Finite Group Databasebeta

← #32876307

Subgroups — #32876307

Order 18176.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601899C211yesmaximal, characteristic, complemented
2#555×D71C211yesmaximal, characteristic, complemented
3#22600962C211yesmaximal, characteristic, complemented
4#22600959C211yesmaximal, characteristic, complemented
5#22600933C211yesmaximal, characteristic, complemented
6#22600930C211yesmaximal, characteristic, complemented
7#22600857C211yesmaximal, characteristic, complemented
8#22600855C211yesmaximal, characteristic, complemented
9#22600854C211yesmaximal, characteristic, complemented
10#22600852C211yesmaximal, characteristic, complemented
11#22600847C211yesmaximal, characteristic, complemented
12#22600845C211yesmaximal, characteristic, complemented
13#22600834C211yesmaximal, characteristic, complemented
14#22600759C211yesmaximal, characteristic, complemented
15#22600757C211yesmaximal, characteristic, complemented
16#22600751C211yesmaximal, characteristic, complemented
17#22600749C211yesmaximal, characteristic, complemented
18#22598885C211yesmaximal, characteristic, complemented
19#22598279C211yesmaximal, characteristic, complemented
20#22598275C211yesmaximal, characteristic, complemented
21#22598268C211yesmaximal, characteristic, complemented
22#22598268C211yesmaximal, characteristic, complemented
23#22598148C211yesmaximal, characteristic, complemented
24#22598135C211yesmaximal, characteristic, complemented
25#22597958C211yesmaximal, characteristic, complemented
26#22597956C211yesmaximal, characteristic, complemented
27#22597151C211yesmaximal, characteristic, complemented
28#22597073C211yesmaximal, characteristic, complemented
29#22596928C211yesmaximal, characteristic, complemented
30#22596927C211yesmaximal, characteristic, complemented
31C71×#3347C211yesmaximal, characteristic, complemented
32C2×#14556152C2211yescharacteristic
33C22×#11765848C2211yescharacteristic
34C2×M16×D71C2211yescharacteristic
35#17986717C2211yescharacteristic, complemented
36#17986715C2211yescharacteristic
37#17986714C2211yescharacteristic
38#17986714C2211yescharacteristic
39#17986713—21no—
40#17986713C2211yescharacteristic
41#17986713C2211yescharacteristic
42#17986713C2211yescharacteristic, complemented
43#17986712—21no—
44#17986712C2211yescharacteristic
45#17986712C2211yescharacteristic
46#17986711—21no—
47#17986711—21no—
48#17986704C2211yescharacteristic, complemented
49#17986699C2211yescharacteristic, complemented
50#17986689C2211yescharacteristic, complemented
51#17986687C2211yescharacteristic, complemented
52#17986685—21no—
53#17986678—21no—
54#17986677—21no—
55#17986649C2211yescharacteristic, complemented
56#17986638—21no—
57#17986555C2211yescharacteristic
58C4⋊Q8×D71C2211yescharacteristic
59#17986532—21no—
60#17986530—21no—
61#17986526—21no—
62#124×D71—21no—
63#124×D71—21no—
64#17986509C2211yescharacteristic
65#17986509C2211yescharacteristic
66#121×D71—21no—
67#121×D71C2211yescharacteristic
68#121×D71C2211yescharacteristic
69C4×#11765864—21no—
70C4×#11765864C2211yescharacteristic
71C4×D4×D71C2211yescharacteristic
72C4×D4×D71C2211yescharacteristic
73C2×#14556086C2211yescharacteristic
74#117×D71—21no—
75#117×D71C2211yescharacteristic
76#117×D71C2211yescharacteristic
77#117×D71C2211yescharacteristic
78#17986409C2211yescharacteristic, complemented
79#17986408C2211yescharacteristic, complemented
80#17986405C2211yescharacteristic, complemented
81#17986403C2211yescharacteristic, complemented
82#17986403C2211yescharacteristic, complemented
83#17986396C2211yescharacteristic, complemented
84#17986396C2211yescharacteristic, complemented
85#17986343C2211yescharacteristic, complemented
86#17986343C2211yescharacteristic, complemented
87#17986342C2211yescharacteristic, complemented
88#17986342C2211yescharacteristic, complemented
89#17986341C2211yescharacteristic, complemented
90#17986341C2211yescharacteristic, complemented
91#17986340C2211yescharacteristic, complemented
92#17986340C2211yescharacteristic, complemented
93#17986326C2211yescharacteristic, complemented
94#17986326C2211yescharacteristic, complemented
95#17986324C2211yescharacteristic, complemented
96#17986323C2211yescharacteristic, complemented
97#17986322C2211yescharacteristic, complemented
98#17986322C2211yescharacteristic, complemented
99#17986322C2211yescharacteristic, complemented
100#17986322C2211yescharacteristic, complemented
101#17986321C2211yescharacteristic, complemented
102#17986321C2211yescharacteristic, complemented
103#17986320C2211yescharacteristic, complemented
104#17986320C2211yescharacteristic, complemented
105#17986320C2211yescharacteristic, complemented
106#17986319C2211yescharacteristic, complemented
107#17986318C2211yescharacteristic, complemented
108#17986316C2211yescharacteristic, complemented
109#17986315C2211yescharacteristic, complemented
110#17986314C2211yescharacteristic, complemented
111#17986312C2211yescharacteristic, complemented
112#17986311C2211yescharacteristic, complemented
113#17986300C2211yescharacteristic, complemented
114#17986299C2211yescharacteristic, complemented
115#17986296C2211yescharacteristic, complemented
