Finite Group Databasebeta

← C2×#20255484 #27092932

Subgroups — C2×#20255484 #27092932

Order 12032.

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×#15689813C211yesmaximal, characteristic, complemented
2#20255484C2116yesmaximal, direct product factor
3C2×#15689491C211yesmaximal, characteristic, complemented
4C2×#15689456C211yesmaximal, characteristic, complemented
5C2×#15689461C211yesmaximal, characteristic, complemented
6C2×#15689423C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689362C211yesmaximal, characteristic, complemented
9C2×#15689330C211yesmaximal, characteristic, complemented
10C2×#15689285C211yesmaximal, characteristic, complemented
11C2×#15689285C211yesmaximal, characteristic, complemented
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×#15689195C211yesmaximal, characteristic, complemented
14C2×#15689124C211yesmaximal, characteristic, complemented
15C2×#15689119C211yesmaximal, characteristic, complemented
16C2×C47×#547C211yesmaximal, characteristic
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625335C2211yescharacteristic
20C22×#10625329C2211yescharacteristic
21C23×C47⋊C8C2211yescharacteristic
22#15689813—24no—
23#15689813C2218yescomplemented
24C2×#13094017—21no—
25C2×#13094016C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094005—21no—
28C2×#13094003C2211yescharacteristic
29C2×#13094003C2211yescharacteristic
30C2×C4×Dic94C2211yescharacteristic
31C2×#13093983C2211yescharacteristic
32C2×#13093980—21no—
33C22×C4⋊Dic47C2211yescharacteristic
34#15689491C2218yescomplemented
35#15689461C2218yescomplemented
36#15689456C2218yescomplemented
37#15689423C2218yescomplemented
38#15689379C2218yescomplemented
39#15689362C2218yescomplemented
40#15689330C2218yescomplemented
41#15689285C2218yescomplemented
42#15689285C2218yescomplemented
43#15689223C2218yescomplemented
44#15689195C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49#15689124C2218yescomplemented
50#15689119C2218yescomplemented
51C2×#13093948C2211yescharacteristic
52C2×#13093948C2211yescharacteristic
53C2×#13093948C2211yescharacteristic
54C2×#13093948C2211yescharacteristic
55C2×#13093948C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093947C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×#13093945C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093935C2211yescharacteristic
64C22×#41×C47C2211yescharacteristic
65C22×#41×C47C2211yescharacteristic
66C47×#547—24no—
67C47×#547C2218yes—
68C2×C4⋊Q8×C47C2211yescharacteristic
69C2×#123×C47—21no—
70C2×#123×C47—21no—
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C2×#121×C47—21no—
74C2×C4×D4×C47C2211yescharacteristic
75C2×C4×D4×C47C2211yescharacteristic
76C22×C4⋊C4×C47—21no—
77C22×Dic94C2311yescharacteristic
78C23×Dic47—21no—
79C2×#10625337—42no—
80C2×#10625337—42no—
81C2×#10625337C2314yes—
82C2×#10625337C2314yes—
83C2×#10625335—24no—
84C2×#10625335C2314yes—
85C2×#10625329—42no—
86C2×#10625329C2314yes—
87C22×C47⋊C8—42no—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2314yes—
93#13094017—28no—
94#13094016—22no—
95#13094016C2314yes—
96#13094014—28no—
97#13094005—28no—
98#13094003—22no—
99#13094003—22no—
100#13094003C2314yes—
101#13094003C2314yes—
102C4×Dic94—22no—
103C4×Dic94C2314yes—
104#13093983—22no—
105#13093983C2314yes—
106#13093980—28no—
107C2×C4⋊Dic47—22no—
108C2×C4⋊Dic47—21no—
109C2×C4⋊Dic47C2314yes—
110C2×C4⋊Dic47C2311yescharacteristic
111C2×C4⋊Dic47C2311yescharacteristic
112C2×C4⋊Dic47C2311yescharacteristic
113C2×Dic47⋊C4—21no—
114C2×Dic47⋊C4—21no—
115C2×Dic47⋊C4—21no—
116C2×Dic47⋊C4—21no—
117C2×Dic47⋊C4—21no—
