865—82no—
488#11765865—82no—
489#11765864—82no—
490C2×Dic142—21no—
491C2×Dic142—21no—
492C2×Dic142—21no—
493C2×Dic142C2×D411yescharacteristic
494C2×D284—21no—
495C2×D284—21no—
496C2×D284—21no—
497C2×D284—21no—
498C2×D284C2×D411yescharacteristic
499C2×D284C2×D411yescharacteristic
500C2×D284C2411yescharacteristic
501C2×D284C2411yescharacteristic
502C2×C22⋊D71—21no—
503C2×C22⋊D71—21no—
504C2×C22⋊D71—21no—
505C2×C22⋊D71—21no—
506C2×C22⋊D71—21no—
507C2×C22⋊D71—21no—
508C2×C22⋊D71—21no—
509C2×C22⋊D71—21no—
510C2×C22⋊D71—21no—
511C2×C22⋊D71—21no—
512C2×C22⋊D71C2×D411yescharacteristic
513C2×C22⋊D71C2×D411yescharacteristic
514C2×C22⋊D71C2×D411yescharacteristic
515C2×C22⋊D71C2×D411yescharacteristic
516D4×D71—22no—
517D4×D71—22no—
518D4×D71—22no—
519D4×D71—22no—
520D4×D71—82no—
521D4×D71—82no—
522C22×Dic71—21no—
523C22×Dic71—21no—
524C22×Dic71—21no—
525C22×Dic71C2×D411yescharacteristic
526C2×C4×D71—22no—
527C2×C4×D71—22no—
528C2×C4×D71—21no—
529C2×C4×D71—21no—
530C2×C4×D71—21no—
531C2×C4×D71—21no—
532C2×C4×D71—21no—
533C2×C4×D71—21no—
534C2×C4×D71—21no—
535C2×C4×D71—21no—
536C2×C4×D71—21no—
537C2×C4×D71—21no—
538C2×C4×D71—21no—
539C2×C4×D71—21no—
540C2×C4×D71C2×D411yescharacteristic
541C2×C4×D71C2×D411yescharacteristic
542C2×C4×D71C2411yescharacteristic
543C2×C4×D71C2411yescharacteristic
544C2×C4×D71C2411yescharacteristic
545D568—22no—
546#11765850—22no—
547#11765850—22no—
548#11765848—22no—
549#11765848—22no—
550#11765848—22no—
551C2×C71⋊C8—22no—
552C2×C71⋊C8—22no—
553C2×C71⋊C8C2411yescharacteristic
554C2×C71⋊C8C2411yescharacteristic
555C2×C71⋊C8C2411yescharacteristic
556C2×C71⋊C8C2411yescharacteristic
557C8×D71—22no—
558C8×D71—22no—
559C8×D71—22no—
560C8×D71—22no—
561C8×D71#4114yescomplemented
562C4⋊Dic71—21no—
563C4⋊Dic71—21no—
564C4⋊Dic71—21no—
565C4⋊Dic71—21no—
566C4⋊Dic71C2×D411yescharacteristic
567C4⋊Dic71C2411yescharacteristic
568C4⋊Dic71C2411yescharacteristic
569C4⋊Dic71C2411yescharacteristic
570C4⋊Dic71C2411yescharacteristic
571C4⋊Dic71C2411yescharacteristic
572C4⋊Dic71C2411yescharacteristic
573Dic71⋊C4—21no—
574Dic71⋊C4—21no—
575Dic71⋊C4—21no—
576Dic71⋊C4—21no—
577Dic71⋊C4—21no—
578Dic71⋊C4—21no—
579Dic71⋊C4—21no—
580Dic71⋊C4—21no—
581Dic71⋊C4—21no—
582Dic71⋊C4—21no—
583Dic71⋊C4—21no—
584Dic71⋊C4—21no—
585Dic71⋊C4—21no—
586Dic71⋊C4—21no—
587Dic71⋊C4C2×D411yescharacteristic
588Dic71⋊C4C2×D411yescharacteristic
589Dic71⋊C4C2×D411yescharacteristic
590Dic71⋊C4C2×D411yescharacteristic
591C22⋊Dic71—21no—
592C22⋊Dic71—21no—
593C22⋊Dic71—21no—
594C22⋊Dic71—21no—
595C22⋊Dic71—21no—
596C22⋊Dic71—21no—
597C22⋊Dic71—21no—
598C22⋊Dic71—21no—
599C22⋊Dic71—21no—
600C22⋊Dic71C2×D411yescharacteristic
601C22⋊Dic71C2×D411yescharacteristic
602(C2×D71)⋊C4—21no—
603(C2×D71)⋊C4—21no—
604(C2×D71)⋊C4—21no—
605(C2×D71)⋊C4—21no—
606(C2×D71)⋊C4—21no—
607(C2×D71)⋊C4—21no—
608(C2×D71)⋊C4—21no—
609(C2×D71)⋊C4—21no—
610(C2×D71)⋊C4—21no—
611(C2×D71)⋊C4—21no—
612(C2×D71)⋊C4—21no—
613(C2×D71)⋊C4—21no—
614(C2×D71)⋊C4—21no—
615(C2×D71)⋊C4—21no—
616(C2×D71)⋊C4—21no—
617(C2×D71)⋊C4—21no—
618(C2×D71)⋊C4—21no—
619(C2×D71)⋊C4—21no—
620(C2×D71)⋊C4C2×D411yescharacteristic
621(C2×D71)⋊C4C2×D411yescharacteristic
622(C2×D71)⋊C4C2×D411yescharacteristic
623(C2×D71)⋊C4C2×D411yescharacteristic
624(C2×D71)⋊C4C2×D411yescharacteristic
625(C2×D71)⋊C4C2×D411yescharacteristic
626C4×Dic71—21no—
627C4×Dic71—21no—
628C4×Dic71—21no—
629C4×Dic71—21no—
630C4×Dic71—21no—
631C4×Dic71—21no—
632C4×Dic71—21no—
633C4×Dic71—21no—
634C4×Dic71—21no—
635C4×Dic71C2411yescharacteristic
636C2×Q8×C71—21no—
637C2×D4×C71—21no—
638C2×D4×C71—21no—
639C2×D4×C71—21no—
640C2×D4×C71—21no—
641C2×D4×C71C2×D411yescharacteristic
642C2×D4×C71C2411yescharacteristic