116#17986293C2211yescharacteristic, complemented
117#17986293C2211yescharacteristic, complemented
118#17986288C2211yescharacteristic, complemented
119#17986287C2211yescharacteristic, complemented
120#17986287C2211yescharacteristic, complemented
121#17986287C2211yescharacteristic, complemented
122#17986285C2211yescharacteristic, complemented
123#17986281C2211yescharacteristic, complemented
124#17986279C2211yescharacteristic, complemented
125#17986278C2211yescharacteristic, complemented
126#17986277C2211yescharacteristic, complemented
127#17986251C2211yescharacteristic, complemented
128#17986250C2211yescharacteristic, complemented
129#17986249C2211yescharacteristic, complemented
130#17986246C2211yescharacteristic, complemented
131#17986245C2211yescharacteristic, complemented
132#17986244C2211yescharacteristic, complemented
133#17986243C2211yescharacteristic, complemented
134#17986234C2211yescharacteristic, complemented
135#17986233C2211yescharacteristic, complemented
136#17986232C2211yescharacteristic, complemented
137#17986229C2211yescharacteristic, complemented
138#17986228C2211yescharacteristic, complemented
139#17986227C2211yescharacteristic, complemented
140#17986226C2211yescharacteristic, complemented
141#17986109C2211yescharacteristic, complemented
142#17986101C2211yescharacteristic, complemented
143#17986099C2211yescharacteristic, complemented
144#17986090C2211yescharacteristic, complemented
145#17986086C2211yescharacteristic, complemented
146D8×Dic71C2211yescharacteristic, complemented
147#17986079C2211yescharacteristic, complemented
148#17986075C2211yescharacteristic, complemented
149#17986074C2211yescharacteristic, complemented
150#17986072C2211yescharacteristic, complemented
151#17986071C2211yescharacteristic, complemented
152#17986069C2211yescharacteristic, complemented
153C8×C22⋊D71C2211yescharacteristic, complemented
154(C22⋊D71)⋊C8C2211yescharacteristic, complemented
155#17986042C2211yescharacteristic, complemented
156#17986041C2211yescharacteristic, complemented
157#17986040C2211yescharacteristic
158#17986040C2211yescharacteristic
159#17986040C2211yescharacteristic
160#17986040C2211yescharacteristic
161#17986040C2211yescharacteristic
162#17986040C2211yescharacteristic, complemented
163#17986040C2211yescharacteristic, complemented
164#17986039C2211yescharacteristic, complemented
165#17986038C2211yescharacteristic
166#17986038C2211yescharacteristic
167#17986038C2211yescharacteristic
168#17986038C2211yescharacteristic
169#17986038C2211yescharacteristic, complemented
170#17986038C2211yescharacteristic, complemented
171#17986037C2211yescharacteristic, complemented
172#17986036C2211yescharacteristic, complemented
173#17986036C2211yescharacteristic, complemented
174#17986035C2211yescharacteristic, complemented
175#17986035C2211yescharacteristic, complemented
176#17986034C2211yescharacteristic, complemented
177#17986034C2211yescharacteristic, complemented
178#17986021C2211yescharacteristic
179#17986002C2211yescharacteristic
180#17986002C2211yescharacteristic
181#17986002C2211yescharacteristic
182#17985997C2211yescharacteristic
183#17985997C2211yescharacteristic
184#17985997C2211yescharacteristic
185#17985961C2211yescharacteristic
186#17985961C2211yescharacteristic
187#17985951C2211yescharacteristic
188#555×C71C2211yescharacteristic
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, complemented
199#442×C71C2211yescharacteristic, complemented
200#435×C71C2211yescharacteristic, complemented
201#428×C71C2211yescharacteristic, complemented
202#427×C71C2211yescharacteristic, complemented
203C2×#11765864—21no—
204C2×#11765864C2311yescharacteristic
205C2×Q8×D71—21no—
206C2×D4×D71—21no—
207C2×D4×D71—21no—
208C2×D4×D71D411yescharacteristic
209C2×D4×D71C2311yescharacteristic
210C22×C4×D71—21no—
211C22×C4×D71C2311yescharacteristic
212C22×C4×D71C2311yescharacteristic
213#14556152—24no—
214C2×#11765854C2311yescharacteristic
215C2×#11765853C2311yescharacteristic
216C2×#11765850C2311yescharacteristic
217C2×#11765849C2311yescharacteristic
218C2×#11765848—24no—
219C2×#11765848C2311yescharacteristic
220C2×#11765848C2311yescharacteristic
221C2×#11765848C2311yescharacteristic
222C2×#11765848C2311yescharacteristic
223C2×#11765848C2311yescharacteristic
224C2×#11765848C2311yescharacteristic
225M16×D71—24no—
226C22×C71⋊C8C2311yescharacteristic
227C2×C8×D71C2311yescharacteristic
228C2×C8×D71C2311yescharacteristic
229#14556128C2311yescharacteristic
230#14556127—21no—
231#14556127C2311yescharacteristic
232#14556127C2311yescharacteristic
233#14556127C2311yescharacteristic
234#14556127C2311yescharacteristic
235#14556126—21no—
236#14556123—21no—
237#14556122—21no—
238#14556121—21no—
239#14556121—21no—
240#14556121—21no—
241#14556120C2311yescharacteristic
242#14556119—21no—
243#14556118—21no—
244#14556118—21no—
245#14556117—21no—
246#14556117—21no—
247#14556116—21no—
248#14556116—21no—
249#14556115—21no—
250#14556115—21no—
251#14556115—21no—
252#14556114—21no—
253#14556114—21no—
254#14556114—21no—
255#14556114—21no—
256#14556114—21no—
257#14556114—21no—
258#14556114—21no—
259#14556114—21no—
260#14556114—21no—
261#14556114—21no—
262#14556113—21no—