118C2×C22⋊Dic47—21no—
119C2×C22⋊Dic47—21no—
120C2×C22⋊Dic47—21no—
121C2×C4×Dic47—21no—
122C2×C4×Dic47—21no—
123#13093957C2314yes—
124#13093957C2314yes—
125#13093955C2314yes—
126C4⋊(C47⋊C8)C2314yes—
127#13093948C2314yes—
128#13093948C2314yes—
129#13093948C2314yes—
130#13093948C2314yes—
131#13093948C2314yes—
132#13093948C2314yes—
133#13093947C2314yes—
134#13093945C2314yes—
135#13093945C2314yes—
136#13093945C2314yes—
137C22⋊(C47⋊C8)C2314yes—
138C22⋊(C47⋊C8)C2314yes—
139#13093935C2314yes—
140C2×#41×C47—22no—
141C2×#41×C47—22no—
142C2×#41×C47—24no—
143C2×#41×C47—24no—
144C2×#41×C47—42no—
145C2×#41×C47—42no—
146C2×#41×C47C2314yes—
147C2×#41×C47C2314yes—
148C22×Q8×C47C2311yescharacteristic
149C22×Q8×C47C2311yescharacteristic
150C22×D4×C47—21no—
151C22×D4×C47—21no—
152C22×D4×C47D411yescharacteristic
153C22×D4×C47C2311yescharacteristic
154C23×C4×C47—21no—
155C23×C4×C47—21no—
156C23×C4×C47—21no—
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C4⋊Q8×C47—22no—
160C4⋊Q8×C47C2314yes—
161#123×C47—28no—
162#123×C47—28no—
163C22⋊Q8×C47—22no—
164C22⋊Q8×C47—22no—
165C22⋊Q8×C47C2314yes—
166C22⋊Q8×C47C2314yes—
167#121×C47—28no—
168C4×D4×C47—22no—
169C4×D4×C47D414yes—
170C4×D4×C47C2314yes—
171C4×D4×C47C2314yes—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47—28no—
177C2×C4⋊C4×C47D411yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47D411yescharacteristic
183C2×C22⋊C4×C47D411yescharacteristic
184C2×C42×C47C2311yescharacteristic
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C24×C47C2×D411yescharacteristic
188#41×C47—28no—
189#41×C47—28no—
190#41×C47—44no—
191#41×C47—44no—
192#41×C47—48no—
193#41×C47—48no—
194C2×Q8×C47—21no—
195C2×Q8×C47—21no—
196C2×Q8×C47—22no—
197C2×Q8×C47—22no—
198C2×Q8×C47—22no—
199C2×Q8×C47—22no—
200C2×Q8×C47C2412yes—
201C2×Q8×C47C2412yes—
202C2×D4×C47—24no—
203C2×D4×C47—24no—
204C2×D4×C47—21no—
205C2×D4×C47—22no—
206C2×D4×C47—42no—
207C2×D4×C47—44no—
208C2×D4×C47—44no—
209C2×D4×C47C2×D414yes—
210C2×D4×C47#4114yes—
211C2×D4×C47C2412yes—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—24no—
220C22×C4×C47—24no—
221C22×C4×C47—24no—
222C22×C4×C47—44no—
223C22×C4×C47—44no—
224C22×C4×C47—44no—
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D412yes—
230C22×C4×C47C2×D412yes—
231C22×C4×C47C2412yes—
232C22×C4×C47C2412yes—
233C22×C4×C47C2411yescharacteristic
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—24no—
239C22×Dic47—44no—
240C2×Dic94—22no—
241C2×Dic94—22no—
242C2×Dic94—21no—
243C2×Dic94C2412yes—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—24no—
246C4⋊C4×C47—24no—
247C4⋊C4×C47—24no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47C2×D414yes—
250C4⋊C4×C47C2412yes—
251C22⋊C4×C47—24no—
252C22⋊C4×C47—24no—
253C22⋊C4×C47—24no—
254C22⋊C4×C47C2×D414yes—
255C22⋊C4×C47C2×D414yes—
256C42×C47C2×D412yes—
257C42×C47C2412yes—
258C22⋊Dic47—24no—
259C22⋊Dic47—24no—
260C22⋊Dic47—24no—
261#10625337—44no—
262#10625337—44no—
263#10625335—28no—
264C4⋊Dic47—21no—
265C4⋊Dic47—21no—
266C4⋊Dic47—24no—
267C4⋊Dic47—21no—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276C4×Dic47—24no—
277C4×Dic47—24no—
278#10625329—44no—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—44no—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287C2×C47⋊C8C2412yes—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—24no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—22no—
296C23×C47—42no—
297C23×C47—42no—
298C23×C47C22×D412yes—
299C23×C47C22×D412yes—
300C23×C47C22×D411yescharacteristic
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—42no—
