Finite Group Databasebeta

← #32013785

Subgroups — #32013785

Order 18176.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986071C211yesmaximal, characteristic
2#22591269C211yesmaximal, characteristic
3#22589314C211yesmaximal, characteristic, complemented
4#22589289C211yesmaximal, characteristic, complemented
5#22588774C211yesmaximal, characteristic, complemented
6#22588764C211yesmaximal, characteristic, complemented
7#22588653C211yesmaximal, characteristic, complemented
8#22588648C211yesmaximal, characteristic, complemented
9#22588435C211yesmaximal, characteristic, complemented
10#22588435C211yesmaximal, characteristic, complemented
11#22588355C211yesmaximal, characteristic, complemented
12#22588170C211yesmaximal, characteristic, complemented
13#22588061C211yesmaximal, characteristic, complemented
14#22588056C211yesmaximal, characteristic, complemented
15C2×#556×C71C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×#14556087C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20#17986071—24no—
21C2×C4⋊(C71⋊C8)C2211yescharacteristic
22C2×#14556052C2211yescharacteristic
23C2×#14556052C2211yescharacteristic
24C2×#14556052C2211yescharacteristic
25C2×#14556052C2211yescharacteristic
26C2×C22⋊(C71⋊C8)C2211yescharacteristic
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×#14556039C2211yescharacteristic
29#17985892—21no—
30#17985885—21no—
31#17985879—21no—
32#17985865C2211yescharacteristic
33#17985859C2211yescharacteristic
34#17985859C2211yescharacteristic
35C4×C4⋊Dic71C2211yescharacteristic
36C22⋊C4×Dic71—21no—
37#17985761C2211yescharacteristic
38#17985761C2211yescharacteristic
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#556×C71—24no—
50#556×C71C418yescomplemented
51C2×C4⋊Q8×C71C2211yescharacteristic
52C2×#126×C71—21no—
53C2×#126×C71—21no—
54C2×#124×C71—21no—
55C2×C22⋊Q8×C71C2211yescharacteristic
56C2×C22⋊Q8×C71C2211yescharacteristic
57C2×C4×Q8×C71—21no—
58C2×C4×Q8×C71C2211yescharacteristic
59C2×C4×D4×C71C2211yescharacteristic
60C2×#117×C71C2211yescharacteristic
61C2×#117×C71C2211yescharacteristic
62C23×Dic71—21no—
63C2×#11765849—22no—
64C2×#11765849—22no—
65C2×#11765849—41no—
66C22×C71⋊C8—22no—
67C22×C71⋊C8—22no—
68C22×C71⋊C8—41no—
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73#14556087—22no—
74#14556087—41no—
75C2×C4⋊Dic71—22no—
76C2×C4⋊Dic71—21no—
77C2×C4⋊Dic71—41no—
78C2×C4⋊Dic71C2311yescharacteristic
79C2×C4⋊Dic71C2311yescharacteristic
80C2×C4⋊Dic71C2311yescharacteristic
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C22⋊Dic71—21no—
83C2×C22⋊Dic71—21no—
84C2×C22⋊Dic71—21no—
85C2×C4×Dic71—21no—
86C2×C4×Dic71—21no—
87C4⋊(C71⋊C8)—22no—
88#14556052—22no—
89#14556052—22no—
90#14556052—41no—
91#14556052—41no—
92C22⋊(C71⋊C8)—22no—
93C22⋊(C71⋊C8)—22no—
94#14556039—22no—
95C71⋊#95—21no—
96C71⋊#95—21no—
97C71⋊#95—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C22×Q8×C71—21no—
101C22×Q8×C71C2311yescharacteristic
102C22×D4×C71D411yescharacteristic
103C23×C4×C71C2311yescharacteristic
