Finite Group Databasebeta

← C2×#22600436 #32874106

Subgroups — C2×#22600436 #32874106

Order 18176.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986689C211yesmaximal, characteristic, complemented
2#22600436C2116yesmaximal, direct product factor
3C2×#17986367C211yesmaximal, characteristic, complemented
4C2×#17986332C211yesmaximal, characteristic, complemented
5C2×#17986337C211yesmaximal, characteristic, complemented
6C2×#17986299C211yesmaximal, characteristic, complemented
7C2×#17986255C211yesmaximal, characteristic, complemented
8C2×#17986238C211yesmaximal, characteristic, complemented
9C2×#17986206C211yesmaximal, characteristic, complemented
10C2×#17986161C211yesmaximal, characteristic, complemented
11C2×#17986161C211yesmaximal, characteristic, complemented
12C2×#17986099C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986000C211yesmaximal, characteristic, complemented
15C2×#17985995C211yesmaximal, characteristic, complemented
16C2×#547×C71C211yesmaximal, characteristic
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765849C2211yescharacteristic
21C23×C71⋊C8C2211yescharacteristic
22#17986689—24no—
23#17986689C2218yescomplemented
24C2×#14556121—21no—
25C2×#14556120C2211yescharacteristic
26C2×#14556118—21no—
27C2×#14556109—21no—
28C2×#14556107C2211yescharacteristic
29C2×#14556107C2211yescharacteristic
30C2×C4×Dic142C2211yescharacteristic
31C2×#14556087C2211yescharacteristic
32C2×#14556084—21no—
33C22×C4⋊Dic71C2211yescharacteristic
34#17986367C2218yescomplemented
35#17986337C2218yescomplemented
36#17986332C2218yescomplemented
37#17986299C2218yescomplemented
38#17986255C2218yescomplemented
39#17986238C2218yescomplemented
40#17986206C2218yescomplemented
41#17986161C2218yescomplemented
42#17986161C2218yescomplemented
43#17986099C2218yescomplemented
44#17986071C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49#17986000C2218yescomplemented
50#17985995C2218yescomplemented
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556049C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65C22×#41×C71C2211yescharacteristic
66#547×C71—24no—
67#547×C71C2218yes—
68C2×C4⋊Q8×C71C2211yescharacteristic
69C2×#123×C71—21no—
70C2×#123×C71—21no—
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×#121×C71—21no—
74C2×C4×D4×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C22×C4⋊C4×C71—21no—
77C22×Dic142C2311yescharacteristic
78C23×Dic71—21no—
79C2×#11765855—42no—
80C2×#11765855—42no—
81C2×#11765855C2314yes—
82C2×#11765855C2314yes—
83C2×#11765853—24no—
84C2×#11765853C2314yes—
85C2×#11765849—42no—
86C2×#11765849C2314yes—
87C22×C71⋊C8—42no—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2314yes—
93#14556121—28no—
94#14556120—22no—
95#14556120C2314yes—
96#14556118—28no—
97#14556109—28no—
98#14556107—22no—
99#14556107—22no—
100#14556107C2314yes—
101#14556107C2314yes—
102C4×Dic142—22no—
103C4×Dic142C2314yes—
104#14556087—22no—
105#14556087C2314yes—
106#14556084—28no—
107C2×C4⋊Dic71—22no—
108C2×C4⋊Dic71—21no—
109C2×C4⋊Dic71C2314yes—
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×C4⋊Dic71C2311yescharacteristic
113C2×Dic71⋊C4—21no—
114C2×Dic71⋊C4—21no—
115C2×Dic71⋊C4—21no—
116C2×Dic71⋊C4—21no—
117C2×Dic71⋊C4—21no—
118C2×C22⋊Dic71—21no—
119C2×C22⋊Dic71—21no—
120C2×C22⋊Dic71—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71—21no—