643C2×D4×C71C2411yescharacteristic
644C22×C4×C71—21no—
645C22×C4×C71—21no—
646C22×C4×C71—21no—
647C22×C4×C71C2411yescharacteristic
648C22×C4×C71C2411yescharacteristic
649D8×C71—22no—
650M16×C71—22no—
651C2×C8×C71—22no—
652C2×C8×C71C2411yescharacteristic
653C2×C8×C71C2411yescharacteristic
654C2×C8×C71C2411yescharacteristic
655C2×C8×C71C2411yescharacteristic
656C4⋊C4×C71—21no—
657C4⋊C4×C71—21no—
658C4⋊C4×C71—21no—
659C4⋊C4×C71—21no—
660C4⋊C4×C71C2×D411yescharacteristic
661C4⋊C4×C71C2411yescharacteristic
662C4⋊C4×C71C2411yescharacteristic
663C4⋊C4×C71C2411yescharacteristic
664C4⋊C4×C71C2411yescharacteristic
665C4⋊C4×C71C2411yescharacteristic
666C4⋊C4×C71C2411yescharacteristic
667C22⋊C4×C71—21no—
668C22⋊C4×C71—21no—
669C22⋊C4×C71—21no—
670C22⋊C4×C71—21no—
671C22⋊C4×C71—21no—
672C22⋊C4×C71—21no—
673C22⋊C4×C71—21no—
674C22⋊C4×C71—21no—
675C22⋊C4×C71—21no—
676C22⋊C4×C71C2×D411yescharacteristic
677C22⋊C4×C71C2×D411yescharacteristic
678C42×C71—21no—
679C42×C71—21no—
680C42×C71—21no—
681C42×C71C2411yescharacteristic
682C23×C71—21no—
683C23×C71—21no—
684C23×C71C22×D411yescharacteristic
685C23×C71C22×D411yescharacteristic
686C22×D71—22no—
687C22×D71—22no—
688C22×D71—21no—
689C22×D71—21no—
690C22×D71—41no—
691C22×D71—42no—
692C22×D71—42no—
693C22×D71—81no—
694C22×D71—81no—
695C22×D71—81no—
696C22×D71—81no—
697C22×D71C22×D411yescharacteristic
698C22×D71C22×D411yescharacteristic
699C22×D71C22×D411yescharacteristic
700Q8×C71—81no—
701D4×C71—21no—
702D4×C71—21no—
703D4×C71—21no—
704D4×C71—21no—
705D4×C71—41no—
706D4×C71—81no—
707D4×C71—81no—
708D4×C71—81no—
709D4×C71—81no—
710C2×C4×C71—21no—
711C2×C4×C71—21no—
712C2×C4×C71—21no—
713C2×C4×C71—21no—
714C2×C4×C71—21no—
715C2×C4×C71—21no—
716C2×C4×C71—21no—
717C2×C4×C71—21no—
718C2×C4×C71—21no—
719C2×C4×C71—21no—
720C2×C4×C71—81no—
721C2×C4×C71—81no—
722C2×C4×C71—81no—
723C2×C4×C71C22×D411yescharacteristic
724C2×C4×C71C22×D411yescharacteristic
725C2×C4×C71C22×D411yescharacteristic
726C2×C4×C71C22×D411yescharacteristic
727C2×C4×C71C2511yescharacteristic
728C22⋊D71—22no—
729C22⋊D71—22no—
730C22⋊D71—22no—
731C22⋊D71—41no—
732C22⋊D71—42no—
733C22⋊D71—42no—
734C22⋊D71—42no—
735C22⋊D71—42no—
736C22⋊D71—81no—
737C22⋊D71—81no—
738C22⋊D71—81no—
739C22⋊D71—81no—
740C22⋊D71—81no—
741C22⋊D71—81no—
742C2×Dic71—22no—
743C2×Dic71—21no—
744C2×Dic71—21no—
745C2×Dic71—21no—
746C2×Dic71—21no—
747C2×Dic71—21no—
748C2×Dic71—21no—
749C2×Dic71—81no—
750C2×Dic71—81no—
751C2×Dic71—81no—
752C2×Dic71C22×D411yescharacteristic
753C2×Dic71C22×D411yescharacteristic
754C2×Dic71C22×D411yescharacteristic
755C2×Dic71C22×D411yescharacteristic
756C2×Dic71C22×D411yescharacteristic
757D284—22no—
758D284—22no—
759D284—21no—
760D284—21no—
761D284—21no—
762D284—21no—
763D284—42no—
764D284—42no—
765D284—81no—
766D284—81no—
767C4×D71—22no—
768C4×D71—21no—
769C4×D71—21no—
770C4×D71—21no—
771C4×D71—21no—
772C4×D71—22no—
773C4×D71—42no—
774C4×D71—42no—
775C4×D71—81no—
776C4×D71—81no—
777C4×D71—81no—
778C4×D71—81no—
779C4×D71—81no—
780C4×D71—81no—
781C4×D71—81no—
782C4×D71—81no—
783C4×D71—81no—
784C4×D71—81no—
785C4×D71C2×#4112yes—
786C4×D712−1+412yes—
787Dic142—22no—
788Dic142—81no—
789Dic142—81no—
790Dic142—81no—
791C8×C71—21no—
792C8×C71—21no—
793C8×C71—21no—
794C8×C71C2×#4112yes—
795C71⋊C8—21no—
796C71⋊C8—21no—
797C71⋊C8—21no—
798C71⋊C8C2×#4112yes—
799C22×C71—21no—
800C22×C71—21no—
801C22×C71—21no—
802C22×C71—21no—
803C22×C71—21no—
804C22×C71—21no—
805C22×C71—41no—
806C22×C71—41no—
807C22×C71—41no—
808C22×C71—41no—
809C22×C71—41no—
810C22×C71—41no—
811C22×C71C23×D411yescharacteristic
812C2×D71—21no—
813C2×D71—21no—
814C2×D71—21no—
815C2×D71—21no—
816C2×D71—21no—
817C2×D71—21no—