104C23×C4×C71C2311yescharacteristic
105C4⋊Q8×C71—22no—
106C4⋊Q8×C71C2×C414yescomplemented
107#126×C71—28no—
108#126×C71—28no—
109#124×C71—28no—
110C22⋊Q8×C71—22no—
111C22⋊Q8×C71—22no—
112C22⋊Q8×C71C2×C414yes—
113C22⋊Q8×C71C2×C414yescomplemented
114C4×Q8×C71—28no—
115C4×Q8×C71—22no—
116C4×Q8×C71C2×C414yescomplemented
117C4×D4×C71C2×C414yes—
118C4×D4×C71D414yes—
119#117×C71—22no—
120#117×C71—22no—
121#117×C71C2×C414yes—
122#117×C71C2×C414yescomplemented
123C2×C4⋊C4×C71—21no—
124C2×C4⋊C4×C71—21no—
125C2×C4⋊C4×C71—21no—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71D411yescharacteristic
128C2×C4⋊C4×C71C2311yescharacteristic
129C2×C4⋊C4×C71C2311yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C22⋊C4×C71—21no—
132C2×C22⋊C4×C71—21no—
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71D411yescharacteristic
136C2×C22⋊C4×C71D411yescharacteristic
137C2×C42×C71—21no—
138C2×C42×C71—21no—
139C2×C42×C71—21no—
140C2×C42×C71C2311yescharacteristic
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C22×Dic71—42no—
146C22×Dic71—42no—
147C22×Dic71—81no—
148#11765849—44no—
149C2×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—44no—
161C2×C71⋊C8#4112yes—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—21no—
168C4⋊Dic71—21no—
169C4⋊Dic71—42no—
170C4⋊Dic71#4112yes—
171C22⋊Dic71—42no—
172C22⋊Dic71—42no—
173C22⋊Dic71—81no—
174C4×Dic71—42no—
175C4×Dic71—81no—
176C24×C71C2×D411yescharacteristic
177C24×C71C2×D411yescharacteristic
178C2×Q8×C71—24no—
179C2×Q8×C71—21no—
180C2×Q8×C71—21no—
181C2×Q8×C71—21no—
182C2×Q8×C71—21no—
183C2×Q8×C71—21no—
184C2×Q8×C71—42no—
185C2×Q8×C71—42no—
186C2×Q8×C71C22×C412yes—
187C2×D4×C71—41no—
188C2×D4×C71—41no—
189C2×D4×C71C22⋊C414yes—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71C22×C412yes—
203C22×C4×C71C22×C412yes—
204C22×C4×C71C2×D411yescharacteristic
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D412yes—
209C22×C4×C71C2×D412yes—
210C22×C4×C71C2411yescharacteristic
211C4⋊C4×C71—24no—
212C4⋊C4×C71—24no—
213C4⋊C4×C71—24no—
214C4⋊C4×C71—24no—
215C4⋊C4×C71—21no—
216C4⋊C4×C71—21no—
217C4⋊C4×C71—21no—
218C4⋊C4×C71C22⋊C414yes—
219C4⋊C4×C71C22×C412yes—
220C4⋊C4×C71C22×C412yes—
221C4⋊C4×C71C22×C412yes—
222C22⋊C4×C71—24no—
223C22⋊C4×C71—24no—
224C22⋊C4×C71—24no—
225C22⋊C4×C71—24no—
226C22⋊C4×C71C22⋊C414yes—
227C22⋊C4×C71C22⋊C414yes—
228C42×C71—24no—
229C42×C71—24no—
230C42×C71—24no—
231C42×C71C22×C412yes—
232C42×C71C2×D412yes—
233C23×C71—21no—
234C23×C71—21no—
235C23×C71—21no—
236C23×C71—21no—
237C23×C71—21no—
238C23×C71—21no—
239C23×C71—21no—
240C23×C71—21no—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71C2×C22⋊C412yes—
246C23×C71C2×C22⋊C412yes—
247C23×C71C22×D411yescharacteristic
248Q8×C71—22no—
249Q8×C71—22no—
250Q8×C71—48no—
251Q8×C71—41no—
252Q8×C71—41no—
253D4×C71—44no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—21no—
261C2×C4×C71—21no—
262C2×C4×C71—22no—
263C2×C4×C71—22no—
264C2×C4×C71—22no—
265C2×C4×C71—22no—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—41no—