263#14556111—21no—
264#14556110—21no—
265#14556110—21no—
266#14556110—21no—
267#14556109—21no—
268#14556109—21no—
269#14556108C2311yescharacteristic
270#14556108C2311yescharacteristic
271#14556107—21no—
272#14556107C2311yescharacteristic
273#14556107C2311yescharacteristic
274#14556106—21no—
275#14556106—21no—
276#14556106—21no—
277#14556105—21no—
278#14556103—21no—
279#14556103C2311yescharacteristic
280#14556103C2311yescharacteristic
281#14556102—21no—
282#14556102C2311yescharacteristic
283#14556102C2311yescharacteristic
284#14556101—21no—
285#14556101—21no—
286#14556101—21no—
287#14556101—21no—
288#14556101—21no—
289#14556100—21no—
290#14556100—21no—
291#14556100—21no—
292#14556100—21no—
293#14556100—21no—
294#14556099—21no—
295#14556099C2311yescharacteristic
296#14556099C2311yescharacteristic
297#14556099C2311yescharacteristic
298#14556099C2311yescharacteristic
299#14556096—21no—
300#14556096—21no—
301C4×Dic142—21no—
302C4×Dic142C2311yescharacteristic
303#14556093—21no—
304#14556093—21no—
305#14556093C2311yescharacteristic
306C4×D284C2311yescharacteristic
307C4×D284C2311yescharacteristic
308D4×Dic71—21no—
309D4×Dic71—21no—
310D4×Dic71D411yescharacteristic
311D4×Dic71C2311yescharacteristic
312D4×Dic71C2311yescharacteristic
313#14556090D411yescharacteristic
314#14556090C2311yescharacteristic
315C4×C22⋊D71—21no—
316C4×C22⋊D71—21no—
317C4×C22⋊D71—21no—
318C4×C22⋊D71—21no—
319C4×C22⋊D71C2311yescharacteristic
320C4×C22⋊D71C2311yescharacteristic
321(C22⋊D71)⋊C4—21no—
322(C22⋊D71)⋊C4—21no—
323(C22⋊D71)⋊C4—21no—
324(C22⋊D71)⋊C4—21no—
325(C22⋊D71)⋊C4D411yescharacteristic
326(C22⋊D71)⋊C4D411yescharacteristic
327#14556087—21no—
328#14556087C2311yescharacteristic
329#14556087C2311yescharacteristic
330#14556087C2311yescharacteristic
331#14556086—21no—
332#14556086—21no—
333#14556086—21no—
334#14556086—21no—
335#14556086—21no—
336#14556086C2311yescharacteristic
337#14556086C2311yescharacteristic
338#14556086C2311yescharacteristic
339#14556086C2311yescharacteristic
340#14556086C2311yescharacteristic
341#14556086C2311yescharacteristic
342#14556086C2311yescharacteristic
343#14556086C2311yescharacteristic
344#14556086C2311yescharacteristic
345#14556085—21no—
346#14556085—21no—
347#14556085—21no—
348#14556085—21no—
349#14556085—21no—
350#14556084—21no—
351#14556084—21no—
352#14556084—21no—
353#14556084—21no—
354#14556084—21no—
355#14556084—21no—
356#14556084—21no—
357#14556084—21no—
358C2×C4⋊Dic71C2311yescharacteristic
359C4⋊C4×D71—21no—
360C4⋊C4×D71D411yescharacteristic
361C4⋊C4×D71C2311yescharacteristic
362C4⋊C4×D71C2311yescharacteristic
363C4⋊C4×D71C2311yescharacteristic
364C4⋊C4×D71C2311yescharacteristic
365C4⋊C4×D71C2311yescharacteristic
366C2×(C2×D71)⋊C4—21no—
367C22⋊C4×D71—21no—
368C22⋊C4×D71—21no—
369C22⋊C4×D71—21no—
370C22⋊C4×D71—21no—
371C22⋊C4×D71—21no—
372C22⋊C4×D71—21no—
373C22⋊C4×D71D411yescharacteristic
374C22⋊C4×D71D411yescharacteristic
375C2×C4×Dic71—21no—
376C2×C4×Dic71—21no—
377C42×D71—21no—
378C42×D71—21no—
379C42×D71—21no—
380C42×D71C2311yescharacteristic
381#14556062C2311yescharacteristic
382#14556062C2311yescharacteristic
383#14556062C2311yescharacteristic
384#14556062C2311yescharacteristic
385#14556061C2311yescharacteristic
386#14556061C2311yescharacteristic
387#14556061C2311yescharacteristic
388#14556061C2311yescharacteristic
389#14556061C2311yescharacteristic
390#14556061C2311yescharacteristic
391#14556061C2311yescharacteristic
392#14556061C2311yescharacteristic
393#14556061C2311yescharacteristic
394#14556060C2311yescharacteristic
395#14556060C2311yescharacteristic
396#14556060C2311yescharacteristic
397#14556060C2311yescharacteristic
398#14556060C2311yescharacteristic
399#14556059C2311yescharacteristic
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#14556053C2311yescharacteristic
412#14556053C2311yescharacteristic
413#14556053C2311yescharacteristic
414#14556051C2311yescharacteristic
415#14556051C2311yescharacteristic
416#14556051C2311yescharacteristic
417#14556050C2311yescharacteristic
418#14556050C2311yescharacteristic
419#14556050C2311yescharacteristic
420#14556049C2311yescharacteristic
421#14556049C2311yescharacteristic
422#14556049C2311yescharacteristic
423#14556049C2311yescharacteristic
424#14556049C2311yescharacteristic
425#14556049C2311yescharacteristic
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#14556039C2311yescharacteristic
436C8×Dic71C2311yescharacteristic
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×D71C2×D411yescharacteristic
483C23×D71C2×D411yescharacteristic
484#11765864—22no—
485#11765864—22no—
486#11765864—44no—
487C2×Dic142—21no—
488C2×Dic142—21no—
489C2×Dic142—21no—
490C2×Dic142—21no—
491C2×Dic142—21no—
492C2×Dic142C2411yescharacteristic
493Q8×D71—82no—
494C2×D284—21no—
495C2×D284—21no—
496C2×D284C2×D411yescharacteristic
497C2×D284C2411yescharacteristic
498C2×C22⋊D71—21no—
499C2×C22⋊D71—21no—
500C2×C22⋊D71—21no—
501C2×C22⋊D71—21no—
502C2×C22⋊D71—21no—
503C2×C22⋊D71—21no—
504C2×C22⋊D71—21no—
505C2×C22⋊D71—21no—
506C2×C22⋊D71C2×D411yescharacteristic
507C2×C22⋊D71C2×D411yescharacteristic
508D4×D71—22no—
509D4×D71—22no—
510D4×D71—42no—
511D4×D71—82no—
512D4×D71—82no—