818C2×D71—21no—
819C2×D71—44no—
820C2×D71—41no—
821C2×D71—41no—
822C2×D71—41no—
823C2×D71—41no—
824C2×D71—41no—
825C2×D71—41no—
826C2×D71—162no—
827C2×D71—162no—
828C2×D71#54712yes—
829C2×D71#57612yes—
830C4×C71—21no—
831C4×C71—21no—
832C4×C71—21no—
833C4×C71—21no—
834C4×C71—41no—
835C4×C71—41no—
836C4×C71—41no—
837C4×C71—41no—
838C4×C71—41no—
839C4×C71—41no—
840C4×C71C22×#4111yescharacteristic
841C4×C71C2×2−1+411yescharacteristic
842Dic71—21no—
843Dic71—21no—
844Dic71—21no—
845Dic71—21no—
846Dic71—41no—
847Dic71—41no—
848Dic71—41no—
849Dic71—41no—
850Dic71—41no—
851Dic71—41no—
852Dic71#54712yes—
853#61262—711nomaximal, Sylow
854C2×C71—41no—
855C2×C71—41no—
856C2×C71—81no—
857C2×C71—81no—
858C2×C71C2×#54711yescharacteristic
859C2×C71C2×#57611yescharacteristic
860C2×C71#358411yescharacteristic
861D71—22no—
862D71—22no—
863D71—41no—
864D71—81no—
865D71—81no—
866#3494—711no—
867#3494—711no—
868#3347—711no—
869#3347—711no—
870#3347—711no—
871#3347D7111yescharacteristic, complemented
872#3345—711no—
873#3345—711no—
874#3345—711no—
875#3345—711no—
876#3341—711no—
877#3341—711no—
878#3339—711no—
879#3339—711no—
880#3339—711no—
881#3339—711no—
882#3334—711no—
883#3334—711no—
884#3164—711no—
885#3096—711no—
886#3096—711no—
887#3094—711no—
888#3094—711no—
889#3081—711no—
890#3081—711no—
891#3058—711no—
892C2×#466—711no—
893#2948—711no—
894#2929—711no—
895#2913—711no—
896C2×#427—711no—
897C71#6126211yescharacteristic, complemented, Sylow
898C22×D8—711no—
899C2×#131—711no—
900C23×C8—711no—
901#555—711no—
902#555—711no—
903#555—711no—
904#555C2×D7111yescharacteristic, complemented
905#553—711no—
906#553—711no—
907#553—711no—
908#553—711no—
909#553—711no—
910#553—711no—
911#553—711no—
912#553C2×D7111yescharacteristic, complemented
913#551—1421no—
914#551—1421no—
915#551—1421no—
916#551—1421no—
917#547—711no—
918#547—711no—
919#547—711no—
920#547—711no—
921#546—1421no—
922#546—1421no—
923#546—1421no—
924#546—1421no—
925#544—711no—
926#544—711no—
927#542—1421no—
928#542—1421no—
929#540—1421no—
930#540—1421no—
931#535—711no—
932#535—711no—
933#532—1421no—
934#532—1421no—
935#529—1421no—
936#529—1421no—
937#525—711no—
938C2×#121—711no—
939C2×#121—711no—
940#520—711no—
941#520—711no—
942#518—711no—
943#518—711no—
944C2×#117—711no—
945C2×#117—711no—
946#501—711no—
947#501—711no—
948#501—711no—
949#501C2×D7111yescharacteristic, complemented
950#500—711no—
951#500—711no—
952#499—711no—
953#499—711no—
954#482—711no—
955#482—711no—
956#482—711no—
957#482—711no—
958#482—711no—
959#482—711no—
960#482—711no—
961#482—711no—
962#482—711no—
963#482—711no—
964#482—711no—
965#482—711no—
966#482—711no—
967#482C2×D7111yescharacteristic, complemented
968#482C2×D7111yescharacteristic, complemented
969#482C2×D7111yescharacteristic, complemented
970#481—711no—
971#481—711no—
972#481—711no—
973#481—711no—
974#481—711no—
975#481—711no—
976#481—711no—
977#481—711no—
978#480—711no—
979#480—711no—
980#480—711no—
981#480—711no—
982#480—711no—
983#480—711no—
984#480—711no—
985#480C2×D7111yescharacteristic, complemented
986#478—711no—
987#478—711no—
988#478—711no—
989#478—711no—
990#478—711no—
991#478—711no—
992#478—711no—
993#478C2×D7111yescharacteristic, complemented
994#476—711no—
995#476—711no—
996#476—711no—
997#476—711no—
998#474—711no—
999#474—711no—
1000#474—711no—
1001#474C2×D7111yescharacteristic, complemented
1002#469—711no—
1003#469—711no—
1004#469—711no—
1005#469C2×D7111yescharacteristic, complemented
1006#466—711no—
1007#466—711no—
1008#466—711no—
1009#466—711no—
1010#466—711no—
1011#466—711no—
1012#466—711no—
1013#466—711no—
1014#466—711no—
1015#466—711no—
1016#466—711no—
1017#466C2×D7111yescharacteristic
