Finite Group Databasebeta

← #32876517

Subgroups — #32876517

Order 18176.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602091C211yesmaximal, characteristic, complemented
2#22602064C211yesmaximal, characteristic
3#22600963C211yesmaximal, characteristic, complemented
4#22600959C211yesmaximal, characteristic, complemented
5#22600924C211yesmaximal, characteristic, complemented
6#22600917C211yesmaximal, characteristic, complemented
7#22600907C211yesmaximal, characteristic, complemented
8#22600903C211yesmaximal, characteristic, complemented
9#22600900C211yesmaximal, characteristic, complemented
10#22600893C211yesmaximal, characteristic, complemented
11#22600887C211yesmaximal, characteristic, complemented
12#22600880C211yesmaximal, characteristic, complemented
13#22600861C211yesmaximal, characteristic, complemented
14#22600854C211yesmaximal, characteristic, complemented
15#22600830C211yesmaximal, characteristic, complemented
16#22600821C211yesmaximal, characteristic, complemented
17#22600781C211yesmaximal, characteristic, complemented
18#22598875C211yesmaximal, characteristic, complemented
19#22598302C211yesmaximal, characteristic, complemented
20#22598291C211yesmaximal, characteristic, complemented
21#22598285C211yesmaximal, characteristic, complemented
22#22598279C211yesmaximal, characteristic, complemented
23#22598177C211yesmaximal, characteristic, complemented
24#22598170C211yesmaximal, characteristic, complemented
25#22597974C211yesmaximal, characteristic, complemented
26#468×D71C211yesmaximal, characteristic, complemented
27#22597196C211yesmaximal, characteristic, complemented
28#22597038C211yesmaximal, characteristic, complemented
29#22596936C211yesmaximal, characteristic, complemented
30#22596927C211yesmaximal, characteristic, complemented
31C71×#3343C211yesmaximal, characteristic, complemented
32C2×SD16×D71C2211yescharacteristic
33C2×#14556134C2211yescharacteristic
34C2×M16×D71C2211yescharacteristic
35#17986720C2211yescharacteristic, complemented
36#17986719C2211yescharacteristic, complemented
37#17986715C2211yescharacteristic
38#17986713C2211yescharacteristic
39#17986709C2211yescharacteristic, complemented
40#17986704C2211yescharacteristic, complemented
41#17986701C2211yescharacteristic
42#17986699C2211yescharacteristic
43#17986697C2211yescharacteristic
44#17986695C2211yescharacteristic
45#17986688—21no—
46#17986688C2211yescharacteristic, complemented
47#17986687C2211yescharacteristic, complemented
48#17986683C2211yescharacteristic, complemented
49#17986681—21no—
50#17986677—21no—
51#17986677—21no—
52#17986676—21no—
53#17986674—21no—
54#17986650C2211yescharacteristic
55#17986641—21no—
56#17986637—21no—
57#17986629C2211yescharacteristic
58#17986626C2211yescharacteristic
59#17986619—21no—
60#17986617—21no—
61#17986606—21no—
62#17986601—21no—
63#17986572C2211yescharacteristic
64#17986565C2211yescharacteristic
65#17986555—21no—
66#17986545—21no—
67#17986527—21no—
68#17986526—21no—
69#17986508C2211yescharacteristic
70C22⋊Q8×D71C2211yescharacteristic
71#121×D71C2211yescharacteristic
72#17986480C2211yescharacteristic
73#17986480C2211yescharacteristic
74#17986475C2211yescharacteristic
75#17986471C2211yescharacteristic
76C2×#14556086C2211yescharacteristic
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#17986343C2211yescharacteristic, complemented
86#17986342C2211yescharacteristic, complemented
87#17986342C2211yescharacteristic, complemented
88#17986341C2211yescharacteristic, complemented
89#17986338C2211yescharacteristic, complemented
90#17986338C2211yescharacteristic, complemented
91#17986338C2211yescharacteristic, complemented
92#17986337C2211yescharacteristic, complemented
93#17986334C2211yescharacteristic, complemented
94#17986334C2211yescharacteristic, complemented
95#17986333C2211yescharacteristic, complemented
96#17986331C2211yescharacteristic, complemented
97#17986330C2211yescharacteristic, complemented
98#17986327C2211yescharacteristic, complemented
99#17986326C2211yescharacteristic, complemented
100#17986324C2211yescharacteristic
101#17986324C2211yescharacteristic, complemented
102#17986323C2211yescharacteristic
103#17986321C2211yescharacteristic, complemented
104#17986320C2211yescharacteristic
105#17986320C2211yescharacteristic, complemented
106#17986319C2211yescharacteristic
107#17986317C2211yescharacteristic, complemented
108#17986316C2211yescharacteristic
109#17986316C2211yescharacteristic, complemented
110#17986314C2211yescharacteristic
111#17986314C2211yescharacteristic, complemented
112#17986311C2211yescharacteristic
113#17986308C2211yescharacteristic, complemented
114#17986307C2211yescharacteristic, complemented
115#17986306C2211yescharacteristic, complemented
116#17986305C2211yescharacteristic, complemented
117#17986301C2211yescharacteristic, complemented
118#17986298C2211yescharacteristic, complemented
119#17986296C2211yescharacteristic, complemented
120#17986293C2211yescharacteristic, complemented
121#17986290C2211yescharacteristic, complemented
122#17986287C2211yescharacteristic, complemented
123#17986282C2211yescharacteristic, complemented
124#17986281C2211yescharacteristic, complemented
125#17986279C2211yescharacteristic, complemented
126#17986278C2211yescharacteristic, complemented