123#14556061C2314yes—
124#14556061C2314yes—
125#14556059C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556052C2314yes—
128#14556052C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556052C2314yes—
133#14556051C2314yes—
134#14556049C2314yes—
135#14556049C2314yes—
136#14556049C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139#14556039C2314yes—
140C2×#41×C71—22no—
141C2×#41×C71—22no—
142C2×#41×C71—24no—
143C2×#41×C71—24no—
144C2×#41×C71—42no—
145C2×#41×C71—42no—
146C2×#41×C71C2314yes—
147C2×#41×C71C2314yes—
148C22×Q8×C71C2311yescharacteristic
149C22×Q8×C71C2311yescharacteristic
150C22×D4×C71—21no—
151C22×D4×C71—21no—
152C22×D4×C71D411yescharacteristic
153C22×D4×C71C2311yescharacteristic
154C23×C4×C71—21no—
155C23×C4×C71—21no—
156C23×C4×C71—21no—
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159C4⋊Q8×C71—22no—
160C4⋊Q8×C71C2314yes—
161#123×C71—28no—
162#123×C71—28no—
163C22⋊Q8×C71—22no—
164C22⋊Q8×C71—22no—
165C22⋊Q8×C71C2314yes—
166C22⋊Q8×C71C2314yes—
167#121×C71—28no—
168C4×D4×C71—22no—
169C4×D4×C71D414yes—
170C4×D4×C71C2314yes—
171C4×D4×C71C2314yes—
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71—21no—
174C2×C4⋊C4×C71—21no—
175C2×C4⋊C4×C71—21no—
176C2×C4⋊C4×C71—28no—
177C2×C4⋊C4×C71D411yescharacteristic
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71—21no—
182C2×C22⋊C4×C71D411yescharacteristic
183C2×C22⋊C4×C71D411yescharacteristic
184C2×C42×C71C2311yescharacteristic
185C2×Dic142—22no—
186C2×Dic142—22no—
187C2×Dic142—21no—
188C2×Dic142C2412yes—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—24no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—44no—
195#11765855—44no—
196#11765855—44no—
197#11765853—28no—
198#11765849—44no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8—22no—
202C2×C71⋊C8—22no—
203C2×C71⋊C8—44no—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C2×C71⋊C8C2412yes—
207C2×C71⋊C8C2412yes—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71—24no—
211C4⋊Dic71—21no—
212C4⋊Dic71C2412yes—
213C4⋊Dic71C2412yes—
214C4⋊Dic71C2412yes—
215Dic71⋊C4—24no—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220C22⋊Dic71—24no—
221C22⋊Dic71—24no—
222C22⋊Dic71—24no—
223C4×Dic71—24no—
224C4×Dic71—24no—
225C24×C71—21no—
226C24×C71C2×D411yescharacteristic
227C24×C71C2×D411yescharacteristic
228#41×C71—28no—
229#41×C71—28no—
230#41×C71—44no—
231#41×C71—44no—
232#41×C71—48no—
233#41×C71—48no—
234C2×Q8×C71—21no—
235C2×Q8×C71—21no—
236C2×Q8×C71—22no—
237C2×Q8×C71—22no—
238C2×Q8×C71—22no—
239C2×Q8×C71—22no—
240C2×Q8×C71C2412yes—
241C2×Q8×C71C2412yes—
242C2×D4×C71—24no—
243C2×D4×C71—24no—
244C2×D4×C71—21no—
245C2×D4×C71—22no—
246C2×D4×C71—42no—
247C2×D4×C71—44no—
248C2×D4×C71—44no—
249C2×D4×C71C2×D414yes—
250C2×D4×C71#4114yes—
251C2×D4×C71C2412yes—
252C22×C4×C71—22no—
253C22×C4×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—24no—
260C22×C4×C71—24no—
261C22×C4×C71—24no—
262C22×C4×C71—44no—
263C22×C4×C71—44no—
264C22×C4×C71—44no—
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2×D411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D412yes—
270C22×C4×C71C2×D412yes—
271C22×C4×C71C2412yes—
272C22×C4×C71C2412yes—
273C22×C4×C71C2411yescharacteristic
274C4⋊C4×C71—24no—
275C4⋊C4×C71—24no—
276C4⋊C4×C71—24no—
277C4⋊C4×C71—24no—
278C4⋊C4×C71—21no—
279C4⋊C4×C71C2×D414yes—
280C4⋊C4×C71C2412yes—