513C22×Dic71—21no—
514C22×Dic71—21no—
515C22×Dic71—21no—
516C22×Dic71—21no—
517C22×Dic71C2×D411yescharacteristic
518C22×Dic71C2×D411yescharacteristic
519C2×C4×D71—22no—
520C2×C4×D71—22no—
521C2×C4×D71—22no—
522C2×C4×D71—22no—
523C2×C4×D71—21no—
524C2×C4×D71—21no—
525C2×C4×D71—21no—
526C2×C4×D71—21no—
527C2×C4×D71—21no—
528C2×C4×D71—21no—
529C2×C4×D71—21no—
530C2×C4×D71—44no—
531C2×C4×D71C2×D411yescharacteristic
532C2×C4×D71C2×D411yescharacteristic
533C2×C4×D71C2×D411yescharacteristic
534C2×C4×D71C2×D411yescharacteristic
535C2×C4×D71C2×D411yescharacteristic
536C2×C4×D71C2×D411yescharacteristic
537C2×C4×D71C2411yescharacteristic
538C2×C4×D71C2411yescharacteristic
539C2×C4×D71C2411yescharacteristic
540#11765854—22no—
541#11765853—22no—
542#11765850—22no—
543#11765849—22no—
544#11765848—22no—
545#11765848—22no—
546#11765848—22no—
547#11765848—22no—
548#11765848—22no—
549#11765848#4114yescomplemented
550C2×C71⋊C8—22no—
551C2×C71⋊C8C2411yescharacteristic
552C2×C71⋊C8C2411yescharacteristic
553C2×C71⋊C8C2411yescharacteristic
554C2×C71⋊C8C2411yescharacteristic
555C8×D71—22no—
556C8×D71—22no—
557C4⋊Dic71—21no—
558C4⋊Dic71—21no—
559C4⋊Dic71—21no—
560C4⋊Dic71—21no—
561C4⋊Dic71C2×D411yescharacteristic
562C4⋊Dic71C2411yescharacteristic
563C4⋊Dic71C2411yescharacteristic
564C4⋊Dic71C2411yescharacteristic
565C4⋊Dic71C2411yescharacteristic
566C4⋊Dic71C2411yescharacteristic
567C4⋊Dic71C2411yescharacteristic
568Dic71⋊C4—21no—
569Dic71⋊C4—21no—
570Dic71⋊C4—21no—
571Dic71⋊C4—21no—
572Dic71⋊C4—21no—
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⋊C4C2×D411yescharacteristic
584Dic71⋊C4C2×D411yescharacteristic
585C22⋊Dic71—21no—
586C22⋊Dic71—21no—
587C22⋊Dic71—21no—
588C22⋊Dic71—21no—
589C22⋊Dic71—21no—
590C22⋊Dic71—21no—
591C22⋊Dic71—21no—
592C22⋊Dic71—21no—
593C22⋊Dic71—21no—
594C22⋊Dic71—21no—
595C22⋊Dic71—21no—
596C22⋊Dic71C2×D411yescharacteristic
597C22⋊Dic71C2×D411yescharacteristic
598(C2×D71)⋊C4—21no—
599(C2×D71)⋊C4—21no—
600(C2×D71)⋊C4—21no—
601(C2×D71)⋊C4—21no—
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)⋊C4C2×D411yescharacteristic
616(C2×D71)⋊C4C2×D411yescharacteristic
617(C2×D71)⋊C4C2×D411yescharacteristic
618(C2×D71)⋊C4C2×D411yescharacteristic
619C4×Dic71—21no—
620C4×Dic71—21no—
621C4×Dic71—21no—
622C4×Dic71—21no—
623C4×Dic71—21no—
624C4×Dic71—21no—
625C4×Dic71—21no—
626C4×Dic71—21no—
627C4×Dic71—21no—
628C4×Dic71—21no—
629C4×Dic71—21no—
630C4×Dic71—21no—
631C4×Dic71—21no—
632C4×Dic71—21no—
633C4×Dic71C2×D411yescharacteristic
634C4×Dic71C2×D411yescharacteristic
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—41no—
690C22×D71—41no—
691C22×D71—41no—
692C22×D71—41no—
693C22×D71—42no—
694C22×D71—42no—
695C22×D71—42no—
696C22×D71C22×D411yescharacteristic
697C22×D71C22×D411yescharacteristic
698C22×D71C22×D411yescharacteristic
699Q8×C71—81no—
700D4×C71—21no—
701D4×C71—21no—
702D4×C71—21no—
703D4×C71—21no—
704D4×C71—41no—
705D4×C71—42no—
706D4×C71—81no—
707D4×C71—81no—
708D4×C71—81no—
709C2×C4×C71—21no—
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—42no—
720C2×C4×C71—81no—
721C2×C4×C71—81no—
722C2×C4×C71C22×D411yescharacteristic
723C2×C4×C71C22×D411yescharacteristic
724C2×C4×C71C22×D411yescharacteristic
725C2×C4×C71C22×D411yescharacteristic
726C2×C4×C71C2511yescharacteristic
727C22⋊D71—22no—
728C22⋊D71—22no—
729C22⋊D71—42no—
730C22⋊D71—42no—
731C22⋊D71—42no—
732C22⋊D71—81no—
733C22⋊D71—81no—
734C22⋊D71—81no—
735C22⋊D71—81no—
736C22⋊D71—81no—
737C2×Dic71—22no—
738C2×Dic71—22no—
739C2×Dic71—21no—
740C2×Dic71—21no—
741C2×Dic71—21no—
742C2×Dic71—21no—
743C2×Dic71—21no—
744C2×Dic71—21no—
745C2×Dic71—21no—
746C2×Dic71—42no—
747C2×Dic71—42no—
748C2×Dic71—42no—
749C2×Dic71—42no—
750C2×Dic71C22×D411yescharacteristic
751C2×Dic71C22×D411yescharacteristic
752C2×Dic71C22×D411yescharacteristic
753C2×Dic71C22×D411yescharacteristic
754C2×Dic71C22×D411yescharacteristic
755D284—21no—
756D284—21no—
757D284—41no—
758D284—81no—
759D284—81no—
760C4×D71—22no—
761C4×D71—22no—
762C4×D71—21no—
763C4×D71—21no—
764C4×D71—21no—
765C4×D71—21no—
766C4×D71—22no—
767C4×D71—22no—
768C4×D71—22no—
769C4×D71—41no—
770C4×D71—42no—
771C4×D71—42no—
772C4×D71—42no—
773C4×D71—42no—
774C4×D71—42no—
775C4×D71—42no—
776C4×D71—81no—
777C4×D71C2×#4112yes—
778C4×D712−1+412yes—
779Dic142—21no—
780Dic142—21no—
781Dic142—42no—
782Dic142—81no—
783Dic142—81no—
784Dic142—81no—
785Dic142—81no—
786C8×C71—21no—
787C8×C71—21no—
788C8×C71—21no—
789C8×C71C2×#4112yes—
790C71⋊C8—21no—
791C71⋊C8—21no—
792C71⋊C8—21no—
793C71⋊C8C2×#4112yes—
794C22×C71—21no—
795C22×C71—21no—
796C22×C71—21no—
797C22×C71—21no—
798C22×C71—21no—
799C22×C71—21no—
800C22×C71—41no—
801C22×C71—41no—
802C22×C71—41no—
803C22×C71—41no—
804C22×C71—41no—
805C22×C71—41no—
806C22×C71C23×D411yescharacteristic
807C2×D71—21no—
808C2×D71—21no—
809C2×D71—21no—
810C2×D71—21no—
811C2×D71—21no—
812C2×D71—21no—
813C2×D71—21no—
814C2×D71—21no—
815C2×D71—41no—
816C2×D71—41no—
817C2×D71—41no—
818C2×D71—82no—
819C2×D71—82no—
820C2×D71—84no—
821C2×D71#54712yes—
822C4×C71—21no—
823C4×C71—21no—
824C4×C71—21no—
825C4×C71—21no—
826C4×C71—41no—
827C4×C71—41no—
828C4×C71—41no—
829C4×C71—41no—
830C4×C71—41no—
831C4×C71—41no—