127#17986248C2211yescharacteristic
128#17986248C2211yescharacteristic, complemented
129#17986247C2211yescharacteristic
130#17986247C2211yescharacteristic, complemented
131#17986246C2211yescharacteristic
132#17986245C2211yescharacteristic
133#17986244C2211yescharacteristic
134#17986244C2211yescharacteristic, complemented
135#17986243C2211yescharacteristic
136#17986243C2211yescharacteristic, complemented
137#17986242C2211yescharacteristic
138#17986229C2211yescharacteristic, complemented
139#17986228C2211yescharacteristic, complemented
140#17986225C2211yescharacteristic, complemented
141#17986101C2211yescharacteristic, complemented
142#17986100C2211yescharacteristic, complemented
143#17986098C2211yescharacteristic, complemented
144#17986090C2211yescharacteristic, complemented
145C4×#11765852C2211yescharacteristic, complemented
146C4×#11765853C2211yescharacteristic, complemented
147#17986084C2211yescharacteristic, complemented
148#17986077C2211yescharacteristic, complemented
149#17986076C2211yescharacteristic, complemented
150#17986074C2211yescharacteristic, complemented
151#17986074C2211yescharacteristic, complemented
152#17986072C2211yescharacteristic, complemented
153#17986070C2211yescharacteristic, complemented
154#17986068C2211yescharacteristic, complemented
155#17986042C2211yescharacteristic, complemented
156#17986041C2211yescharacteristic, complemented
157#17986040C2211yescharacteristic
158#17986040C2211yescharacteristic
159#17986040C2211yescharacteristic
160#17986040C2211yescharacteristic, complemented
161#17986040C2211yescharacteristic, complemented
162#17986040C2211yescharacteristic, complemented
163#17986040C2211yescharacteristic, complemented
164#17986039C2211yescharacteristic, complemented
165#17986039C2211yescharacteristic, complemented
166#17986039C2211yescharacteristic, complemented
167#17986038C2211yescharacteristic
168#17986038C2211yescharacteristic, complemented
169#17986038C2211yescharacteristic, complemented
170#17986037C2211yescharacteristic, complemented
171#17986036C2211yescharacteristic
172#17986036C2211yescharacteristic
173#17986036C2211yescharacteristic, complemented
174#17986034C2211yescharacteristic
175#17986034C2211yescharacteristic
176#107×D71C2211yescharacteristic
177#107×D71C2211yescharacteristic, complemented
178#17986024C2211yescharacteristic
179#17986006C2211yescharacteristic
180#17986006C2211yescharacteristic
181#17986002C2211yescharacteristic
182#17986002C2211yescharacteristic
183#103×D71C2211yescharacteristic
184#102×D71C2211yescharacteristic
185#17985964C2211yescharacteristic
186#17985961C2211yescharacteristic
187#17985956C2211yescharacteristic
188#552×C71C2211yescharacteristic, complemented
189#547×C71C2211yescharacteristic
190#501×C71C2211yescharacteristic, complemented
191#484×C71C2211yescharacteristic, complemented
192#483×C71C2211yescharacteristic, complemented
193#482×C71C2211yescharacteristic
194#480×C71C2211yescharacteristic, complemented
195#478×C71C2211yescharacteristic, complemented
196#477×C71C2211yescharacteristic, complemented
197#468×C71C2211yescharacteristic
198#465×C71C2211yescharacteristic, complemented
199#440×C71C2211yescharacteristic, complemented
200#435×C71C2211yescharacteristic, complemented
201#428×C71C2211yescharacteristic, complemented
202C2×#107×C71C2211yescharacteristic, complemented
203C2×#11765865—21no—
204C2×#11765865C2311yescharacteristic
205C2×Q8×D71C2311yescharacteristic
206C2×D4×D71—21no—
207C2×D4×D71C2311yescharacteristic
208C22×C4×D71C2311yescharacteristic
209C2×#11765854C2311yescharacteristic
210C2×#11765853C2311yescharacteristic
211C2×#11765852C2311yescharacteristic
212SD16×D71—24no—
213#14556134—24no—
214C2×#11765849C2311yescharacteristic
215C2×#11765849C2311yescharacteristic
216C2×#11765848C2311yescharacteristic
217C2×#11765848C2311yescharacteristic
218C2×#11765848C2311yescharacteristic
219C2×#11765848C2311yescharacteristic
220C2×#11765848C2311yescharacteristic
221M16×D71—24no—
222C2×C8×D71C2311yescharacteristic
223C2×C8×D71C2311yescharacteristic
224C2×C8×D71C2311yescharacteristic
225#14556128C2311yescharacteristic
226#14556127—21no—
227#14556127—21no—
228#14556127C2311yescharacteristic
229#14556127C2311yescharacteristic
230#14556126—21no—
231#14556124—21no—
232#14556123—21no—
233#14556123—21no—
234#14556123—21no—
235#14556123—21no—
236#14556121—21no—
237#14556121—21no—
238#14556121—21no—
239#14556121—21no—
240#14556121—21no—
241#14556121—21no—
242#14556121—21no—
243#14556120—21no—
244#14556120—21no—
245#14556120C2311yescharacteristic
246#14556119—21no—
247#14556119C2311yescharacteristic
248#14556119C2311yescharacteristic
249#14556118—21no—
250#14556118—21no—
251#14556118—21no—
252#14556118—21no—
253#14556117—21no—
254#14556117—21no—
255#14556115—21no—
256#14556115—21no—
257#14556114—21no—
258#14556114—21no—
259#14556114—21no—
260#14556114—21no—
261#14556113—21no—
262#14556113—21no—
263#14556113—21no—
264#14556113—21no—
265#14556113D411yescharacteristic
266#14556112—21no—
267#14556111—21no—
268#14556111—21no—
269#14556110—21no—
270#14556110—21no—
271#14556110—21no—
272#14556110—21no—
273#14556110D411yescharacteristic
274#14556108—21no—
275#14556108C2311yescharacteristic
276#14556108C2311yescharacteristic