1018#442—711no—
1019#442—711no—
1020#442—711no—
1021#442C2×D7111yescharacteristic, complemented
1022C4×D8—711no—
1023C4×D8—711no—
1024C4×D8—711no—
1025C4×D8—711no—
1026#435—711no—
1027#435—711no—
1028#435—711no—
1029#435C2×D7111yescharacteristic, complemented
1030C8×D4—711no—
1031C8×D4—711no—
1032C8×D4—711no—
1033C8×D4—711no—
1034#428—711no—
1035#428—711no—
1036#428—711no—
1037#428—711no—
1038#428—711no—
1039#428—711no—
1040#428—711no—
1041#428C2×D7111yescharacteristic, complemented
1042#427—711no—
1043#427—711no—
1044#427—711no—
1045#427—711no—
1046#427—711no—
1047#427—711no—
1048#427—711no—
1049#427—711no—
1050#427—711no—
1051#427C2×D7111yescharacteristic, complemented
1052C2×#107—711no—
1053C2×#107—711no—
1054C2×#107—711no—
1055C2×#107—711no—
1056C2×#107—711no—
1057C2×#106—711no—
1058C2×#106—711no—
1059#424—711no—
1060#418—711no—
1061#418—711no—
1062#418—711no—
1063#418—711no—
1064C2×#102—711no—
1065C2×#102—711no—
1066#408—711no—
1067#407—711no—
1068#405—711no—
1069C2×#41—711no—
1070C2×#41—1421no—
1071C2×#41—1421no—
1072C2×#41—1421no—
1073C2×#41—1421no—
1074C22×D4—711no—
1075C22×D4—711no—
1076C22×D4—1421no—
1077C22×D4—1421no—
1078C23×C4—711no—
1079C2×D8—711no—
1080C2×D8—711no—
1081C2×D8—711no—
1082C2×D8—1424no—
1083C2×D8C22×D7111yescharacteristic
1084#131—1424no—
1085C2×M16—711no—
1086C2×M16—711no—
1087C2×M16—711no—
1088C2×M16C22×D7111yescharacteristic
1089C22×C8—711no—
1090C22×C8—711no—
1091C22×C8—711no—
1092C22×C8—711no—
1093C22×C8—711no—
1094C22×C8—711no—
1095C22×C8—711no—
1096C22×C8—1424no—
1097C22×C8C22×D7111yescharacteristic
1098C4⋊Q8—711no—
1099C4⋊Q8—711no—
1100C4⋊Q8—711no—
1101C4⋊Q8—1421no—
1102C4⋊Q8—1421no—
1103C4⋊Q8C22×D7111yescharacteristic
1104#127—1421no—
1105#127—1421no—
1106#126—21no—
1107#126—1421no—
1108#126—1421no—
1109#126—1421no—
1110#126—1421no—
1111#126—1421no—
1112#126—1421no—
1113#126—1421no—
1114#125—711no—
1115#125—711no—
1116#125—711no—
1117#125—1421no—
1118#125—1421no—
1119#125C22×D7111yescharacteristic
1120#124—21no—
1121#124—21no—
1122#124—1421no—
1123#124—1421no—
1124#124—1421no—
1125#124—1421no—
1126#124—1421no—
1127#124—1421no—
1128#124—1421no—
1129#124—1421no—
1130#123—21no—
1131#123—711no—
1132#123—711no—
1133#123—1421no—
1134#123—1421no—
1135#123—1421no—
1136#123—1421no—
1137#123—1421no—
1138#123—1421no—
1139#123—1421no—
1140#123—1421no—
1141#123—1421no—
1142#123—1421no—
1143#123—1421no—
1144#123—1421no—
1145#123—1421no—
1146#123—1421no—
1147#123—1421no—
1148C22⋊Q8—711no—
1149C22⋊Q8—711no—
1150C22⋊Q8—1421no—
1151C22⋊Q8—1421no—
1152C22⋊Q8—1421no—
1153C22⋊Q8—1421no—
1154C22⋊Q8—1421no—
1155C22⋊Q8—1421no—
1156C22⋊Q8—1421no—
1157C22⋊Q8—1421no—
1158#121—21no—
1159#121—21no—
1160#121—711no—
1161#121—711no—
1162#121—711no—
1163#121—711no—
1164#121—711no—
1165#121—711no—
1166#121—711no—
1167#121—711no—
1168#121—711no—
1169#121—711no—
1170#121—711no—
1171#121—711no—
1172#121—711no—
1173#121—711no—
1174#121—1421no—
1175#121—1421no—
1176#121—1421no—
1177#121—1421no—
1178#121—1421no—
1179#121—1421no—
1180#121—1421no—
1181#121—1421no—
1182#121—1421no—
1183#121—1421no—
1184#121—1421no—
1185#121—1421no—
1186#121—1421no—
1187#121—1421no—
1188#121C22×D7111yescharacteristic
1189#121C22×D7111yescharacteristic
1190#121C22×D7111yescharacteristic
1191#121C22×D7111yescharacteristic
1192#120—711no—
1193#120—711no—
1194#120—1421no—
1195#120—1421no—
1196#120—1421no—
1197#120—1421no—
1198C4×Q8—1421no—
1199C4×Q8—1421no—
1200C4×D4—21no—
1201C4×D4—711no—
1202C4×D4—711no—
1203C4×D4—711no—
1204C4×D4—711no—
1205C4×D4—711no—
1206C4×D4—711no—
1207C4×D4—711no—
1208C4×D4—711no—
1209C4×D4—711no—
1210C4×D4—1421no—
1211C4×D4—1421no—
1212C4×D4—1421no—
1213C4×D4—1421no—