832C4×C71C22×#4111yescharacteristic
833C4×C71C2×2−1+411yescharacteristic
834Dic71—21no—
835Dic71—21no—
836Dic71—21no—
837Dic71—41no—
838Dic71—41no—
839Dic71—41no—
840Dic71—41no—
841Dic71—41no—
842Dic71—41no—
843Dic71—41no—
844Dic71#54712yes—
845Dic71#57512yes—
846#61256—711nomaximal, Sylow
847C2×C71—41no—
848C2×C71—41no—
849C2×C71—81no—
850C2×C71—81no—
851C2×C71C2×#54711yescharacteristic
852C2×C71C2×#57511yescharacteristic
853C2×C71#358511yescharacteristic
854D71—22no—
855D71—41no—
856D71—41no—
857D71—81no—
858#3475—711no—
859C2×#555—711no—
860#3357—711no—
861#3357—711no—
862#3354—711no—
863#3354—711no—
864#3348—711no—
865#3348—711no—
866#3348—711no—
867#3348—711no—
868#3347—711no—
869#3347—711no—
870#3347—711no—
871#3347D7111yescharacteristic, complemented
872#3341—711no—
873#3341—711no—
874#3340—711no—
875#3340—711no—
876#3165—711no—
877#3094—711no—
878#3094—711no—
879#3093—711no—
880#3093—711no—
881#3079—711no—
882#3077—711no—
883#3055—711no—
884#3055—711no—
885C4×AGL(1,ℤ/8)—711no—
886D4×M16—711no—
887#2911—711no—
888#2911—711no—
889C71#6125611yescharacteristic, complemented, Sylow
890C2×AGL(1,ℤ/8)—711no—
891C22×M16—711no—
892C22×M16—711no—
893#556—711no—
894#555—711no—
895#555—711no—
896#555—711no—
897#555—711no—
898#555—711no—
899#555—711no—
900#555—711no—
901#555—711no—
902#555—1421no—
903#555—1421no—
904#555—1421no—
905#555—1421no—
906#555C2×D7111yescharacteristic
907#554—711no—
908#553—711no—
909#553C2×D7111yescharacteristic, complemented
910#552—711no—
911#552—711no—
912#552—1421no—
913#551—1421no—
914#551—1421no—
915#547—711no—
916#546—1421no—
917#533—711no—
918C2×C4⋊Q8—711no—
919#529—1421no—
920#529—1421no—
921#529—1421no—
922C2×#124—1421no—
923C2×#124—1421no—
924#525—711no—
925#525—711no—
926C2×#121—711no—
927C2×#121—711no—
928C2×#121—1421no—
929C4×#41—711no—
930C4×#41—1421no—
931C2×C4×D4—711no—
932C2×C4×D4—711no—
933C2×#117—711no—
934C2×#117—711no—
935C2×#117—711no—
936C2×#117—711no—
937C2×#117—1421no—
938#501—711no—
939#501—711no—
940#501—711no—
941#501C2×D7111yescharacteristic, complemented
942#500—711no—
943#500—711no—
944#498—711no—
945#498—711no—
946#485—711no—
947#485—711no—
948#485—711no—
949#485—711no—
950#485—711no—
951#485—711no—
952#485—711no—
953#485—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#480—711no—
975#480—711no—
976#480—711no—
977#480C2×D7111yescharacteristic, complemented
978#478—711no—
979#478—711no—
980#478—711no—
981#478C2×D7111yescharacteristic, complemented
982#477—711no—
983#477—711no—
984#476—711no—
985#476—711no—
986#476—711no—
987#476—711no—
988#475—711no—
989#475—711no—
990#474—711no—
991#474—711no—
992#474—711no—
993#474C2×D7111yescharacteristic, complemented
994#469—711no—
995#469—711no—
996#469—711no—
997#469C2×D7111yescharacteristic, complemented
998#468—711no—
999#468—711no—
1000#468—711no—
1001#468—711no—
1002#466—711no—
1003#466—711no—
1004#466—711no—
1005#466C2×D7111yescharacteristic, complemented
1006#465—711no—
1007#465—711no—
1008#465—711no—
1009#465—711no—
1010#442—711no—
1011#442C2×D7111yescharacteristic, complemented
1012#440—711no—
1013#440—711no—
1014C4×SD16—711no—
1015C4×SD16—711no—
1016C4×D8—711no—
1017C4×D8—711no—
1018#436—711no—
1019#436—711no—
1020#435—711no—
1021#435—711no—
1022#435—711no—
1023#435C2×D7111yescharacteristic, complemented
1024C8×D4—711no—
1025C8×D4—711no—
1026#428—711no—
1027#428—711no—
1028#428—711no—
1029#428—711no—
1030#428—711no—
1031#428—711no—
1032#428—711no—
1033#428—711no—
1034#428—711no—
1035#428—711no—
1036#428—711no—
1037#428—711no—
1038#428—711no—
1039#428—711no—
1040#428—711no—
1041#428—711no—
1042#428C2×D7111yescharacteristic, complemented
1043#427—711no—
1044#427—711no—
1045#427—711no—
1046#427—711no—
1047#427—711no—
1048#427—711no—
1049#427—711no—
1050#427C2×D7111yescharacteristic, complemented
1051#423—711no—
1052#418—711no—
1053#418—711no—
1054#418—711no—
1055#417—711no—
1056#417—711no—
1057#417—711no—
1058#407—711no—
1059#407—711no—
1060C4×M16—711no—
1061C2×#41—711no—
1062C2×#41—1421no—
1063C22×Q8—1421no—
1064C22×D4—711no—
1065C22×D4—711no—
1066C22×D4—1421no—
1067C22×D4—1421no—
1068C23×C4—711no—
1069C23×C4—711no—
1070C23×C4—1421no—
1071AGL(1,ℤ/8)—1424no—
1072C2×SD16—711no—
1073C2×SD16—711no—
1074C2×D8—711no—
1075C2×D8C22×D7111yescharacteristic
1076C2×M16—711no—
1077C2×M16—711no—
1078C2×M16—711no—
1079C2×M16—711no—
1080C2×M16—711no—
1081C2×M16—711no—
1082C2×M16—711no—
1083C2×M16—1424no—
1084C2×M16—1424no—
1085C2×M16C22×D7111yescharacteristic
1086C22×C8—711no—
1087C22×C8—711no—
1088C22×C8—711no—
1089C22×C8C22×D7111yescharacteristic
1090C4⋊Q8—711no—
1091C4⋊Q8—711no—
1092C4⋊Q8—711no—
1093C4⋊Q8—711no—
1094C4⋊Q8—711no—
1095C4⋊Q8—1421no—
1096C4⋊Q8—1421no—
1097C4⋊Q8C22×D7111yescharacteristic
1098#126—21no—
1099#126—1421no—
1100#126—1421no—
1101#126—1421no—
1102#126—1421no—
1103#126—1421no—
1104#125—711no—
1105#125—1421no—
1106#125—1421no—
1107#125—1421no—
1108#125C22×D7111yescharacteristic
1109#124—21no—
1110#124—21no—
1111#124—1421no—
1112#124—1421no—
1113#124—1421no—
1114#124—1421no—
1115#124—1421no—
1116#124—1421no—
1117#124—1421no—
1118#124—1421no—
1119#124—1421no—
1120#124—1421no—
1121#124—1421no—
1122#124—1421no—