277#14556107—21no—
278#14556107C2311yescharacteristic
279#14556107C2311yescharacteristic
280#14556106—21no—
281#14556106—21no—
282#14556106—21no—
283#14556106—21no—
284#14556106—21no—
285#14556106—21no—
286#14556106—21no—
287#14556106D411yescharacteristic
288#14556105—21no—
289#14556105D411yescharacteristic
290#14556104—21no—
291#14556104C2311yescharacteristic
292#14556104C2311yescharacteristic
293#14556103—21no—
294#14556103C2311yescharacteristic
295#14556103C2311yescharacteristic
296#14556102—21no—
297#14556102C2311yescharacteristic
298#14556102C2311yescharacteristic
299#14556101—21no—
300#14556101—21no—
301#14556101D411yescharacteristic
302#14556100—21no—
303#14556100—21no—
304#14556100—21no—
305#14556100—21no—
306#14556100D411yescharacteristic
307#14556099C2311yescharacteristic
308#14556099C2311yescharacteristic
309#14556098—21no—
310#14556098D411yescharacteristic
311#14556096—21no—
312#14556096D411yescharacteristic
313Q8×Dic71C2311yescharacteristic
314C4×Dic142—21no—
315C4×Dic142C2311yescharacteristic
316#14556093—21no—
317#14556093—21no—
318#14556093—21no—
319#14556093—21no—
320#14556093—21no—
321#14556093C2311yescharacteristic
322C4×D284—21no—
323C4×D284C2311yescharacteristic
324C4×D284C2311yescharacteristic
325D4×Dic71—21no—
326D4×Dic71C2311yescharacteristic
327#14556090—21no—
328#14556090—21no—
329#14556090C2311yescharacteristic
330C4×C22⋊D71—21no—
331C4×C22⋊D71—21no—
332C4×C22⋊D71—21no—
333C4×C22⋊D71—21no—
334C4×C22⋊D71—21no—
335C4×C22⋊D71—21no—
336C4×C22⋊D71—21no—
337C4×C22⋊D71—21no—
338C4×C22⋊D71C2311yescharacteristic
339C4×C22⋊D71C2311yescharacteristic
340(C22⋊D71)⋊C4—21no—
341(C22⋊D71)⋊C4—21no—
342#14556087C2311yescharacteristic
343#14556087C2311yescharacteristic
344#14556087C2311yescharacteristic
345#14556086—21no—
346#14556086—21no—
347#14556086—21no—
348#14556086—21no—
349#14556086—21no—
350#14556086—21no—
351#14556086C2311yescharacteristic
352#14556086C2311yescharacteristic
353#14556086C2311yescharacteristic
354#14556086C2311yescharacteristic
355#14556086C2311yescharacteristic
356#14556086C2311yescharacteristic
357#14556086C2311yescharacteristic
358#14556086C2311yescharacteristic
359#14556085—21no—
360#14556085—21no—
361#14556085—21no—
362#14556085C2311yescharacteristic
363#14556084—21no—
364#14556084—21no—
365C2×C4⋊Dic71C2311yescharacteristic
366C4⋊C4×D71—21no—
367C4⋊C4×D71C2311yescharacteristic
368C4⋊C4×D71C2311yescharacteristic
369C4⋊C4×D71C2311yescharacteristic
370C4⋊C4×D71C2311yescharacteristic
371C4⋊C4×D71C2311yescharacteristic
372C4⋊C4×D71C2311yescharacteristic
373C2×(C2×D71)⋊C4—21no—
374C2×(C2×D71)⋊C4—21no—
375C22⋊C4×D71—21no—
376C22⋊C4×D71—21no—
377C22⋊C4×D71—21no—
378C22⋊C4×D71—21no—
379C2×C4×Dic71—21no—
380C42×D71—21no—
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#14556061C2311yescharacteristic
395#14556060C2311yescharacteristic
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#14556053C2311yescharacteristic
412#14556053C2311yescharacteristic
413#14556053C2311yescharacteristic
414#14556052C2311yescharacteristic
415#14556052C2311yescharacteristic
416#14556052C2311yescharacteristic
417#14556051C2311yescharacteristic
418#14556051C2311yescharacteristic
419#14556051C2311yescharacteristic
420#14556050C2311yescharacteristic
421#14556050C2311yescharacteristic
422#14556050C2311yescharacteristic
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#14556038C2311yescharacteristic
436C4×C71⋊C8C2311yescharacteristic
437C8×Dic71C2311yescharacteristic
438C2×#41×C71—21no—
439C2×SD16×C71C2311yescharacteristic
440C2×M16×C71C2311yescharacteristic
441C22×C8×C71C2311yescharacteristic
442C4⋊Q8×C71C2311yescharacteristic
443#126×C71—21no—
444#125×C71—21no—
445#125×C71C2311yescharacteristic
446#123×C71—21no—
447#123×C71—21no—
448#123×C71—21no—
449C22⋊Q8×C71—21no—
450C22⋊Q8×C71C2311yescharacteristic
451C22⋊Q8×C71C2311yescharacteristic
452#121×C71C2311yescharacteristic
453#121×C71C2311yescharacteristic
454C4×Q8×C71C2311yescharacteristic
455C4×D4×C71C2311yescharacteristic
456C4×D4×C71C2311yescharacteristic
457#117×C71—21no—
458#117×C71C2311yescharacteristic
459C2×C4⋊C4×C71C2311yescharacteristic
460C2×C4⋊C4×C71C2311yescharacteristic
461C2×C4⋊C4×C71C2311yescharacteristic
462#107×C71C2311yescharacteristic
463#107×C71C2311yescharacteristic
464#107×C71C2311yescharacteristic
465#107×C71C2311yescharacteristic
466#107×C71C2311yescharacteristic
467#107×C71C2311yescharacteristic
468#106×C71C2311yescharacteristic
469#106×C71C2311yescharacteristic
470#106×C71C2311yescharacteristic
471C4⋊C8×C71C2311yescharacteristic
472#103×C71C2311yescharacteristic
473#103×C71C2311yescharacteristic
474#103×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
483#11765865—22no—
484#11765865—22no—
485#11765865—82no—
486C2×Dic142—21no—
487C2×Dic142—21no—
488C2×Dic142—21no—
489C2×Dic142—21no—
490C2×Dic142C2×D411yescharacteristic
491C2×Dic142C2411yescharacteristic
492Q8×D71—22no—
493Q8×D71—22no—
494C2×D284—21no—
495C2×D284—21no—
496C2×D284C2×D411yescharacteristic
497C2×D284C2×D411yescharacteristic
498C2×D284C2411yescharacteristic
499C2×C22⋊D71—21no—
500C2×C22⋊D71—21no—
501C2×C22⋊D71—21no—
502C2×C22⋊D71—21no—
503C2×C22⋊D71—21no—
504C2×C22⋊D71C2×D411yescharacteristic
505C2×C22⋊D71C2×D411yescharacteristic