1214C4×D4—1421no—
1215C4×D4—1421no—
1216C4×D4—1421no—
1217C4×D4—1421no—
1218C4×D4—1421no—
1219C4×D4—1421no—
1220C4×D4—1421no—
1221C4×D4—1421no—
1222C4×D4—1421no—
1223C4×D4—1421no—
1224C4×D4—1421no—
1225C4×D4—1421no—
1226C4×D4—1421no—
1227C4×D4C22×D7111yescharacteristic
1228C4×D4C22×D7111yescharacteristic
1229C4×D4C22×D7111yescharacteristic
1230#117—21no—
1231#117—711no—
1232#117—711no—
1233#117—711no—
1234#117—711no—
1235#117—711no—
1236#117—711no—
1237#117—711no—
1238#117—711no—
1239#117—711no—
1240#117—711no—
1241#117—1421no—
1242#117—1421no—
1243#117—1421no—
1244#117—1421no—
1245#117—1421no—
1246#117—1421no—
1247#117—1421no—
1248#117C22×D7111yescharacteristic
1249#117C22×D7111yescharacteristic
1250#117C22×D7111yescharacteristic
1251C2×C4⋊C4—711no—
1252C2×C4⋊C4—711no—
1253C2×C4⋊C4—711no—
1254C2×C4⋊C4—711no—
1255C2×C4⋊C4—711no—
1256C2×C4⋊C4—711no—
1257C2×C4⋊C4—711no—
1258C2×C4⋊C4—711no—
1259C2×C4⋊C4—711no—
1260C2×C4⋊C4C22×D7111yescharacteristic
1261C2×C22⋊C4—1421no—
1262C2×C22⋊C4—1421no—
1263C2×C22⋊C4—1421no—
1264C2×C22⋊C4—1421no—
1265C2×C22⋊C4—1421no—
1266C2×C22⋊C4—1421no—
1267C2×C22⋊C4—1421no—
1268C2×C22⋊C4—1421no—
1269C2×C42—1421no—
1270C2×C42—1421no—
1271#107—711no—
1272#107—711no—
1273#107—711no—
1274#107—711no—
1275#107—711no—
1276#107—711no—
1277#107—711no—
1278#107—711no—
1279#107—711no—
1280#107—711no—
1281#107—711no—
1282#107—711no—
1283#107—711no—
1284#107—711no—
1285#107—711no—
1286#107C22×D7111yescharacteristic
1287#107C22×D7111yescharacteristic
1288#107C22×D7111yescharacteristic
1289#107C22×D7111yescharacteristic
1290#107C22×D7111yescharacteristic
1291#106—711no—
1292#106—711no—
1293#106—711no—
1294#106—711no—
1295#106—711no—
1296#106—711no—
1297#106—711no—
1298#106—711no—
1299#106—711no—
1300#106—711no—
1301#106—711no—
1302#106—711no—
1303#106C22×D7111yescharacteristic
1304#106C22×D7111yescharacteristic
1305#106C22×D7111yescharacteristic
1306#106C22×D7111yescharacteristic
1307C4⋊C8—711no—
1308C4⋊C8—711no—
1309C4⋊C8—711no—
1310C4⋊C8C22×D7111yescharacteristic
1311#102—711no—
1312#102—711no—
1313#102—711no—
1314#102—711no—
1315#102—711no—
1316#102—711no—
1317#102—711no—
1318#102—711no—
1319#102—711no—
1320#102—711no—
1321#102—711no—
1322#102—711no—
1323#102—711no—
1324#102—711no—
1325#102—711no—
1326#102—711no—
1327#102—711no—
1328#102—711no—
1329#102C22×D7111yescharacteristic
1330#102C22×D7111yescharacteristic
1331#102C22×D7111yescharacteristic
1332#102C22×D7111yescharacteristic
1333#102C22×D7111yescharacteristic
1334#102C22×D7111yescharacteristic
1335C22⋊C8—711no—
1336C22⋊C8—711no—
1337C22⋊C8—711no—
1338C22⋊C8—711no—
1339C22⋊C8—711no—
1340C22⋊C8—711no—
1341C22⋊C8C22×D7111yescharacteristic
1342C22⋊C8C22×D7111yescharacteristic
1343#97—711no—
1344#97C22×D7111yescharacteristic
1345C4×C8—711no—
1346C4×C8—711no—
1347C24—711no—
1348C24—1421no—
1349C24—1421no—
1350#41—5682no—
1351#41—5682no—
1352#41—5682no—
1353#41—5682no—
1354#41—1422no—
1355#41—1422no—
1356C2×Q8—21no—
1357C2×Q8—711no—
1358C2×Q8—1421no—
1359C2×Q8—1421no—
1360C2×Q8—1421no—
1361C2×D4—21no—
1362C2×D4—21no—
1363C2×D4—21no—
1364C2×D4—21no—
1365C2×D4—5682no—
1366C2×D4—5682no—
1367C2×D4—711no—
1368C2×D4—711no—
1369C2×D4—711no—
1370C2×D4—711no—
1371C2×D4—711no—
1372C2×D4—711no—
1373C2×D4—711no—
1374C2×D4—711no—
1375C2×D4—1421no—
1376C2×D4—1421no—
1377C2×D4—1421no—
1378C2×D4—1421no—
1379C2×D4—1422no—
1380C2×D4—1422no—
1381C2×D4—1422no—
1382C2×D4—1422no—
1383C2×D4—1421no—
1384C2×D4—1421no—
1385C2×D4—1421no—
1386C2×D4—1421no—
1387C2×D4—1421no—
1388C2×D4—1421no—
1389C2×D4—1421no—
1390C2×D4—1421no—
1391C2×D4—1421no—
1392C2×D4—1421no—
1393C2×D4D4×D7111yescharacteristic
1394C2×D4C23×D7111yescharacteristic