1123#124—1421no—
1124#124—1421no—
1125#124—1421no—
1126#124—1421no—
1127#124—1421no—
1128#123—21no—
1129#123—1421no—
1130#123—1421no—
1131#123—1421no—
1132#123—1421no—
1133#123—1421no—
1134#123—1421no—
1135#123—1421no—
1136C22⋊Q8—711no—
1137C22⋊Q8—711no—
1138C22⋊Q8—711no—
1139C22⋊Q8—711no—
1140C22⋊Q8—1421no—
1141C22⋊Q8—1421no—
1142C22⋊Q8—1421no—
1143C22⋊Q8—1421no—
1144C22⋊Q8—1421no—
1145#121—21no—
1146#121—21no—
1147#121—711no—
1148#121—711no—
1149#121—711no—
1150#121—711no—
1151#121—711no—
1152#121—711no—
1153#121—711no—
1154#121—711no—
1155#121—1421no—
1156#121—1421no—
1157#121—1421no—
1158#121—1421no—
1159#121—1421no—
1160#121—1421no—
1161#121—1421no—
1162#121—1421no—
1163#121—1421no—
1164#121—1421no—
1165#121—1421no—
1166#121—1421no—
1167#121—1421no—
1168#121C22×D7111yescharacteristic
1169#121C22×D7111yescharacteristic
1170#121C22×D7111yescharacteristic
1171#121C22×D7111yescharacteristic
1172#120—1421no—
1173#120—1421no—
1174C4×Q8—711no—
1175C4×Q8—711no—
1176C4×Q8—1421no—
1177C4×Q8—1421no—
1178C4×Q8—1421no—
1179C4×D4—21no—
1180C4×D4—711no—
1181C4×D4—711no—
1182C4×D4—711no—
1183C4×D4—711no—
1184C4×D4—711no—
1185C4×D4—711no—
1186C4×D4—711no—
1187C4×D4—711no—
1188C4×D4—711no—
1189C4×D4—711no—
1190C4×D4—711no—
1191C4×D4—1421no—
1192C4×D4—1421no—
1193C4×D4—1421no—
1194C4×D4—1421no—
1195C4×D4—1421no—
1196C4×D4—1421no—
1197C4×D4—1421no—
1198C4×D4—1421no—
1199C4×D4—1421no—
1200C4×D4—1421no—
1201C4×D4C22×D7111yescharacteristic
1202C4×D4C22×D7111yescharacteristic
1203C4×D4C22×D7111yescharacteristic
1204#117—21no—
1205#117—711no—
1206#117—711no—
1207#117—711no—
1208#117—711no—
1209#117—711no—
1210#117—711no—
1211#117—711no—
1212#117—711no—
1213#117—711no—
1214#117—711no—
1215#117—711no—
1216#117—711no—
1217#117—1421no—
1218#117—1421no—
1219#117—1421no—
1220#117—1421no—
1221#117—1421no—
1222#117—1421no—
1223#117—1421no—
1224#117—1421no—
1225#117—1421no—
1226#117—1421no—
1227#117—1421no—
1228#117—1421no—
1229#117—1421no—
1230#117—1421no—
1231#117—1421no—
1232#117—1421no—
1233#117—1421no—
1234#117—1421no—
1235#117—1421no—
1236#117C22×D7111yescharacteristic
1237#117C22×D7111yescharacteristic
1238#117C22×D7111yescharacteristic
1239C2×C4⋊C4—711no—
1240C2×C4⋊C4—711no—
1241C2×C4⋊C4—711no—
1242C2×C4⋊C4—711no—
1243C2×C4⋊C4—711no—
1244C2×C4⋊C4—711no—
1245C2×C4⋊C4—711no—
1246C2×C4⋊C4—1421no—
1247C2×C4⋊C4C22×D7111yescharacteristic
1248C2×C22⋊C4—711no—
1249C2×C22⋊C4—711no—
1250C2×C22⋊C4—1421no—
1251C2×C22⋊C4—1421no—
1252C2×C22⋊C4—1421no—
1253C2×C22⋊C4—1421no—
1254C2×C22⋊C4—1421no—
1255C2×C22⋊C4—1421no—
1256C2×C22⋊C4—1421no—
1257C2×C42—711no—
1258C2×C42—1421no—
1259C2×C42—1421no—
1260C2×C42—1421no—
1261C2×C42—1421no—
1262C2×C42—1421no—
1263#107—711no—
1264#107—711no—
1265#107—711no—
1266#107—711no—
1267#107—711no—
1268#107—711no—
1269#107—711no—
1270#107—711no—
1271#107—711no—
1272#107—711no—
1273#107—711no—
1274#107—711no—
1275#107—711no—
1276#107C22×D7111yescharacteristic
1277#107C22×D7111yescharacteristic
1278#107C22×D7111yescharacteristic
1279#107C22×D7111yescharacteristic
1280#107C22×D7111yescharacteristic
1281#106—711no—
1282#106—711no—
1283#106—711no—
1284#106—711no—
1285#106—711no—
1286#106—711no—
1287#106—711no—
1288#106—711no—
1289#106—711no—
1290#106—711no—
1291#106—711no—
1292#106—711no—
1293#106—711no—
1294#106—711no—
1295#106C22×D7111yescharacteristic
1296#106C22×D7111yescharacteristic
1297#106C22×D7111yescharacteristic
1298#106C22×D7111yescharacteristic
1299C4⋊C8—711no—
1300C4⋊C8—711no—
1301C4⋊C8—711no—
1302C4⋊C8C22×D7111yescharacteristic
1303#103—711no—
1304#103—711no—
1305#103—711no—
1306#103—711no—
1307#103—711no—
1308#103—711no—
1309#102—711no—
1310#102—711no—
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#102C22×D7111yescharacteristic
1322#102C22×D7111yescharacteristic
1323#102C22×D7111yescharacteristic
1324#102C22×D7111yescharacteristic
1325#102C22×D7111yescharacteristic
1326#102C22×D7111yescharacteristic
1327C22⋊C8—711no—
1328C22⋊C8—711no—
1329C22⋊C8—711no—
1330C22⋊C8—711no—
1331C22⋊C8—711no—
1332C22⋊C8—711no—
1333C22⋊C8C22×D7111yescharacteristic
1334C22⋊C8C22×D7111yescharacteristic
1335#97—711no—
1336#97C22×D7111yescharacteristic
1337C4×C8—711no—
1338C4×C8—711no—
1339C24—711no—
1340C24—711no—
1341C24—1421no—
1342#41—2844no—
1343#41—1422no—
1344#41—1422no—
1345C2×Q8—21no—
1346C2×Q8—5682no—
1347C2×Q8—711no—
1348C2×Q8—1421no—
1349C2×Q8—1421no—
1350C2×Q8—1421no—
1351C2×Q8—1421no—
1352C2×Q8—1421no—
1353C2×D4—21no—
1354C2×D4—21no—
1355C2×D4—21no—
1356C2×D4—21no—
1357C2×D4—2842no—
1358C2×D4—5682no—
1359C2×D4—5682no—
1360C2×D4—711no—
1361C2×D4—711no—
1362C2×D4—711no—
1363C2×D4—711no—
1364C2×D4—1421no—
1365C2×D4—1421no—
1366C2×D4—1422no—
1367C2×D4—1422no—
1368C2×D4—1421no—
1369C2×D4—1421no—
1370C2×D4—1421no—
1371C2×D4—1421no—
1372C2×D4—1421no—
1373C2×D4—1421no—
1374C2×D4—1421no—
1375C2×D4—1421no—
1376C2×D4D4×D7111yescharacteristic
1377C2×D4C23×D7111yescharacteristic
1378C2×D4C23×D7111yescharacteristic
1379C22×C4—21no—
1380C22×C4—21no—
1381C22×C4—21no—
1382C22×C4—2844no—
1383C22×C4—711no—
1384C22×C4—711no—
1385C22×C4—711no—
1386C22×C4—711no—
1387C22×C4—711no—
1388C22×C4—711no—
1389C22×C4—711no—
1390C22×C4—711no—