506C2×C22⋊D71C2×D411yescharacteristic
507C2×C22⋊D71C2×D411yescharacteristic
508D4×D71—22no—
509D4×D71—22no—
510D4×D71—82no—
511C22×Dic71—21no—
512C22×Dic71—21no—
513C22×Dic71C2×D411yescharacteristic
514C2×C4×D71—22no—
515C2×C4×D71—22no—
516C2×C4×D71—21no—
517C2×C4×D71—21no—
518C2×C4×D71—21no—
519C2×C4×D71—21no—
520C2×C4×D71—21no—
521C2×C4×D71—21no—
522C2×C4×D71—21no—
523C2×C4×D71—21no—
524C2×C4×D71—21no—
525C2×C4×D71C2×D411yescharacteristic
526C2×C4×D71C2×D411yescharacteristic
527C2×C4×D71C2411yescharacteristic
528C2×C4×D71C2411yescharacteristic
529C2×C4×D71C2411yescharacteristic
530#11765854—22no—
531#11765853—22no—
532#11765852—22no—
533#11765849—22no—
534#11765849—22no—
535#11765848—22no—
536#11765848—22no—
537#11765848—22no—
538#11765848—22no—
539#11765848—22no—
540C2×C71⋊C8C2411yescharacteristic
541C2×C71⋊C8C2411yescharacteristic
542C2×C71⋊C8C2411yescharacteristic
543C2×C71⋊C8C2411yescharacteristic
544C8×D71—22no—
545C8×D71—22no—
546C8×D71#4114yescomplemented
547C4⋊Dic71—21no—
548C4⋊Dic71—21no—
549C4⋊Dic71—21no—
550C4⋊Dic71—21no—
551C4⋊Dic71—21no—
552C4⋊Dic71—21no—
553C4⋊Dic71—21no—
554C4⋊Dic71C2×D411yescharacteristic
555C4⋊Dic71C2411yescharacteristic
556C4⋊Dic71C2411yescharacteristic
557C4⋊Dic71C2411yescharacteristic
558C4⋊Dic71C2411yescharacteristic
559C4⋊Dic71C2411yescharacteristic
560C4⋊Dic71C2411yescharacteristic
561Dic71⋊C4—21no—
562Dic71⋊C4—21no—
563Dic71⋊C4—21no—
564Dic71⋊C4—21no—
565Dic71⋊C4—21no—
566Dic71⋊C4—21no—
567Dic71⋊C4—21no—
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⋊C4C2×D411yescharacteristic
580Dic71⋊C4C2×D411yescharacteristic
581Dic71⋊C4C2×D411yescharacteristic
582Dic71⋊C4C2×D411yescharacteristic
583C22⋊Dic71—21no—
584C22⋊Dic71—21no—
585C22⋊Dic71—21no—
586C22⋊Dic71—21no—
587C22⋊Dic71—21no—
588C22⋊Dic71—21no—
589C22⋊Dic71—21no—
590C22⋊Dic71—21no—
591C22⋊Dic71C2×D411yescharacteristic
592C22⋊Dic71C2×D411yescharacteristic
593(C2×D71)⋊C4—21no—
594(C2×D71)⋊C4—21no—
595(C2×D71)⋊C4—21no—
596(C2×D71)⋊C4—21no—
597(C2×D71)⋊C4—21no—
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)⋊C4C2×D411yescharacteristic
612(C2×D71)⋊C4C2×D411yescharacteristic
613(C2×D71)⋊C4C2×D411yescharacteristic
614(C2×D71)⋊C4C2×D411yescharacteristic
615(C2×D71)⋊C4C2×D411yescharacteristic
616(C2×D71)⋊C4C2×D411yescharacteristic
617C4×Dic71—21no—
618C4×Dic71—21no—
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×Dic71C2411yescharacteristic
632#41×C71—82no—
633C2×Q8×C71—21no—
634C2×Q8×C71C2411yescharacteristic
635C2×D4×C71—21no—
636C2×D4×C71—21no—
637C2×D4×C71C2×D411yescharacteristic
638C2×D4×C71C2411yescharacteristic
639C22×C4×C71—21no—
640C22×C4×C71—21no—
641C22×C4×C71—21no—
642C22×C4×C71—21no—
643C22×C4×C71C2411yescharacteristic
644C22×C4×C71C2411yescharacteristic
645SD16×C71—22no—
646M16×C71—22no—
647C2×C8×C71—22no—
648C2×C8×C71C2411yescharacteristic
649C2×C8×C71C2411yescharacteristic
650C2×C8×C71C2411yescharacteristic
651C2×C8×C71C2411yescharacteristic
652C4⋊C4×C71—21no—
653C4⋊C4×C71—21no—
654C4⋊C4×C71—21no—
655C4⋊C4×C71—21no—
656C4⋊C4×C71—21no—
657C4⋊C4×C71—21no—
658C4⋊C4×C71—21no—
659C4⋊C4×C71—21no—
660C4⋊C4×C71—21no—
661C4⋊C4×C71C2×D411yescharacteristic
662C4⋊C4×C71C2411yescharacteristic
663C4⋊C4×C71C2411yescharacteristic
664C4⋊C4×C71C2411yescharacteristic
665C4⋊C4×C71C2411yescharacteristic
666C4⋊C4×C71C2411yescharacteristic
667C4⋊C4×C71C2411yescharacteristic
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×C71C2×D411yescharacteristic
675C22⋊C4×C71C2×D411yescharacteristic
676C42×C71—21no—
677C42×C71—21no—
678C42×C71C2411yescharacteristic
679C23×C71—21no—
680C23×C71C22×D411yescharacteristic
681C23×C71C22×D411yescharacteristic
682C22×D71—22no—
683C22×D71—21no—
684C22×D71—41no—
685C22×D71—41no—
686C22×D71—42no—
687C22×D71—81no—
688C22×D71—81no—
689C22×D71C22×D411yescharacteristic
690C22×D71C22×D411yescharacteristic
691C22×D71C22×D411yescharacteristic
692Q8×C71—21no—
693Q8×C71—21no—
694Q8×C71—81no—
695D4×C71—21no—
696D4×C71—21no—
697D4×C71—41no—
698D4×C71—42no—
699D4×C71—81no—
700C2×C4×C71—21no—
701C2×C4×C71—21no—
702C2×C4×C71—21no—
703C2×C4×C71—21no—
704C2×C4×C71—21no—
705C2×C4×C71—21no—
706C2×C4×C71—21no—
707C2×C4×C71—21no—
708C2×C4×C71—21no—
709C2×C4×C71—21no—
710C2×C4×C71—21no—
711C2×C4×C71—42no—
712C2×C4×C71—81no—
713C2×C4×C71—81no—
714C2×C4×C71—81no—
715C2×C4×C71C22×D411yescharacteristic
716C2×C4×C71C22×D411yescharacteristic
717C2×C4×C71C22×D411yescharacteristic
718C2×C4×C71C22×D411yescharacteristic
719C2×C4×C71C2511yescharacteristic
720C22⋊D71—22no—
721C22⋊D71—22no—
722C22⋊D71—41no—
723C22⋊D71—41no—
724C22⋊D71—42no—
725C22⋊D71—42no—
726C22⋊D71—81no—
727C22⋊D71—81no—
728C22⋊D71—81no—
729C2×Dic71—22no—
730C2×Dic71—21no—
731C2×Dic71—21no—
732C2×Dic71—21no—
733C2×Dic71—21no—
734C2×Dic71—21no—
735C2×Dic71—21no—
736C2×Dic71—21no—
737C2×Dic71—81no—
738C2×Dic71—81no—
739C2×Dic71C22×D411yescharacteristic
740C2×Dic71C22×D411yescharacteristic
741C2×Dic71C22×D411yescharacteristic
742C2×Dic71C22×D411yescharacteristic
743C2×Dic71C22×D411yescharacteristic
744D284—22no—
745D284—21no—
746D284—21no—
747D284—41no—
748D284—81no—
749D284—81no—
750C4×D71—22no—
751C4×D71—21no—
752C4×D71—21no—
753C4×D71—21no—
754C4×D71—21no—
755C4×D71—22no—
756C4×D71—42no—
757C4×D71—42no—
758C4×D71—81no—
759C4×D71—81no—
760C4×D71—81no—