275C2×C4×C71—41no—
276C2×C4×C71—41no—
277C2×C4×C71—41no—
278C2×C4×C71—41no—
279C2×C4×C71—41no—
280C2×C4×C71—41no—
281C2×C4×C71—41no—
282C2×C4×C71C2×C22⋊C412yes—
283C2×C4×C71C2×C22⋊C412yes—
284C2×C4×C71C2×C22⋊C412yes—
285C2×C4×C71C2×C22⋊C412yes—
286C2×C4×C71C23×C411yescharacteristic
287C2×C4×C71C22×D411yescharacteristic
288C2×C4×C71C2×#4111yescharacteristic
289C2×C4×C71C2×#4111yescharacteristic
290C2×C4×C71H(5,𝔽2)11yescharacteristic
291C2×C4×C712−1+411yescharacteristic
292C2×Dic71—22no—
293C2×Dic71—41no—
294C2×Dic71—41no—
295C2×Dic71—41no—
296C2×Dic71—41no—
297C2×Dic71—41no—
298C2×Dic71—41no—
299C2×Dic71—41no—
300C2×Dic71—41no—
301C2×Dic71—41no—
302C2×Dic71—41no—
303C2×Dic71—41no—
304C2×Dic71—84no—
305C71⋊C8—22no—
306C71⋊C8—41no—
307C71⋊C8—41no—
308C71⋊C8—41no—
309C22×C71—22no—
310C22×C71—22no—
311C22×C71—22no—
312C22×C71—22no—
313C22×C71—22no—
314C22×C71—22no—
315C22×C71—41no—
316C22×C71—41no—
317C22×C71—41no—
318C22×C71—41no—
319C22×C71—41no—
320C22×C71—41no—
321C22×C71—41no—
322C22×C71—41no—
323C22×C71C22×C22⋊C411yescharacteristic
324C22×C71#54611yescharacteristic
325C22×C71#54711yescharacteristic
326C22×C71#57511yescharacteristic
327C22×C71#57511yescharacteristic
328C22×C71#57711yescharacteristic
329C22×C71#57811yescharacteristic
330C4×C71—22no—
331C4×C71—22no—
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—42no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71—42no—
338C4×C71C4×#4111yescharacteristic
339C4×C71#52011yescharacteristic
340C4×C71#54611yescharacteristic
341C4×C71#54711yescharacteristic
342Dic71—42no—
343Dic71—81no—
344Dic71—81no—
345Dic71—81no—
346#22494—711nomaximal, Sylow
347C2×C71—42no—
348C2×C71—42no—
349C2×C71#233911yescharacteristic
350C2×C71#289611yescharacteristic
351C2×C71#289811yescharacteristic
352C2×C71#331111yescharacteristic
353C2×C71#331311yescharacteristic
354C2×C71#334911yescharacteristic
355C2×C71#335011yescharacteristic
356C2×#556D7111yescharacteristic
357C2×#435—711no—
358#2352—711no—
359#1993—711no—
360#1987—711no—
361#1894—711no—
362#1892—711no—
363#1873—711no—
364#1872—711no—
365#1825—711no—
366#1825—711no—
367#1805—711no—
368#1763—711no—
369#1736—711no—
370#1735—711no—
371C71#2249411yescharacteristic, complemented, Sylow
372C22×M16—711no—
373C23×C8—711no—
374#556—24no—
375#556Dic7118yescomplemented
376C2×C4⋊Q8C2×D7111yescharacteristic
377C2×#126—21no—
378C2×#126—21no—
379C2×#124—21no—
380C2×C22⋊Q8C2×D7111yescharacteristic
381C2×C22⋊Q8C2×D7111yescharacteristic
382C2×C4×Q8—21no—
383C2×C4×Q8C2×D7111yescharacteristic
384C2×C4×D4C2×D7111yescharacteristic
385C2×#117—711no—
386C2×#117C2×D7111yescharacteristic
387C2×#117C2×D7111yescharacteristic
388C22×C4⋊C4—711no—
389#435—1424no—
390C2×C4⋊C8—711no—
391C2×#103—711no—
392C2×#103—711no—
393C2×#103—711no—
394C2×#103—711no—
395C2×C22⋊C8—711no—
396C2×C22⋊C8—711no—
397C2×#97—711no—
398#388—1421no—
399#387—1421no—
400#386—1421no—
401#382—711no—
402#380—711no—
403#380—711no—