1391C22×C4—711no—
1392C22×C4—711no—
1393C22×C4—711no—
1394C22×C4—1421no—
1395C22×C4—1421no—
1396C22×C4—1421no—
1397C22×C4—1421no—
1398C22×C4—1421no—
1399C22×C4—1421no—
1400C22×C4—1422no—
1401C22×C4—1422no—
1402C22×C4—1422no—
1403C22×C4—1422no—
1404C22×C4—1421no—
1405C22×C4—1421no—
1406C22×C4—1421no—
1407C22×C4—1421no—
1408C22×C4—1421no—
1409C22×C4C23×D7111yescharacteristic
1410C22×C4C23×D7111yescharacteristic
1411SD16—1422no—
1412SD16—1422no—
1413D8—22no—
1414D8—1422no—
1415M16—22no—
1416M16—714no—
1417M16—1422no—
1418M16—1422no—
1419M16—1422no—
1420M16—1422no—
1421M16—1422no—
1422M16—1422no—
1423C2×C8—22no—
1424C2×C8—711no—
1425C2×C8—711no—
1426C2×C8—711no—
1427C2×C8—711no—
1428C2×C8—1422no—
1429C2×C8—1422no—
1430C2×C8—1422no—
1431C2×C8C23×D7111yescharacteristic
1432C2×C8C23×D7111yescharacteristic
1433C2×C8C23×D7111yescharacteristic
1434C2×C8C23×D7111yescharacteristic
1435C4⋊C4—21no—
1436C4⋊C4—21no—
1437C4⋊C4—21no—
1438C4⋊C4—21no—
1439C4⋊C4—711no—
1440C4⋊C4—711no—
1441C4⋊C4—711no—
1442C4⋊C4—711no—
1443C4⋊C4—711no—
1444C4⋊C4—711no—
1445C4⋊C4—711no—
1446C4⋊C4—711no—
1447C4⋊C4—711no—
1448C4⋊C4—1421no—
1449C4⋊C4—1421no—
1450C4⋊C4—1421no—
1451C4⋊C4—1421no—
1452C4⋊C4—1421no—
1453C4⋊C4—1421no—
1454C4⋊C4—1421no—
1455C4⋊C4—1421no—
1456C4⋊C4—1421no—
1457C4⋊C4—1421no—
1458C4⋊C4—1421no—
1459C4⋊C4—1421no—
1460C4⋊C4—1421no—
1461C4⋊C4—1421no—
1462C4⋊C4—1421no—
1463C4⋊C4—1421no—
1464C4⋊C4—1421no—
1465C4⋊C4—1421no—
1466C4⋊C4—1421no—
1467C4⋊C4D4×D7111yescharacteristic
1468C4⋊C4C23×D7111yescharacteristic
1469C4⋊C4C23×D7111yescharacteristic
1470C4⋊C4C23×D7111yescharacteristic
1471C4⋊C4C23×D7111yescharacteristic
1472C4⋊C4C23×D7111yescharacteristic
1473C4⋊C4C23×D7111yescharacteristic
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—21no—
1479C22⋊C4—21no—
1480C22⋊C4—21no—
1481C22⋊C4—21no—
1482C22⋊C4—21no—
1483C22⋊C4—711no—
1484C22⋊C4—711no—
1485C22⋊C4—711no—
1486C22⋊C4—711no—
1487C22⋊C4—711no—
1488C22⋊C4—711no—
1489C22⋊C4—1421no—
1490C22⋊C4—1421no—
1491C22⋊C4—1421no—
1492C22⋊C4—1421no—
1493C22⋊C4—1421no—
1494C22⋊C4—1421no—
1495C22⋊C4—1421no—
1496C22⋊C4—1421no—
1497C22⋊C4—1421no—
1498C22⋊C4—1421no—
1499C22⋊C4—1421no—
1500C22⋊C4—1421no—
1501C22⋊C4—1421no—
1502C22⋊C4—1421no—
1503C22⋊C4—1421no—
1504C22⋊C4—1421no—
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⋊C4D4×D7111yescharacteristic
1518C22⋊C4D4×D7111yescharacteristic
1519C42—21no—
1520C42—21no—
1521C42—21no—
1522C42—711no—
1523C42—711no—
1524C42—711no—
1525C42—1421no—
1526C42—1421no—
1527C42—1421no—
1528C42—1421no—
1529C42—1421no—
1530C42—1421no—
1531C42—1421no—
1532C42—1421no—
1533C42—1421no—
1534C42—1421no—
1535C42—1421no—
1536C42—1421no—
1537C42—1421no—
1538C42—1421no—
1539C42C23×D7111yescharacteristic
1540C23—21no—
1541C23—21no—
1542C23—2841no—
1543C23—2841no—
1544C23—2841no—
1545C23—2841no—
1546C23—2842no—
1547C23—2842no—
1548C23—2842no—
1549C23—711no—
1550C23—711no—
1551C23—711no—
1552C23—1422no—
1553C23—1422no—
1554C23—1421no—
1555C23C2×D4×D7111yescharacteristic
1556C23C2×D4×D7111yescharacteristic
1557Q8—81no—
1558Q8—2842no—
1559Q8—5681no—
1560Q8—5681no—
1561Q8—5681no—
1562Q8—5681no—
1563Q8—1421no—
1564Q8—1421no—
1565D4—21no—
1566D4—21no—
1567D4—21no—
1568D4—21no—
1569D4—41no—
1570D4—42no—
1571D4—81no—
1572D4—81no—
1573D4—81no—
1574D4—2841no—
1575D4—2842no—
1576D4—2842no—
1577D4—2842no—
1578D4—5681no—
1579D4—5681no—
1580D4—5681no—
1581D4—5681no—
1582D4—5681no—
1583D4—5681no—
1584D4—5681no—
1585D4—1422no—
1586D4—1422no—
1587D4—1421no—
1588D4—1421no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—42no—
1600C2×C4—81no—
1601C2×C4—81no—
1602C2×C4—2842no—
1603C2×C4—2841no—
1604C2×C4—2842no—
1605C2×C4—2842no—
1606C2×C4—2842no—
1607C2×C4—2842no—
1608C2×C4—2842no—
1609C2×C4—2842no—
1610C2×C4—2842no—
1611C2×C4—2842no—
1612C2×C4—2842no—
1613C2×C4—5681no—
1614C2×C4—711no—
1615C2×C4—711no—
1616C2×C4—712no—
1617C2×C4—712no—
1618C2×C4—711no—
1619C2×C4—711no—
1620C2×C4—711no—
1621C2×C4—1422no—
1622C2×C4—1422no—
1623C2×C4—1422no—
1624C2×C4—1422no—
1625C2×C4—1422no—
1626C2×C4—1421no—
1627C2×C4—1421no—
1628C2×C4—1421no—
1629C2×C4—1421no—
1630C2×C4—1421no—
1631C2×C4—1421no—
1632C2×C4—1421no—
1633C2×C4—1422no—
1634C2×C4—1422no—
1635C2×C4—1421no—
1636C2×C4—1421no—
1637C2×C4—1421no—
1638C2×C4—1421no—
1639C2×C4C2×D4×D7111yescharacteristic
1640C2×C4C2×D4×D7111yescharacteristic
1641C2×C4C2×D4×D7111yescharacteristic
1642C2×C4C2×D4×D7111yescharacteristic
1643C2×C4C24×D7111yescharacteristic
1644C8—21no—
1645C8—21no—
1646C8—21no—
1647C8—712no—
1648C8—1421no—
1649C8—1421no—
1650C8—1421no—
1651C8#41×D7112yes—
1652C22—21no—
1653C22—21no—
1654C22—21no—
1655C22—21no—
1656C22—21no—
1657C22—21no—
1658C22—41no—
1659C22—41no—
1660C22—41no—
1661C22—41no—
1662C22—41no—
1663C22—41no—
1664C22—2841no—
1665C22—2841no—
1666C22—2841no—
1667C22—5682no—
1668C22—5682no—
1669C22—5684no—
1670C22—712no—
1671C22—1421no—
1672C22—1421no—
1673C22—1421no—
1674C22—1421no—
1675C22—1421no—
1676C22—1421no—
1677C22—1421no—
1678C22—1421no—
1679C22C22×D4×D7111yescharacteristic
1680C4—21no—
1681C4—21no—
1682C4—21no—
1683C4—21no—
1684C4—41no—
1685C4—41no—
1686C4—41no—
1687C4—41no—
1688C4—41no—
1689C4—41no—
1690C4—2841no—
1691C4—2841no—