761C4×D71—81no—
762C4×D71—81no—
763C4×D71—81no—
764C4×D71—81no—
765C4×D71C2×#4112yes—
766C4×D712−1+412yes—
767Dic142—22no—
768Dic142—21no—
769Dic142—21no—
770Dic142—42no—
771Dic142—81no—
772Dic142—81no—
773Dic142—81no—
774C8×C71—21no—
775C8×C71—21no—
776C8×C71—21no—
777C8×C71C2×#4112yes—
778C71⋊C8—21no—
779C71⋊C8—21no—
780C71⋊C8—21no—
781C71⋊C8C2×#4112yes—
782C22×C71—21no—
783C22×C71—21no—
784C22×C71—21no—
785C22×C71—21no—
786C22×C71—21no—
787C22×C71—21no—
788C22×C71—41no—
789C22×C71—41no—
790C22×C71—41no—
791C22×C71C23×D411yescharacteristic
792C2×D71—21no—
793C2×D71—21no—
794C2×D71—21no—
795C2×D71—21no—
796C2×D71—21no—
797C2×D71—21no—
798C2×D71—21no—
799C2×D71—21no—
800C2×D71—41no—
801C2×D71—41no—
802C2×D71—41no—
803C2×D71—82no—
804C2×D71—162no—
805C2×D71#54712yes—
806C4×C71—21no—
807C4×C71—21no—
808C4×C71—21no—
809C4×C71—21no—
810C4×C71—41no—
811C4×C71—41no—
812C4×C71—41no—
813C4×C71—41no—
814C4×C71—41no—
815C4×C71—41no—
816C4×C71—41no—
817C4×C71C22×#4111yescharacteristic
818C4×C71C2×2−1+411yescharacteristic
819Dic71—21no—
820Dic71—21no—
821Dic71—21no—
822Dic71—21no—
823Dic71—41no—
824Dic71—41no—
825Dic71—41no—
826Dic71—41no—
827Dic71—41no—
828Dic71—41no—
829Dic71—41no—
830Dic71#54712yes—
831#61268—711nomaximal, Sylow
832C2×C71—41no—
833C2×C71—41no—
834C2×C71—81no—
835C2×C71C2×#54711yescharacteristic
836C2×C71#358511yescharacteristic
837C2×C71#358611yescharacteristic
838D71—22no—
839D71—41no—
840D71—41no—
841D71—81no—
842#3495—711no—
843#3494—711no—
844#3357—711no—
845#3357—711no—
846#3353—711no—
847#3353—711no—
848#3351—711no—
849#3351—711no—
850#3351—711no—
851#3351—711no—
852#3350—711no—
853#3350—711no—
854#3348—711no—
855#3348—711no—
856#3346—711no—
857#3346—711no—
858#3343—711no—
859#3343D7111yescharacteristic, complemented
860#3164—711no—
861#3097—711no—
862#3096—711no—
863#3095—711no—
864#3094—711no—
865#3082—711no—
866#3081—711no—
867#3057—711no—
868C2×#468—711no—
869#2949—711no—
870#2930—711no—
871#2913—711no—
872#2911—711no—
873C71#6126811yescharacteristic, complemented, Sylow
874C22×SD16—711no—
875C2×#131—711no—
876C22×M16—711no—
877#556—711no—
878#556—711no—
879#555—711no—
880#555—711no—
881#554—711no—
882#554—711no—
883#553—711no—
884#553—711no—
885#553—711no—
886#553—711no—
887#552—711no—
888#552—711no—
889#552—711no—
890#552—1421no—
891#552—1421no—
892#552C2×D7111yescharacteristic, complemented
893#551—1421no—
894#551—1421no—
895#551—1421no—
896#551—1421no—
897#547—711no—
898#547C2×D7111yescharacteristic
899#546—1421no—
900#546—1421no—
901#544—711no—
902#544—711no—
903#542—1421no—
904#542—1421no—
905#541—1421no—
906#540—1421no—
907#536—711no—
908#535—711no—
909#533—1421no—
910#532—1421no—
911#529—1421no—
912#529—1421no—
913#525—711no—
914C2×C22⋊Q8—711no—
915C2×#121—711no—
916#520—711no—
917#520—711no—
918#519—711no—
919#518—711no—
920C2×#117—711no—
921C2×#117—711no—
922#501—711no—
923#501—711no—
924#501—711no—
925#501C2×D7111yescharacteristic, complemented
926#500—711no—
927#500—711no—
928#499—711no—
929#499—711no—
930#485—711no—
931#485—711no—
932#485—711no—
933#485—711no—
934#485—711no—
935#485—711no—
936#485—711no—
937#485—711no—
938#484—711no—
939#484—711no—
940#484—711no—
941#484C2×D7111yescharacteristic, complemented
942#483—711no—
943#483—711no—
944#483—711no—
945#483C2×D7111yescharacteristic, complemented
946#482—711no—
947#482—711no—
948#482—711no—
949#482—711no—
950#482—711no—
951#482—711no—
952#482—711no—
953#482C2×D7111yescharacteristic
954#481—711no—
955#481—711no—
956#481—711no—
957#481—711no—
958#480—711no—
959#480—711no—
960#480—711no—
961#480C2×D7111yescharacteristic, complemented
962#479—711no—
963#479—711no—
964#479—711no—
965#479—711no—
966#478—711no—
967#478—711no—
968#478—711no—
969#478C2×D7111yescharacteristic, complemented
970#477—711no—
971#477C2×D7111yescharacteristic, complemented
972#476—711no—
973#476—711no—
974#475—711no—
975#475—711no—
976#474—711no—
977#474—711no—
978#468—711no—
979#468—711no—
980#468—711no—
981#468—711no—
982#468—711no—
983#468—711no—
984#468—711no—
985#468—711no—
986#468—711no—
987#468—711no—
988#468—711no—
989#468C2×D7111yescharacteristic
990#465—711no—
991#465—711no—
992#465—711no—
993#465C2×D7111yescharacteristic, complemented
994#440—711no—
995#440—711no—
996#440—711no—
997#440C2×D7111yescharacteristic, complemented
998C4×SD16—711no—
999C4×SD16—711no—
1000C4×SD16—711no—
1001C4×SD16—711no—
1002#436—711no—
1003#436—711no—
1004#436—711no—
1005#436—711no—
1006#435—711no—
1007#435—711no—
1008#435—711no—
1009#435C2×D7111yescharacteristic, complemented
1010#428—711no—
1011#428—711no—
1012#428—711no—
1013#428—711no—
1014#428—711no—
1015#428—711no—
1016#428—711no—
1017#428—711no—
1018#428—711no—
1019#428—711no—
1020#428—711no—
1021#428—711no—
1022#428—711no—
1023#428—711no—
1024#428—711no—
1025#428C2×D7111yescharacteristic, complemented
1026#427—711no—
1027#427—711no—
1028#427—711no—
1029#427—711no—
1030#427—711no—
1031#427—711no—
1032C2×#107—711no—
1033C2×#107—711no—
1034C2×#107C2×D7111yescharacteristic, complemented
1035#424—711no—
1036#419—711no—
1037#419—711no—
1038#418—711no—
1039#418—711no—
1040C2×#103—711no—
1041C2×#102—711no—
1042#408—711no—
1043#407—711no—
1044#405—711no—
1045C2×#41—21no—
1046C2×#41—711no—
1047C2×#41—1421no—