1395C2×D4C23×D7111yescharacteristic
1396C22×C4—21no—
1397C22×C4—21no—
1398C22×C4—21no—
1399C22×C4—711no—
1400C22×C4—711no—
1401C22×C4—711no—
1402C22×C4—711no—
1403C22×C4—711no—
1404C22×C4—711no—
1405C22×C4—1421no—
1406C22×C4—1421no—
1407C22×C4—1421no—
1408C22×C4—1421no—
1409C22×C4—1421no—
1410C22×C4—1421no—
1411C22×C4—1421no—
1412C22×C4—1421no—
1413C22×C4—1421no—
1414C22×C4—1421no—
1415C22×C4—1422no—
1416C22×C4—1422no—
1417C22×C4—1421no—
1418C22×C4—1421no—
1419C22×C4—1421no—
1420C22×C4—1421no—
1421C22×C4—1421no—
1422C22×C4C23×D7111yescharacteristic
1423C22×C4C23×D7111yescharacteristic
1424D8—22no—
1425D8—1422no—
1426D8—1422no—
1427D8—1422no—
1428M16—22no—
1429M16—1422no—
1430M16—1422no—
1431M16—1422no—
1432C2×C8—22no—
1433C2×C8—711no—
1434C2×C8—714no—
1435C2×C8—711no—
1436C2×C8—711no—
1437C2×C8—711no—
1438C2×C8—1422no—
1439C2×C8—1422no—
1440C2×C8—1422no—
1441C2×C8—1422no—
1442C2×C8—1422no—
1443C2×C8—1422no—
1444C2×C8C23×D7111yescharacteristic
1445C2×C8C23×D7111yescharacteristic
1446C2×C8C23×D7111yescharacteristic
1447C2×C8C23×D7111yescharacteristic
1448C4⋊C4—21no—
1449C4⋊C4—21no—
1450C4⋊C4—21no—
1451C4⋊C4—21no—
1452C4⋊C4—711no—
1453C4⋊C4—711no—
1454C4⋊C4—711no—
1455C4⋊C4—711no—
1456C4⋊C4—711no—
1457C4⋊C4—711no—
1458C4⋊C4—711no—
1459C4⋊C4—711no—
1460C4⋊C4—711no—
1461C4⋊C4—711no—
1462C4⋊C4—711no—
1463C4⋊C4—1421no—
1464C4⋊C4—1421no—
1465C4⋊C4—1421no—
1466C4⋊C4—1421no—
1467C4⋊C4—1421no—
1468C4⋊C4—1421no—
1469C4⋊C4—1421no—
1470C4⋊C4—1421no—
1471C4⋊C4—1421no—
1472C4⋊C4—1421no—
1473C4⋊C4—1421no—
1474C4⋊C4—1421no—
1475C4⋊C4—1421no—
1476C4⋊C4—1421no—
1477C4⋊C4—1421no—
1478C4⋊C4—1421no—
1479C4⋊C4—1421no—
1480C4⋊C4—1421no—
1481C4⋊C4D4×D7111yescharacteristic
1482C4⋊C4C23×D7111yescharacteristic
1483C4⋊C4C23×D7111yescharacteristic
1484C4⋊C4C23×D7111yescharacteristic
1485C4⋊C4C23×D7111yescharacteristic
1486C4⋊C4C23×D7111yescharacteristic
1487C4⋊C4C23×D7111yescharacteristic
1488C22⋊C4—21no—
1489C22⋊C4—21no—
1490C22⋊C4—21no—
1491C22⋊C4—21no—
1492C22⋊C4—21no—
1493C22⋊C4—21no—
1494C22⋊C4—21no—
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—711no—
1498C22⋊C4—711no—
1499C22⋊C4—711no—
1500C22⋊C4—711no—
1501C22⋊C4—711no—
1502C22⋊C4—711no—
1503C22⋊C4—711no—
1504C22⋊C4—711no—
1505C22⋊C4—1421no—
1506C22⋊C4—1421no—
1507C22⋊C4—1421no—
1508C22⋊C4—1421no—
1509C22⋊C4—1421no—
1510C22⋊C4—1421no—
1511C22⋊C4—1421no—
1512C22⋊C4—1421no—
1513C22⋊C4—1421no—
1514C22⋊C4—1421no—
1515C22⋊C4—1421no—
1516C22⋊C4—1421no—
1517C22⋊C4—1421no—
1518C22⋊C4—1421no—
1519C22⋊C4—1421no—
1520C22⋊C4—1421no—
1521C22⋊C4—1421no—
1522C22⋊C4—1421no—
1523C22⋊C4—1421no—
1524C22⋊C4—1421no—
1525C22⋊C4—1421no—
1526C22⋊C4—1421no—
1527C22⋊C4—1421no—
1528C22⋊C4—1421no—
1529C22⋊C4—1421no—
1530C22⋊C4—1421no—
1531C22⋊C4—1421no—
1532C22⋊C4D4×D7111yescharacteristic
1533C22⋊C4D4×D7111yescharacteristic
1534C42—21no—
1535C42—21no—
1536C42—21no—
1537C42—711no—
1538C42—1421no—
1539C42—1421no—
1540C42—1421no—
1541C42—1421no—
1542C42—1421no—
1543C42—1421no—
1544C42—1421no—
1545C42—1421no—
1546C42—1421no—
1547C42C23×D7111yescharacteristic
1548C23—21no—
1549C23—21no—
1550C23—2841no—
1551C23—2842no—
1552C23—2842no—
1553C23—5681no—
1554C23—5681no—
1555C23—5681no—
1556C23—5681no—
1557C23—711no—
1558C23—711no—
1559C23—711no—
1560C23—1422no—
1561C23—1422no—
1562C23—1421no—
1563C23—1421no—
1564C23C2×D4×D7111yescharacteristic
1565C23C2×D4×D7111yescharacteristic
1566Q8—81no—
1567Q8—5681no—
1568Q8—5681no—
1569Q8—5681no—
1570Q8—1422no—
1571D4—21no—
1572D4—21no—
1573D4—21no—
1574D4—21no—
1575D4—41no—
1576D4—81no—
1577D4—81no—
1578D4—81no—
1579D4—81no—
1580D4—2842no—
1581D4—2842no—
1582D4—2842no—
1583D4—2842no—
1584D4—2842no—
1585D4—2842no—
1586D4—2841no—