1692C4—2841no—
1693C4—2841no—
1694C4—2841no—
1695C4—2841no—
1696C4—2841no—
1697C4—712no—
1698C4—712no—
1699C4—1421no—
1700C4—1421no—
1701C4—1421no—
1702C4C2×#41×D7111yescharacteristic
1703C42−1+4×D7111yescharacteristic
1704C2—41no—
1705C2—41no—
1706C2—81no—
1707C2—81no—
1708C2—2841no—
1709C2—2841no—
1710C2—5681no—
1711C2—1422no—
1712C2#547×D7111yescharacteristic
1713C2#575×D7111yescharacteristic
1714C2#2260311511yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3347C2
socleC22×C71C23×D4
hypercenter#3347D71
hypocenterC71#61256
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. #22601899C2semidirect
2. #555×D71C2semidirect
3. #22600962C2semidirect
4. #22600959C2semidirect
5. #22600933C2semidirect
6. #22600930C2semidirect
7. #22600857C2semidirect
8. #22600855C2semidirect
9. #22600854C2semidirect
10. #22600852C2semidirect
11. #22600847C2semidirect
12. #22600845C2semidirect
13. #22600834C2semidirect
14. #22600759C2semidirect
15. #22600757C2semidirect
16. #22600751C2semidirect
17. #22600749C2semidirect
18. #22598885C2semidirect
19. #22598279C2semidirect
20. #22598275C2semidirect
21. #22598268C2semidirect
22. #22598268C2semidirect
23. #22598148C2semidirect
24. #22598135C2semidirect
25. #22597958C2semidirect
26. #22597956C2semidirect
27. #22597151C2semidirect
28. #22597073C2semidirect
29. #22596928C2semidirect
30. #22596927C2semidirect
31. C71×#3347C2semidirect
35. #17986717C22semidirect
42. #17986713C22semidirect
48. #17986704C22semidirect
49. #17986699C22semidirect
50. #17986689C22semidirect
51. #17986687C22semidirect
55. #17986649C22semidirect
78. #17986409C22semidirect
79. #17986408C22semidirect
80. #17986405C22semidirect
81. #17986403C22semidirect
82. #17986403C22semidirect
83. #17986396C22semidirect
84. #17986396C22semidirect
85. #17986343C22semidirect
86. #17986343C22semidirect
87. #17986342C22semidirect
88. #17986342C22semidirect
89. #17986341C22semidirect
90. #17986341C22semidirect
91. #17986340C22semidirect
92. #17986340C22semidirect
93. #17986326C22semidirect
94. #17986326C22semidirect
95. #17986324C22semidirect
96. #17986323C22semidirect
97. #17986322C22semidirect
98. #17986322C22semidirect
99. #17986322C22semidirect
100. #17986322C22semidirect
101. #17986321C22semidirect
102. #17986321C22semidirect
103. #17986320C22semidirect
104. #17986320C22semidirect
105. #17986320C22semidirect
106. #17986319C22semidirect
107. #17986318C22semidirect
108. #17986316C22semidirect
109. #17986315C22semidirect
110. #17986314C22semidirect
111. #17986312C22semidirect
112. #17986311C22semidirect
113. #17986300C22semidirect
114. #17986299C22semidirect
115. #17986296C22semidirect
116. #17986293C22semidirect
117. #17986293C22semidirect
118. #17986288C22semidirect
119. #17986287C22semidirect
120. #17986287C22semidirect
121. #17986287C22semidirect
122. #17986285C22semidirect
123. #17986281C22semidirect
124. #17986279C22semidirect
125. #17986278C22semidirect
126. #17986277C22semidirect
127. #17986251C22semidirect
128. #17986250C22semidirect
129. #17986249C22semidirect
130. #17986246C22semidirect
131. #17986245C22semidirect
132. #17986244C22semidirect
133. #17986243C22semidirect
134. #17986234C22semidirect
135. #17986233C22semidirect
136. #17986232C22semidirect
137. #17986229C22semidirect
138. #17986228C22semidirect
139. #17986227C22semidirect
140. #17986226C22semidirect
141. #17986109C22semidirect
142. #17986101C22semidirect
143. #17986099C22semidirect
144. #17986090C22semidirect
145. #17986086C22semidirect
146. D8×Dic71C22semidirect
147. #17986079C22semidirect
148. #17986075C22semidirect
149. #17986074C22semidirect
150. #17986072C22semidirect
151. #17986071C22semidirect
152. #17986069C22semidirect
153. C8×C22⋊D71C22semidirect
154. (C22⋊D71)⋊C8C22semidirect
155. #17986042C22semidirect
156. #17986041C22semidirect
162. #17986040C22semidirect
163. #17986040C22semidirect
164. #17986039C22semidirect
169. #17986038C22semidirect
170. #17986038C22semidirect
171. #17986037C22semidirect
172. #17986036C22semidirect
173. #17986036C22semidirect
174. #17986035C22semidirect
175. #17986035C22semidirect
176. #17986034C22semidirect
177. #17986034C22semidirect
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
198. #466×C71C22semidirect
199. #442×C71C22semidirect
200. #435×C71C22semidirect
201. #428×C71C22semidirect
202. #427×C71C22semidirect
549. #11765848#41semidirect
871. #3347D71semidirect
889. C71#61256semidirect
909. #553C2×D71semidirect
941. #501C2×D71semidirect
967. #482C2×D71semidirect
968. #482C2×D71semidirect
969. #482C2×D71semidirect
977. #480C2×D71semidirect
981. #478C2×D71semidirect
993. #474C2×D71semidirect
997. #469C2×D71semidirect
1005. #466C2×D71semidirect
1011. #442C2×D71semidirect
1023. #435C2×D71semidirect
1042. #428C2×D71semidirect
1050. #427C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226018992
#555×D712
#226009622
#226009592
#226009332
#226009302
#226008572
#226008552
#226008542
#226008522
#226008472
#226008452
#226008342
#226007592
#226007572
#226007512
#226007492
#225988852
#225982792
#225982752
#225982682
#225981482
#225981352
#225979582
#225979562
#225971512
#225970732
#225969282
#225969272
C71×#33472
#6125671