1048C22×Q8—711no—
1049C22×D4—711no—
1050C22×D4—1421no—
1051C23×C4—711no—
1052C2×SD16—711no—
1053C2×SD16—711no—
1054C2×SD16—711no—
1055C2×SD16—1424no—
1056C2×SD16C22×D7111yescharacteristic
1057#131—1424no—
1058C2×M16—711no—
1059C2×M16—711no—
1060C2×M16—711no—
1061C2×M16—711no—
1062C2×M16—711no—
1063C2×M16—711no—
1064C2×M16—711no—
1065C2×M16—1424no—
1066C2×M16C22×D7111yescharacteristic
1067C22×C8—711no—
1068C22×C8—711no—
1069C22×C8—711no—
1070C22×C8C22×D7111yescharacteristic
1071C4⋊Q8—711no—
1072C4⋊Q8—711no—
1073C4⋊Q8—711no—
1074C4⋊Q8—1421no—
1075C4⋊Q8—1421no—
1076C4⋊Q8—1421no—
1077C4⋊Q8C22×D7111yescharacteristic
1078#127—1421no—
1079#126—21no—
1080#126—1421no—
1081#126—1421no—
1082#126—1421no—
1083#126—1421no—
1084#126—1421no—
1085#126—1421no—
1086#126—1421no—
1087#126—1421no—
1088#126—1421no—
1089#126—1421no—
1090#126—1421no—
1091#125—21no—
1092#125—711no—
1093#125—711no—
1094#125—711no—
1095#125—1421no—
1096#125—1421no—
1097#125—1421no—
1098#125—1421no—
1099#125—1421no—
1100#125—1421no—
1101#125—1421no—
1102#125C22×D7111yescharacteristic
1103#124—1421no—
1104#124—1421no—
1105#124—1421no—
1106#124—1421no—
1107#124—1421no—
1108#124—1421no—
1109#124—1421no—
1110#124—1421no—
1111#123—21no—
1112#123—21no—
1113#123—21no—
1114#123—711no—
1115#123—711no—
1116#123—1421no—
1117#123—1421no—
1118#123—1421no—
1119#123—1421no—
1120#123—1421no—
1121#123—1421no—
1122#123—1421no—
1123#123—1421no—
1124#123—1421no—
1125#123—1421no—
1126#123—1421no—
1127C22⋊Q8—21no—
1128C22⋊Q8—711no—
1129C22⋊Q8—711no—
1130C22⋊Q8—711no—
1131C22⋊Q8—711no—
1132C22⋊Q8—711no—
1133C22⋊Q8—711no—
1134C22⋊Q8—711no—
1135C22⋊Q8—711no—
1136C22⋊Q8—1421no—
1137C22⋊Q8—1421no—
1138C22⋊Q8—1421no—
1139C22⋊Q8—1421no—
1140C22⋊Q8—1421no—
1141C22⋊Q8—1421no—
1142C22⋊Q8—1421no—
1143C22⋊Q8—1421no—
1144C22⋊Q8—1421no—
1145C22⋊Q8—1421no—
1146C22⋊Q8—1421no—
1147C22⋊Q8C22×D7111yescharacteristic
1148C22⋊Q8C22×D7111yescharacteristic
1149#121—711no—
1150#121—711no—
1151#121—711no—
1152#121—711no—
1153#121—711no—
1154#121—711no—
1155#121—711no—
1156#121—711no—
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#121C22×D7111yescharacteristic
1166#121C22×D7111yescharacteristic
1167#120—711no—
1168#120—711no—
1169#120—1421no—
1170#120—1421no—
1171C4×Q8—711no—
1172C4×Q8—711no—
1173C4×Q8—711no—
1174C4×Q8—1421no—
1175C4×Q8—1421no—
1176C4×Q8—1421no—
1177C4×Q8—1421no—
1178C4×Q8—1421no—
1179C4×Q8—1421no—
1180C4×Q8C22×D7111yescharacteristic
1181C4×D4—711no—
1182C4×D4—711no—
1183C4×D4—711no—
1184C4×D4—711no—
1185C4×D4—711no—
1186C4×D4—711no—
1187C4×D4—1421no—
1188C4×D4—1421no—
1189C4×D4—1421no—
1190C4×D4—1421no—
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
1203#117—21no—
1204#117—711no—
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—1421no—
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#117C22×D7111yescharacteristic
1228C2×C4⋊C4—711no—
1229C2×C4⋊C4—711no—
1230C2×C4⋊C4—711no—
1231C2×C4⋊C4—711no—
1232C2×C4⋊C4—711no—
1233C2×C4⋊C4—711no—
1234C2×C4⋊C4—711no—
1235C2×C4⋊C4—1421no—
1236C2×C4⋊C4C22×D7111yescharacteristic
1237C2×C4⋊C4C22×D7111yescharacteristic
1238C2×C4⋊C4C22×D7111yescharacteristic
1239C2×C22⋊C4—1421no—
1240C2×C22⋊C4—1421no—
1241C2×C22⋊C4—1421no—
1242C2×C22⋊C4—1421no—
1243C2×C22⋊C4—1421no—
1244C2×C22⋊C4—1421no—
1245C2×C42—1421no—
1246C2×C42—1421no—
1247#107—711no—
1248#107—711no—
1249#107—711no—
1250#107—711no—
1251#107—711no—
1252#107—711no—
1253#107—711no—
1254#107—711no—
1255#107—711no—
1256#107—711no—
1257#107—711no—
1258#107—711no—
1259#107—711no—
1260#107—711no—
1261#107C22×D7111yescharacteristic
1262#107C22×D7111yescharacteristic
1263#107C22×D7111yescharacteristic
1264#107C22×D7111yescharacteristic
1265#107C22×D7111yescharacteristic
1266#107C22×D7111yescharacteristic
1267#106—711no—
1268#106—711no—
1269#106—711no—
1270#106—711no—
1271#106—711no—
1272#106—711no—
1273#106—711no—
1274#106—711no—
1275#106—711no—
1276#106—711no—
1277#106—711no—
1278#106—711no—
1279#106—711no—
1280#106C22×D7111yescharacteristic
1281#106C22×D7111yescharacteristic
1282#106C22×D7111yescharacteristic
1283C4⋊C8—711no—
1284C4⋊C8—711no—
1285C4⋊C8—711no—
1286C4⋊C8C22×D7111yescharacteristic
1287#103—711no—
1288#103—711no—
1289#103—711no—
1290#103—711no—
1291#103—711no—
1292#103—711no—
1293#103—711no—
1294#103—711no—
1295#103—711no—
1296#103C22×D7111yescharacteristic
1297#103C22×D7111yescharacteristic
1298#103C22×D7111yescharacteristic
1299#102—711no—
1300#102—711no—
1301#102—711no—
1302#102—711no—
1303#102—711no—
1304#102—711no—
1305#102—711no—
1306#102—711no—
1307#102—711no—
1308#102C22×D7111yescharacteristic
1309#102C22×D7111yescharacteristic
1310#102C22×D7111yescharacteristic
1311C22⋊C8—711no—
1312C22⋊C8—711no—
1313C22⋊C8—711no—
1314C22⋊C8—711no—
1315C22⋊C8—711no—
1316C22⋊C8—711no—
1317C22⋊C8C22×D7111yescharacteristic
1318C22⋊C8C22×D7111yescharacteristic
1319#97—711no—
1320#97C22×D7111yescharacteristic
1321C4×C8—711no—
1322C4×C8—711no—
1323C24—711no—
1324C24—1421no—
1325#41—82no—
1326#41—5682no—
1327#41—1422no—
1328#41—1422no—
1329C2×Q8—21no—
1330C2×Q8—711no—
1331C2×Q8—711no—
1332C2×Q8—1421no—
1333C2×Q8—1421no—
1334C2×Q8—1421no—
1335C2×Q8—1422no—
1336C2×Q8—1422no—
1337C2×Q8—1421no—
1338C2×Q8C23×D7111yescharacteristic
1339C2×D4—21no—
1340C2×D4—21no—
1341C2×D4—5682no—