1587D4—5681no—
1588D4—5681no—
1589D4—5681no—
1590D4—5681no—
1591D4—5681no—
1592D4—5681no—
1593D4—5681no—
1594D4—5681no—
1595D4—1422no—
1596D4—1422no—
1597D4—1422no—
1598D4—1422no—
1599D4—1422no—
1600D4—1421no—
1601D4—1421no—
1602D4—1421no—
1603D4—1421no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—81no—
1615C2×C4—81no—
1616C2×C4—81no—
1617C2×C4—2842no—
1618C2×C4—2842no—
1619C2×C4—5681no—
1620C2×C4—5681no—
1621C2×C4—5681no—
1622C2×C4—5681no—
1623C2×C4—5681no—
1624C2×C4—5681no—
1625C2×C4—5681no—
1626C2×C4—5681no—
1627C2×C4—5681no—
1628C2×C4—5681no—
1629C2×C4—5681no—
1630C2×C4—5681no—
1631C2×C4—5681no—
1632C2×C4—711no—
1633C2×C4—712no—
1634C2×C4—712no—
1635C2×C4—711no—
1636C2×C4—711no—
1637C2×C4—711no—
1638C2×C4—711no—
1639C2×C4—1422no—
1640C2×C4—1422no—
1641C2×C4—1421no—
1642C2×C4—1421no—
1643C2×C4—1421no—
1644C2×C4—1421no—
1645C2×C4—1421no—
1646C2×C4—1421no—
1647C2×C4—1422no—
1648C2×C4—1421no—
1649C2×C4—1421no—
1650C2×C4—1421no—
1651C2×C4—1421no—
1652C2×C4C2×D4×D7111yescharacteristic
1653C2×C4C2×D4×D7111yescharacteristic
1654C2×C4C2×D4×D7111yescharacteristic
1655C2×C4C2×D4×D7111yescharacteristic
1656C2×C4C24×D7111yescharacteristic
1657C8—21no—
1658C8—21no—
1659C8—21no—
1660C8—712no—
1661C8—1421no—
1662C8—1421no—
1663C8—1421no—
1664C8#41×D7112yes—
1665C22—21no—
1666C22—21no—
1667C22—21no—
1668C22—21no—
1669C22—21no—
1670C22—21no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22—41no—
1677C22—2844no—
1678C22—2841no—
1679C22—2841no—
1680C22—2841no—
1681C22—2841no—
1682C22—2841no—
1683C22—2841no—
1684C22—712no—
1685C22—712no—
1686C22—11362no—
1687C22—11362no—
1688C22—1421no—
1689C22—1421no—
1690C22—1421no—
1691C22—1421no—
1692C22—1421no—
1693C22—1421no—
1694C22—1421no—
1695C22C22×D4×D7111yescharacteristic
1696C4—21no—
1697C4—21no—
1698C4—21no—
1699C4—21no—
1700C4—41no—
1701C4—41no—
1702C4—41no—
1703C4—41no—
1704C4—41no—
1705C4—41no—
1706C4—2841no—
1707C4—2841no—
1708C4—2841no—
1709C4—2841no—
1710C4—2841no—
1711C4—2841no—
1712C4—712no—
1713C4—1421no—
1714C4—1421no—
1715C4—1421no—
1716C4—1421no—
1717C4C2×#41×D7111yescharacteristic
1718C42−1+4×D7111yescharacteristic
1719C2—41no—
1720C2—41no—
1721C2—81no—
1722C2—81no—
1723C2—2841no—
1724C2—5681no—
1725C2—5681no—
1726C2—1422no—
1727C2—1422no—
1728C2#547×D7111yescharacteristic
1729C2#576×D7111yescharacteristic
1730C2#2260311311yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3347C2
socleC22×C71C23×D4
hypercenter#3347D71
hypocenterC71#61262
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3347

Complements

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

NH ≅ G/Ntype
1. #22602074C2semidirect
2. #22602068C2semidirect
3. #22600846C2semidirect
4. #22600842C2semidirect
5. #22600836C2semidirect
6. #22600815C2semidirect
7. #22600811C2semidirect
8. #22600809C2semidirect
9. #22600805C2semidirect
10. #22600758C2semidirect
11. #22600757C2semidirect
12. #22600739C2semidirect
13. #22600736C2semidirect
14. #22600735C2semidirect
15. #22600735C2semidirect
16. #22600686C2semidirect
17. #22600682C2semidirect
18. #22598875C2semidirect
19. #22598295C2semidirect
20. #22598291C2semidirect
21. #22598279C2semidirect
22. #22598279C2semidirect
23. #22598168C2semidirect
24. #22598164C2semidirect
25. #22597986C2semidirect
26. #466×D71C2semidirect
27. #22597189C2semidirect
28. #22597031C2semidirect
29. #22596939C2semidirect
30. #427×D71C2semidirect
31. C71×#3347C2semidirect
35. #17986714C22semidirect
36. #17986713C22semidirect
37. #17986712C22semidirect
38. #17986702C22semidirect
39. #17986699C22semidirect
40. #17986696C22semidirect
41. #17986696C22semidirect
42. #17986695C22semidirect
43. #17986693C22semidirect
44. #17986693C22semidirect