281C22⋊C4×C71—24no—
282C22⋊C4×C71—24no—
283C22⋊C4×C71—24no—
284C22⋊C4×C71C2×D414yes—
285C22⋊C4×C71C2×D414yes—
286C42×C71C2×D412yes—
287C42×C71C2412yes—
288C23×C71—22no—
289C23×C71—22no—
290C23×C71—24no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—42no—
297C23×C71—42no—
298C23×C71C22×D412yes—
299C23×C71C22×D412yes—
300C23×C71C22×D411yescharacteristic
301Q8×C71—22no—
302Q8×C71—22no—
303Q8×C71—22no—
304Q8×C71—22no—
305Q8×C71—42no—
306Q8×C71—42no—
307D4×C71—24no—
308D4×C71—22no—
309D4×C71—44no—
310D4×C71—48no—
311D4×C71—48no—
312D4×C71C2×#4114yes—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—24no—
318C2×C4×C71—24no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—48no—
327C2×C4×C71—48no—
328C2×C4×C71—48no—
329C2×C4×C71—42no—
330C2×C4×C71—42no—
331C2×C4×C71—42no—
332C2×C4×C71C22×D412yes—
333C2×C4×C71C22×D412yes—
334C2×C4×C71C22×D412yes—
335C2×C4×C71C22×D412yes—
336C2×C4×C71C22×D411yescharacteristic
337C2×C4×C71C2×#4112yes—
338C2×C4×C71H(5,𝔽2)12yes—
339C2×C4×C71C2511yescharacteristic
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—48no—
345C2×Dic71—42no—
346C2×Dic71—42no—
347C2×Dic71—42no—
348C2×Dic71—42no—
349Dic142—22no—
350Dic142—22no—
351Dic142—42no—
352C71⋊C8—22no—
353C71⋊C8—22no—
354C71⋊C8—22no—
355C71⋊C8—22no—
356C22×C71—22no—
357C22×C71—22no—
358C22×C71—24no—
359C22×C71—22no—
360C22×C71—22no—
361C22×C71—22no—
362C22×C71—22no—
363C22×C71—44no—
364C22×C71—44no—
365C22×C71—48no—
366C22×C71—42no—
367C22×C71—42no—
368C22×C71#54612yes—
369C22×C71#57512yes—
370C22×C71#57812yes—
371C22×C71C23×D411yescharacteristic
372C4×C71—22no—
373C4×C71—22no—
374C4×C71—22no—
375C4×C71—22no—
376C4×C71—42no—
377C4×C71—42no—
378C4×C71—42no—
379C4×C71#54612yes—
380C4×C71C22×#4111yescharacteristic
381C4×C71C2×H(5,𝔽2)11yescharacteristic
382Dic71—42no—
383Dic71—42no—
384Dic71—42no—
385Dic71—42no—
386C2×#3315—711nomaximal, Sylow
387C2×C71—42no—
388C2×C71—42no—
389C2×C71—44no—
390C2×C71#331514yescomplemented
391C2×C71C2×#54611yescharacteristic
392C2×C71C2×#57511yescharacteristic
393C2×C71C2×#57811yescharacteristic
394C2×#552—711no—
395C2×#547D7111yescharacteristic
396#3315—7116no—
397C2×#491—711no—
398C2×#484—711no—
399C2×#485—711no—
400C2×#478—711no—
401C2×#470—711no—
402C2×#467—711no—
403C2×#462—711no—
404C2×#452—711no—
405C2×#452—711no—
406C2×#440—711no—
407C2×#435—711no—
408C2×#417—711no—
409C2×#416—711no—
410C71C2×#331511yescharacteristic, complemented, Sylow
411C22×#41C2×D7111yescharacteristic
412C22×#41C2×D7111yescharacteristic
413C22×Q16—711no—
414C22×Q16—711no—
415C22×SD16—711no—
416C22×M16—711no—
417C23×C8—711no—
418#552—718no—
419#552—1424no—
420#547—24no—
421#547C2×D7118yes—
422C2×C4⋊Q8C2×D7111yescharacteristic
423C2×#126—1421no—
424C2×#125—711no—
425C2×#125—1421no—
426C2×#123—21no—
427C2×#123—21no—
428C2×#123—1421no—
429C2×C22⋊Q8—711no—
430C2×C22⋊Q8—711no—
431C2×C22⋊Q8C2×D7111yescharacteristic
432C2×C22⋊Q8C2×D7111yescharacteristic
433C2×#121—21no—
434C2×C4×Q8—711no—
435C2×C4×D4C2×D7111yescharacteristic
436C2×C4×D4C2×D7111yescharacteristic
437C2×#117—711no—
438C2×#117—1421no—
439C22×C4⋊C4—21no—
440C22×C4⋊C4—711no—
441#491—718no—
442#485—718no—
443#484—718no—
444#478—718no—
445#470—718no—
446#467—718no—
447#462—718no—
448#452—718no—
449#452—718no—
450#440—718no—
451#435—718no—
452C2×#107—711no—
453C2×#107—711no—
454C2×#106—711no—