404C4×C4⋊C4—711no—
405C4×C22⋊C4—1421no—
406#340—711no—
407#340—711no—
408#340—711no—
409#340—711no—
410#340—711no—
411#340—711no—
412#340—711no—
413#340—711no—
414#340—711no—
415#340—711no—
416#340—711no—
417#340—711no—
418C22×Q8—21no—
419C22×Q8C22×D7111yescharacteristic
420C22×D4C22⋊D7111yescharacteristic
421C23×C4—1421no—
422C23×C4C22×D7111yescharacteristic
423C23×C4C22×D7111yescharacteristic
424C2×M16—2841no—
425C2×M16—1422no—
426C2×M16—1422no—
427C22×C8—2841no—
428C22×C8—711no—
429C22×C8—711no—
430C22×C8—711no—
431C22×C8—711no—
432C22×C8—1422no—
433C22×C8—1422no—
434C4⋊Q8—22no—
435C4⋊Q8C2×Dic7114yescomplemented
436#126—28no—
437#126—28no—
438#124—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8C2×Dic7114yes—
442C22⋊Q8C2×Dic7114yescomplemented
443C4×Q8—28no—
444C4×Q8—22no—
445C4×Q8C2×Dic7114yescomplemented
446C4×D4C2×Dic7114yes—
447C4×D4C22⋊D7114yes—
448#117—22no—
449#117—22no—
450#117—2841no—
451#117—1422no—
452#117C2×Dic7114yes—
453#117C2×Dic7114yescomplemented
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—2841no—
459C2×C4⋊C4—711no—
460C2×C4⋊C4—711no—
461C2×C4⋊C4—711no—
462C2×C4⋊C4—711no—
463C2×C4⋊C4—1421no—
464C2×C4⋊C4—1422no—
465C2×C4⋊C4C22⋊D7111yescharacteristic
466C2×C4⋊C4C22×D7111yescharacteristic
467C2×C4⋊C4C22×D7111yescharacteristic
468C2×C4⋊C4C22×D7111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—1421no—
474C2×C22⋊C4—1421no—
475C2×C22⋊C4—1421no—
476C2×C22⋊C4C22⋊D7111yescharacteristic
477C2×C22⋊C4C22⋊D7111yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1421no—
482C2×C42—1421no—
483C2×C42C22×D7111yescharacteristic
484C4⋊C8—1422no—
485#103—2841no—
486#103—2841no—
487#103—1422no—
488#103—1422no—
489C22⋊C8—1422no—
490C22⋊C8—1422no—
491#97—1422no—
492#95—1421no—
493#95—1421no—
494#95—1421no—
495#95—1421no—
496#95—1421no—
497C24C2×C22⋊D7111yescharacteristic
498C24C2×C22⋊D7111yescharacteristic
499C2×Q8—21no—
500C2×Q8—24no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8C22×Dic7112yes—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4C22⋊Dic7114yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—2842no—
524C22×C4—2842no—
525C22×C4—5681no—
526C22×C4—1421no—
527C22×C4—1421no—
528C22×C4—1421no—
529C22×C4—1421no—
530C22×C4C22×Dic7112yes—
531C22×C4C22×Dic7112yes—
532C22×C4C2×C22⋊D7112yes—
533C22×C4C2×C22⋊D7112yes—
534C22×C4C2×C22⋊D7111yescharacteristic
535C22×C4C2×C22⋊D7111yescharacteristic
536C22×C4C2×C22⋊D7111yescharacteristic
537C22×C4C2×C22⋊D7111yescharacteristic
538C22×C4C23×D7111yescharacteristic
539M16—2844no—
540C2×C8—2844no—
541C2×C8—712no—
542C2×C8—1421no—
543C2×C8—1421no—
544C2×C8—1421no—
545C2×C8—1421no—
546C2×C8—1421no—
547C2×C8—1421no—
548C2×C8—1421no—
549C2×C8—1421no—
550C2×C8—1421no—
551C2×C8—1421no—
552C2×C8—1421no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—2842no—
561C4⋊C4—712no—
562C4⋊C4—1421no—
563C4⋊C4—1421no—
564C4⋊C4—1421no—
565C4⋊C4—1421no—
566C4⋊C4—1421no—
567C4⋊C4—1421no—
568C4⋊C4—1421no—
569C4⋊C4C22⋊Dic7114yes—
570C4⋊C4C22×Dic7112yes—