49. #17986654C22semidirect
50. #17986652C22semidirect
51. #17986650C22semidirect
52. #17986649C22semidirect
78. #17986408C22semidirect
79. #17986407C22semidirect
80. #17986406C22semidirect
81. #17986403C22semidirect
82. #17986402C22semidirect
83. #17986399C22semidirect
84. #17986398C22semidirect
85. #17986326C22semidirect
86. #17986326C22semidirect
87. #17986324C22semidirect
88. #17986324C22semidirect
89. #17986324C22semidirect
90. #17986323C22semidirect
91. #17986323C22semidirect
92. #17986323C22semidirect
93. #17986321C22semidirect
94. #17986321C22semidirect
95. #17986320C22semidirect
96. #17986320C22semidirect
97. #17986320C22semidirect
98. #17986319C22semidirect
99. #17986319C22semidirect
100. #17986319C22semidirect
101. #17986317C22semidirect
102. #17986316C22semidirect
103. #17986316C22semidirect
104. #17986316C22semidirect
105. #17986315C22semidirect
106. #17986314C22semidirect
107. #17986314C22semidirect
108. #17986314C22semidirect
109. #17986313C22semidirect
110. #17986311C22semidirect
111. #17986311C22semidirect
112. #17986311C22semidirect
113. #17986302C22semidirect
114. #17986302C22semidirect
115. #17986300C22semidirect
116. #17986299C22semidirect
117. #17986297C22semidirect
118. #17986297C22semidirect
119. #17986296C22semidirect
120. #17986289C22semidirect
121. #17986288C22semidirect
122. #17986287C22semidirect
123. #17986286C22semidirect
124. #17986280C22semidirect
125. #17986278C22semidirect
126. #17986277C22semidirect
127. #17986253C22semidirect
128. #17986252C22semidirect
129. #17986249C22semidirect
134. #17986234C22semidirect
135. #17986234C22semidirect
138. #17986233C22semidirect
139. #17986233C22semidirect
141. #17986112C22semidirect
142. #17986111C22semidirect
143. #17986110C22semidirect
144. C4×#11765850C22semidirect
145. C4×#11765850C22semidirect
146. #17986079C22semidirect
147. #17986079C22semidirect
148. #17986072C22semidirect
149. #17986070C22semidirect
150. #17986068C22semidirect
151. D4×C71⋊C8C22semidirect
152. #17986064C22semidirect
153. (C22⋊D71)⋊C8C22semidirect
154. (C22⋊D71)⋊C8C22semidirect
155. #17986041C22semidirect
158. #17986040C22semidirect
161. #17986038C22semidirect
162. #17986037C22semidirect
165. #17986035C22semidirect
166. #17986035C22semidirect
167. #17986035C22semidirect
170. #17986034C22semidirect
171. C2×#14556061C22semidirect
173. #107×D71C22semidirect
174. #107×D71C22semidirect
175. #107×D71C22semidirect
176. #106×D71C22semidirect
177. #106×D71C22semidirect
188. #555×C71C22semidirect
189. #553×C71C22semidirect
190. #501×C71C22semidirect
191. #482×C71C22semidirect
192. #482×C71C22semidirect
193. #482×C71C22semidirect
194. #480×C71C22semidirect
195. #478×C71C22semidirect
196. #474×C71C22semidirect
197. #469×C71C22semidirect
199. #442×C71C22semidirect
200. #435×C71C22semidirect
201. #428×C71C22semidirect
202. #427×C71C22semidirect
561. C8×D71#41semidirect
871. #3347D71semidirect
897. C71#61262semidirect
904. #555C2×D71semidirect
912. #553C2×D71semidirect
949. #501C2×D71semidirect
967. #482C2×D71semidirect
968. #482C2×D71semidirect
969. #482C2×D71semidirect
985. #480C2×D71semidirect
993. #478C2×D71semidirect
1001. #474C2×D71semidirect
1005. #469C2×D71semidirect
1021. #442C2×D71semidirect
1029. #435C2×D71semidirect
1041. #428C2×D71semidirect
1051. #427C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226020742
#226020682
#226008462
#226008422
#226008362
#226008152
#226008112
#226008092
#226008052
#226007582
#226007572
#226007392
#226007362
#226007352
#226006862
#226006822
#225988752
#225982952
#225982912
#225982792
#225981682
#225981642
#225979862
#466×D712
#225971892
#225970312
#225969392
#427×D712
C71×#33472
#6126271