455C2×C4⋊C8—711no—
456#417—718no—
457#416—718no—
458C2×#103—711no—
459C2×#103—711no—
460C2×#103—711no—
461C2×#103—711no—
462C2×#103—711no—
463C2×#103—711no—
464C2×#103—711no—
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C2×C22⋊C8—711no—
469C2×C22⋊C8—711no—
470C2×#97—711no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—24no—
474C2×#41—24no—
475C2×#41—42no—
476C2×#41—42no—
477C2×#41C22×D7114yes—
478C2×#41C22×D7114yes—
479C22×Q8—711no—
480C22×Q8C22×D7111yescharacteristic
481C22×Q8C22×D7111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C22⋊D7111yescharacteristic
485C22×D4C22×D7111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—1421no—
490C23×C4C22×D7111yescharacteristic
491C23×C4C22×D7111yescharacteristic
492C2×Q16—2842no—
493C2×Q16—2842no—
494C2×Q16—714no—
495C2×Q16—714no—
496C2×SD16—714no—
497C2×SD16—1424no—
498C2×M16—2842no—
499C2×M16—714no—
500C22×C8—2842no—
501C22×C8—714no—
502C22×C8—711no—
503C22×C8—711no—
504C22×C8—711no—
505C22×C8—711no—
506C4⋊Q8—22no—
507C4⋊Q8C22×D7114yes—
508#126—1428no—
509#125—714no—
510#125—1428no—
511#125—1422no—
512#123—28no—
513#123—28no—
514#123—1428no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—714no—
518C22⋊Q8—714no—
519C22⋊Q8—1422no—
520C22⋊Q8—1422no—
521C22⋊Q8C22×D7114yes—
522C22⋊Q8C22×D7114yes—
523#121—28no—
524C4×Q8—714no—
525C4×Q8—1422no—
526C4×D4—22no—
527C4×D4C22⋊D7114yes—
528C4×D4C22×D7114yes—
529C4×D4C22×D7114yes—
530#117—714no—
531#117—1422no—
532#117—1428no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—28no—
538C2×C4⋊C4—711no—
539C2×C4⋊C4—711no—
540C2×C4⋊C4—714no—
541C2×C4⋊C4—711no—
542C2×C4⋊C4—1421no—
543C2×C4⋊C4—1422no—
544C2×C4⋊C4—1421no—
545C2×C4⋊C4—1421no—
546C2×C4⋊C4—1421no—
547C2×C4⋊C4—1421no—
548C2×C4⋊C4—1421no—
549C2×C4⋊C4C22⋊D7111yescharacteristic
550C2×C4⋊C4C22×D7111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C22⋊C4C22⋊D7111yescharacteristic
558C2×C22⋊C4C22⋊D7111yescharacteristic
559C2×C42—1421no—
560C2×C42—1421no—
561C2×C42C22×D7111yescharacteristic
562#107—714no—
563#107—714no—
564#106—714no—
565C4⋊C8—714no—
566#103—714no—
567#103—714no—
568#103—714no—
569#103—714no—
570#103—714no—
571#103—714no—
572#103—714no—
573#102—714no—
574#102—714no—
575#102—714no—
576C22⋊C8—714no—
577C22⋊C8—714no—
578#97—714no—
579C24—21no—
580C24C2×C22⋊D7111yescharacteristic
581C24C2×C22⋊D7111yescharacteristic
582#41—28no—
583#41—28no—
584#41—44no—
585#41—44no—
586#41—48no—
587#41—48no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—712no—
595C2×Q8—1422no—
596C2×Q8—1422no—
597C2×Q8—1421no—
598C2×Q8C23×D7112yes—
599C2×Q8C23×D7112yes—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—42no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4C2×C22⋊D7114yes—
608C2×D4#1176586414yes—
609C2×D4C23×D7112yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—2844no—
624C22×C4—1424no—
625C22×C4—1421no—
626C22×C4—1421no—
627C22×C4—1421no—
628C22×C4—1421no—
629C22×C4C2×C22⋊D7112yes—
630C22×C4C2×C22⋊D7112yes—
631C22×C4C2×C22⋊D7111yescharacteristic
632C22×C4C2×C22⋊D7111yescharacteristic
633C22×C4C2×C22⋊D7111yescharacteristic
634C22×C4C2×C22⋊D7111yescharacteristic
635C22×C4C23×D7112yes—
636C22×C4C23×D7112yes—
637C22×C4C23×D7111yescharacteristic
638Q16—2844no—
639Q16—2844no—
640SD16—1428no—
641M16—2844no—
642C2×C8—2844no—
643C2×C8—712no—
644C2×C8—712no—
645C2×C8—712no—