571C4⋊C4C22×Dic7112yes—
572C4⋊C4C22×Dic7112yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—2842no—
578C22⋊C4—2842no—
579C22⋊C4—5681no—
580C22⋊C4C22⋊Dic7114yes—
581C22⋊C4C22⋊Dic7114yes—
582C42—24no—
583C42—24no—
584C42—24no—
585C42—2842no—
586C42—5681no—
587C42C22×Dic7112yes—
588C42C2×C22⋊D7112yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×C22⋊Dic7112yes—
602C23C2×C22⋊Dic7112yes—
603C23C22×C22⋊D7111yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—48no—
607Q8—41no—
608Q8—41no—
609D4—44no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—2841no—
639C2×C4—2841no—
640C2×C4—2841no—
641C2×C4—2841no—
642C2×C4—2841no—
643C2×C4—2841no—
644C2×C4—2841no—
645C2×C4—2841no—
646C2×C4—2841no—
647C2×C4—2841no—
648C2×C4—2841no—
649C2×C4—5684no—
650C2×C4—1422no—
651C2×C4C2×C22⋊Dic7112yes—
652C2×C4C2×C22⋊Dic7112yes—
653C2×C4C2×C22⋊Dic7112yes—
654C2×C4C2×C22⋊Dic7112yes—
655C2×C4C23×Dic7111yescharacteristic
656C2×C4C22×C22⋊D7111yescharacteristic
657C2×C4#41×D7111yescharacteristic
658C2×C4#41×D7111yescharacteristic
659C2×C4#1455617411yescharacteristic
660C2×C4#1455617511yescharacteristic
661C8—2841no—
662C8—2841no—
663C8—2841no—
664C8—1422no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×C22⋊Dic7111yescharacteristic
680C22#1798663711yescharacteristic
681C22#1798664811yescharacteristic
682C22#1798679711yescharacteristic
683C22#1798679711yescharacteristic
684C22#1798680711yescharacteristic
685C22#1798681411yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—2842no—
695C4—5681no—
696C4—5681no—
697C4—5681no—
698C4#41×Dic7111yescharacteristic
699C4#1798648211yescharacteristic
700C4#1798663711yescharacteristic
701C4#1798664811yescharacteristic
702C2—42no—
703C2—42no—
704C2#2259117011yescharacteristic
705C2#2259685911yescharacteristic
706C2#2259687311yescharacteristic
707C2#2260037011yescharacteristic
708C2#2260040011yescharacteristic
709C2#2260086411yescharacteristic
710C2#2260088511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#556×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71D4
cosocleC22×C4×C71C24
hypercenterC2×#556D71
hypocenterC71#22494
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
3. #22589314C2semidirect
4. #22589289C2semidirect
5. #22588774C2semidirect
6. #22588764C2semidirect
7. #22588653C2semidirect
8. #22588648C2semidirect
9. #22588435C2semidirect
10. #22588435C2semidirect
11. #22588355C2semidirect
12. #22588170C2semidirect
13. #22588061C2semidirect
14. #22588056C2semidirect
50. #556×C71C4semidirect
106. C4⋊Q8×C71C2×C4semidirect
113. C22⋊Q8×C71C2×C4semidirect
116. C4×Q8×C71C2×C4semidirect
122. #117×C71C2×C4semidirect
371. C71#22494semidirect
375. #556Dic71semidirect
435. C4⋊Q8C2×Dic71semidirect
442. C22⋊Q8C2×Dic71semidirect
445. C4×Q8C2×Dic71semidirect
453. #117C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860712
#225912692
#225893142
#225892892
#225887742
#225887642
#225886532
#225886482
#225884352
#225883552
#225881702
#225880612
#225880562
C2×#556×C712
#2249471