1342C2×D4—711no—
1343C2×D4—711no—
1344C2×D4—711no—
1345C2×D4—711no—
1346C2×D4—711no—
1347C2×D4—711no—
1348C2×D4—711no—
1349C2×D4—1421no—
1350C2×D4—1421no—
1351C2×D4—1422no—
1352C2×D4—1422no—
1353C2×D4—1421no—
1354C2×D4—1421no—
1355C2×D4—1421no—
1356C2×D4—1421no—
1357C2×D4—1421no—
1358C2×D4D4×D7111yescharacteristic
1359C2×D4C23×D7111yescharacteristic
1360C22×C4—21no—
1361C22×C4—21no—
1362C22×C4—21no—
1363C22×C4—21no—
1364C22×C4—711no—
1365C22×C4—711no—
1366C22×C4—711no—
1367C22×C4—711no—
1368C22×C4—711no—
1369C22×C4—711no—
1370C22×C4—1421no—
1371C22×C4—1421no—
1372C22×C4—1421no—
1373C22×C4—1421no—
1374C22×C4—1421no—
1375C22×C4—1421no—
1376C22×C4—1421no—
1377C22×C4—1421no—
1378C22×C4—1422no—
1379C22×C4—1422no—
1380C22×C4—1421no—
1381C22×C4—1421no—
1382C22×C4—1421no—
1383C22×C4C23×D7111yescharacteristic
1384C22×C4C23×D7111yescharacteristic
1385SD16—22no—
1386SD16—1422no—
1387SD16—1422no—
1388SD16—1422no—
1389M16—22no—
1390M16—1422no—
1391M16—1422no—
1392M16—1422no—
1393M16—1422no—
1394M16—1422no—
1395M16—1422no—
1396M16—1422no—
1397C2×C8—22no—
1398C2×C8—711no—
1399C2×C8—714no—
1400C2×C8—711no—
1401C2×C8—711no—
1402C2×C8—711no—
1403C2×C8—1422no—
1404C2×C8—1422no—
1405C2×C8C23×D7111yescharacteristic
1406C2×C8C23×D7111yescharacteristic
1407C2×C8C23×D7111yescharacteristic
1408C2×C8C23×D7111yescharacteristic
1409C4⋊C4—21no—
1410C4⋊C4—21no—
1411C4⋊C4—21no—
1412C4⋊C4—21no—
1413C4⋊C4—21no—
1414C4⋊C4—21no—
1415C4⋊C4—21no—
1416C4⋊C4—21no—
1417C4⋊C4—21no—
1418C4⋊C4—711no—
1419C4⋊C4—711no—
1420C4⋊C4—711no—
1421C4⋊C4—711no—
1422C4⋊C4—711no—
1423C4⋊C4—711no—
1424C4⋊C4—711no—
1425C4⋊C4—711no—
1426C4⋊C4—711no—
1427C4⋊C4—711no—
1428C4⋊C4—711no—
1429C4⋊C4—1421no—
1430C4⋊C4—1421no—
1431C4⋊C4—1421no—
1432C4⋊C4—1421no—
1433C4⋊C4—1421no—
1434C4⋊C4—1421no—
1435C4⋊C4—1421no—
1436C4⋊C4—1421no—
1437C4⋊C4—1421no—
1438C4⋊C4—1421no—
1439C4⋊C4—1421no—
1440C4⋊C4—1421no—
1441C4⋊C4—1421no—
1442C4⋊C4—1421no—
1443C4⋊C4—1421no—
1444C4⋊C4—1421no—
1445C4⋊C4—1421no—
1446C4⋊C4—1421no—
1447C4⋊C4—1421no—
1448C4⋊C4—1421no—
1449C4⋊C4—1421no—
1450C4⋊C4—1421no—
1451C4⋊C4—1421no—
1452C4⋊C4—1421no—
1453C4⋊C4—1421no—
1454C4⋊C4D4×D7111yescharacteristic
1455C4⋊C4C23×D7111yescharacteristic
1456C4⋊C4C23×D7111yescharacteristic
1457C4⋊C4C23×D7111yescharacteristic
1458C4⋊C4C23×D7111yescharacteristic
1459C4⋊C4C23×D7111yescharacteristic
1460C4⋊C4C23×D7111yescharacteristic
1461C22⋊C4—21no—
1462C22⋊C4—21no—
1463C22⋊C4—21no—
1464C22⋊C4—21no—
1465C22⋊C4—21no—
1466C22⋊C4—21no—
1467C22⋊C4—711no—
1468C22⋊C4—711no—
1469C22⋊C4—711no—
1470C22⋊C4—711no—
1471C22⋊C4—711no—
1472C22⋊C4—711no—
1473C22⋊C4—711no—
1474C22⋊C4—711no—
1475C22⋊C4—1421no—
1476C22⋊C4—1421no—
1477C22⋊C4—1421no—
1478C22⋊C4—1421no—
1479C22⋊C4—1421no—
1480C22⋊C4—1421no—
1481C22⋊C4—1421no—
1482C22⋊C4—1421no—
1483C22⋊C4—1421no—
1484C22⋊C4—1421no—
1485C22⋊C4—1421no—
1486C22⋊C4—1421no—
1487C22⋊C4—1421no—
1488C22⋊C4—1421no—
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⋊C4D4×D7111yescharacteristic
1502C22⋊C4D4×D7111yescharacteristic
1503C42—21no—
1504C42—21no—
1505C42—711no—
1506C42—1421no—
1507C42—1421no—
1508C42—1421no—
1509C42—1421no—
1510C42—1421no—
1511C42—1421no—
1512C42—1421no—
1513C42—1421no—
1514C42—1421no—
1515C42—1421no—
1516C42—1421no—
1517C42—1421no—
1518C42—1421no—
1519C42—1421no—
1520C42C23×D7111yescharacteristic
1521C23—21no—
1522C23—2841no—
1523C23—2841no—
1524C23—2842no—
1525C23—5681no—
1526C23—5681no—
1527C23—711no—
1528C23—711no—
1529C23—711no—
1530C23—1422no—
1531C23—1421no—
1532C23C2×D4×D7111yescharacteristic
1533C23C2×D4×D7111yescharacteristic
1534Q8—21no—
1535Q8—21no—
1536Q8—81no—
1537Q8—2842no—
1538Q8—5681no—
1539Q8—5681no—
1540Q8—5681no—
1541Q8—1422no—
1542Q8—1421no—
1543Q8—1421no—
1544D4—21no—
1545D4—21no—
1546D4—41no—
1547D4—42no—
1548D4—81no—
1549D4—2841no—
1550D4—2842no—
1551D4—2842no—
1552D4—2841no—
1553D4—2841no—
1554D4—5681no—
1555D4—5681no—
1556D4—5681no—
1557D4—5681no—
1558D4—5681no—
1559D4—1422no—
1560D4—1422no—
1561D4—1422no—
1562D4—1421no—
1563D4—1421no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—42no—
1576C2×C4—81no—
1577C2×C4—81no—
1578C2×C4—81no—
1579C2×C4—2842no—
1580C2×C4—2842no—
1581C2×C4—5681no—
1582C2×C4—5681no—
1583C2×C4—5681no—
1584C2×C4—5681no—
1585C2×C4—5681no—
1586C2×C4—5681no—
1587C2×C4—5681no—
1588C2×C4—5681no—
1589C2×C4—5681no—
1590C2×C4—711no—
1591C2×C4—712no—
1592C2×C4—712no—
1593C2×C4—711no—
1594C2×C4—711no—
1595C2×C4—711no—
1596C2×C4—711no—
1597C2×C4—1422no—
1598C2×C4—1422no—
1599C2×C4—1421no—
1600C2×C4—1421no—
1601C2×C4—1421no—
1602C2×C4—1421no—
1603C2×C4—1421no—
1604C2×C4—1421no—
1605C2×C4—1421no—
1606C2×C4—1422no—
1607C2×C4—1421no—
1608C2×C4—1421no—
1609C2×C4—1421no—
1610C2×C4—1421no—
1611C2×C4C2×D4×D7111yescharacteristic
1612C2×C4C2×D4×D7111yescharacteristic
1613C2×C4C2×D4×D7111yescharacteristic
1614C2×C4C2×D4×D7111yescharacteristic
1615C2×C4C24×D7111yescharacteristic
1616C8—21no—
1617C8—21no—
1618C8—21no—
1619C8—712no—
1620C8—1421no—
1621C8—1421no—
1622C8—1421no—
1623C8#41×D7112yes—
1624C22—21no—
1625C22—21no—
1626C22—21no—
1627C22—21no—
1628C22—21no—
1629C22—21no—
1630C22—41no—
1631C22—41no—
1632C22—41no—
1633C22—2841no—
1634C22—2841no—
1635C22—2841no—
1636C22—5682no—
1637C22—712no—
1638C22—11362no—
1639C22—1421no—
1640C22—1421no—