646C2×C8—712no—
647C2×C8—1422no—
648C2×C8—1422no—
649C2×C8—1422no—
650C2×C8—1422no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—712no—
657C4⋊C4—712no—
658C4⋊C4—712no—
659C4⋊C4—1424no—
660C4⋊C4—1424no—
661C4⋊C4—1424no—
662C4⋊C4—1424no—
663C4⋊C4—1424no—
664C4⋊C4—1421no—
665C4⋊C4—1421no—
666C4⋊C4—1424no—
667C4⋊C4—1421no—
668C4⋊C4C2×C22⋊D7114yes—
669C4⋊C4C23×D7112yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—1424no—
674C22⋊C4—1424no—
675C22⋊C4—1424no—
676C22⋊C4C2×C22⋊D7114yes—
677C22⋊C4C2×C22⋊D7114yes—
678C42—1424no—
679C42—1424no—
680C42C2×C22⋊D7112yes—
681C42C23×D7112yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊D7112yes—
693C23C22×C22⋊D7112yes—
694C23C22×C22⋊D7111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—2842no—
702Q8—1422no—
703Q8—1422no—
704D4—22no—
705D4—24no—
706D4—44no—
707D4—48no—
708D4—48no—
709D4C2×#1176586414yes—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—48no—
724C2×C4—48no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—2848no—
730C2×C4—2842no—
731C2×C4—2842no—
732C2×C4—2842no—
733C2×C4—2842no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4C22×C22⋊D7112yes—
739C2×C4C22×C22⋊D7112yes—
740C2×C4C22×C22⋊D7112yes—
741C2×C4C22×C22⋊D7112yes—
742C2×C4C22×C22⋊D7111yescharacteristic
743C2×C4C2×#1176586412yes—
744C2×C4#1455617312yes—
745C2×C4C24×D7111yescharacteristic
746C8—1422no—
747C8—1422no—
748C8—1422no—
749C8—1422no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—42no—
758C22—42no—
759C22—44no—
760C22—44no—
761C22—48no—
762C22#1798664312yes—
763C22#1798679712yes—
764C22#1798681412yes—
765C22C23×C22⋊D7111yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—2842no—
774C4—2842no—
775C4—2842no—
776C4—2842no—
777C4#1798664312yes—
778C4C22×#1176586411yescharacteristic
779C4C2×#1455617311yescharacteristic
780C2—42no—
781C2—42no—
782C2—44no—
783C2#2260043614yesdirect product factor
784C2C2×#1798664311yescharacteristic
785C2C2×#1798679711yescharacteristic
786C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
Fitting, prime radicalC2×#547×C71C2
socleC23×C71C22×D4
hypercenterC2×#547D71
hypocenterC71C2×#3315
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#17986689C2semidirect
2. #22600436C2direct (N × H)
3. C2×#17986367C2semidirect
4. C2×#17986332C2semidirect
5. C2×#17986337C2semidirect
6. C2×#17986299C2semidirect
7. C2×#17986255C2semidirect
8. C2×#17986238C2semidirect
9. C2×#17986206C2semidirect
10. C2×#17986161C2semidirect
11. C2×#17986161C2semidirect
12. C2×#17986099C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986000C2semidirect
15. C2×#17985995C2semidirect
23. #17986689C22semidirect
34. #17986367C22semidirect
35. #17986337C22semidirect
36. #17986332C22semidirect
37. #17986299C22semidirect
38. #17986255C22semidirect
39. #17986238C22semidirect
40. #17986206C22semidirect
41. #17986161C22semidirect
42. #17986161C22semidirect
43. #17986099C22semidirect
44. #17986071C22semidirect
49. #17986000C22semidirect
50. #17985995C22semidirect
390. C2×C71#3315semidirect
410. C71C2×#3315semidirect
783. C2#22600436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866892
#226004362
C2×#179863672
C2×#179863322
C2×#179863372
C2×#179862992
C2×#179862552
C2×#179862382
C2×#179862062
C2×#179861612
C2×#179860992
C2×#179860712
C2×#179860002
C2×#179859952
C2×#547×C712
C2×#331571