1641C22—1421no—
1642C22—1421no—
1643C22—1421no—
1644C22—1421no—
1645C22—1421no—
1646C22—1421no—
1647C22C22×D4×D7111yescharacteristic
1648C4—21no—
1649C4—21no—
1650C4—21no—
1651C4—21no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4—41no—
1657C4—41no—
1658C4—41no—
1659C4—2841no—
1660C4—2841no—
1661C4—2841no—
1662C4—2841no—
1663C4—2841no—
1664C4—2841no—
1665C4—2841no—
1666C4—712no—
1667C4—1421no—
1668C4—1421no—
1669C4—1421no—
1670C4—1421no—
1671C4C2×#41×D7111yescharacteristic
1672C42−1+4×D7111yescharacteristic
1673C2—41no—
1674C2—41no—
1675C2—81no—
1676C2—2841no—
1677C2—2841no—
1678C2—5681no—
1679C2—1422no—
1680C2#547×D7111yescharacteristic
1681C2#2260311611yescharacteristic
1682C2#2260312511yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3343C2
socleC22×C71C23×D4
prime radical#22602064C2
hypercenter#3343D71
hypocenterC71#61268
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3343

Complements

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

NH ≅ G/Ntype
1. #22602091C2semidirect
3. #22600963C2semidirect
4. #22600959C2semidirect
5. #22600924C2semidirect
6. #22600917C2semidirect
7. #22600907C2semidirect
8. #22600903C2semidirect
9. #22600900C2semidirect
10. #22600893C2semidirect
11. #22600887C2semidirect
12. #22600880C2semidirect
13. #22600861C2semidirect
14. #22600854C2semidirect
15. #22600830C2semidirect
16. #22600821C2semidirect
17. #22600781C2semidirect
18. #22598875C2semidirect
19. #22598302C2semidirect
20. #22598291C2semidirect
21. #22598285C2semidirect
22. #22598279C2semidirect
23. #22598177C2semidirect
24. #22598170C2semidirect
25. #22597974C2semidirect
26. #468×D71C2semidirect
27. #22597196C2semidirect
28. #22597038C2semidirect
29. #22596936C2semidirect
30. #22596927C2semidirect
31. C71×#3343C2semidirect
35. #17986720C22semidirect
36. #17986719C22semidirect
39. #17986709C22semidirect
40. #17986704C22semidirect
46. #17986688C22semidirect
47. #17986687C22semidirect
48. #17986683C22semidirect
78. #17986408C22semidirect
79. #17986407C22semidirect
80. #17986406C22semidirect
81. #17986403C22semidirect
82. #17986402C22semidirect
83. #17986399C22semidirect
84. #17986398C22semidirect
85. #17986343C22semidirect
86. #17986342C22semidirect
87. #17986342C22semidirect
88. #17986341C22semidirect
89. #17986338C22semidirect
90. #17986338C22semidirect
91. #17986338C22semidirect
92. #17986337C22semidirect
93. #17986334C22semidirect
94. #17986334C22semidirect
95. #17986333C22semidirect
96. #17986331C22semidirect
97. #17986330C22semidirect
98. #17986327C22semidirect
99. #17986326C22semidirect
101. #17986324C22semidirect
103. #17986321C22semidirect
105. #17986320C22semidirect
107. #17986317C22semidirect
109. #17986316C22semidirect
111. #17986314C22semidirect
113. #17986308C22semidirect
114. #17986307C22semidirect
115. #17986306C22semidirect
116. #17986305C22semidirect
117. #17986301C22semidirect
118. #17986298C22semidirect
119. #17986296C22semidirect
120. #17986293C22semidirect
121. #17986290C22semidirect
122. #17986287C22semidirect
123. #17986282C22semidirect
124. #17986281C22semidirect
125. #17986279C22semidirect
126. #17986278C22semidirect
128. #17986248C22semidirect
130. #17986247C22semidirect
134. #17986244C22semidirect
136. #17986243C22semidirect
138. #17986229C22semidirect
139. #17986228C22semidirect
140. #17986225C22semidirect
141. #17986101C22semidirect
142. #17986100C22semidirect
143. #17986098C22semidirect
144. #17986090C22semidirect
145. C4×#11765852C22semidirect
146. C4×#11765853C22semidirect
147. #17986084C22semidirect
148. #17986077C22semidirect
149. #17986076C22semidirect
150. #17986074C22semidirect
151. #17986074C22semidirect
152. #17986072C22semidirect
153. #17986070C22semidirect
154. #17986068C22semidirect
155. #17986042C22semidirect
156. #17986041C22semidirect
160. #17986040C22semidirect
161. #17986040C22semidirect
162. #17986040C22semidirect
163. #17986040C22semidirect
164. #17986039C22semidirect
165. #17986039C22semidirect
166. #17986039C22semidirect
168. #17986038C22semidirect
169. #17986038C22semidirect
170. #17986037C22semidirect
173. #17986036C22semidirect
177. #107×D71C22semidirect
188. #552×C71C22semidirect
190. #501×C71C22semidirect
191. #484×C71C22semidirect
192. #483×C71C22semidirect
194. #480×C71C22semidirect
195. #478×C71C22semidirect
196. #477×C71C22semidirect
198. #465×C71C22semidirect
199. #440×C71C22semidirect
200. #435×C71C22semidirect
201. #428×C71C22semidirect
202. C2×#107×C71C22semidirect
546. C8×D71#41semidirect
859. #3343D71semidirect
873. C71#61268semidirect
892. #552C2×D71semidirect
925. #501C2×D71semidirect
941. #484C2×D71semidirect
945. #483C2×D71semidirect
961. #480C2×D71semidirect
969. #478C2×D71semidirect
971. #477C2×D71semidirect
993. #465C2×D71semidirect
997. #440C2×D71semidirect
1009. #435C2×D71semidirect
1025. #428C2×D71semidirect
1034. C2×#107C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226020912
#226020642
#226009632
#226009592
#226009242
#226009172
#226009072
#226009032
#226009002
#226008932
#226008872
#226008802
#226008612
#226008542
#226008302
#226008212
#226007812
#225988752
#225983022
#225982912
#225982852
#225982792
#225981772
#225981702
#225979742
#468×D712
#225971962
#225970382
#225969362
#225969272
C71×#33432
#6126871