306Q8×C47—42no—
307D4×C47—24no—
308D4×C47—22no—
309D4×C47—44no—
310D4×C47—48no—
311D4×C47—48no—
312D4×C47C2×#4114yes—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—24no—
318C2×C4×C47—24no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—48no—
327C2×C4×C47—48no—
328C2×C4×C47—48no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—42no—
332C2×C4×C47C22×D412yes—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D412yes—
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47C2×#4112yes—
338C2×C4×C47H(5,𝔽2)12yes—
339C2×C4×C47C2511yescharacteristic
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—48no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349Dic94—22no—
350Dic94—22no—
351Dic94—42no—
352C47⋊C8—22no—
353C47⋊C8—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3315—471nomaximal, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—24no—
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—44no—
365C22×C47—44no—
366C22×C47—48no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47#54612yes—
370C22×C47#57512yes—
371C22×C47#57812yes—
372C22×C47C23×D411yescharacteristic
373C4×C47—22no—
374C4×C47—22no—
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—42no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47#54612yes—
381C4×C47C22×#4111yescharacteristic
382C4×C47C2×H(5,𝔽2)11yescharacteristic
383Dic47—42no—
384Dic47—42no—
385Dic47—42no—
386Dic47—42no—
387C2×#552—471no—
388C2×#547D4711yescharacteristic
389#3315—4716no—
390C2×#491—471no—
391C2×#484—471no—
392C2×#485—471no—
393C2×#478—471no—
394C2×#470—471no—
395C2×#467—471no—
396C2×#462—471no—
397C2×#452—471no—
398C2×#452—471no—
399C2×#440—471no—
400C2×#435—471no—
401C2×#417—471no—
402C2×#416—471no—
403C2×C47—42no—
404C2×C47—42no—
405C2×C47—44no—
406C2×C47#331514yescomplemented
407C2×C47C2×#54611yescharacteristic
408C2×C47C2×#57511yescharacteristic
409C2×C47C2×#57811yescharacteristic
410C22×#41C2×D4711yescharacteristic
411C22×#41C2×D4711yescharacteristic
412C22×Q16—471no—
413C22×Q16—471no—
414C22×SD16—471no—
415C22×M16—471no—
416C23×C8—471no—
417#552—478no—
418#552—944no—
419#547—24no—
420#547C2×D4718yes—
421C2×C4⋊Q8C2×D4711yescharacteristic
422C2×#126—941no—
423C2×#125—471no—
424C2×#125—941no—
425C2×#123—21no—
426C2×#123—21no—
427C2×#123—941no—
428C2×C22⋊Q8—471no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8C2×D4711yescharacteristic
431C2×C22⋊Q8C2×D4711yescharacteristic
432C2×#121—21no—
433C2×C4×Q8—471no—
434C2×C4×D4C2×D4711yescharacteristic
435C2×C4×D4C2×D4711yescharacteristic
436C2×#117—471no—
437C2×#117—941no—
438C22×C4⋊C4—21no—
439C22×C4⋊C4—471no—
440#491—478no—
441#485—478no—
442#484—478no—
443#478—478no—
444#470—478no—
445#467—478no—
446#462—478no—
447#452—478no—
448#452—478no—
449#440—478no—
450#435—478no—
451C2×#107—471no—
452C2×#107—471no—
453C2×#106—471no—
454C2×C4⋊C8—471no—
455#417—478no—
456#416—478no—
457C2×#103—471no—
458C2×#103—471no—
459C2×#103—471no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103—471no—
463C2×#103—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×C22⋊C8—471no—
468C2×C22⋊C8—471no—
469C2×#97—471no—
470C47C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—24no—
474C2×#41—24no—
475C2×#41—42no—
476C2×#41—42no—
477C2×#41C22×D4714yes—
478C2×#41C22×D4714yes—
479C22×Q8—471no—
480C22×Q8C22×D4711yescharacteristic
481C22×Q8C22×D4711yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C22⋊D4711yescharacteristic
485C22×D4C22×D4711yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—941no—
490C23×C4C22×D4711yescharacteristic
491C23×C4C22×D4711yescharacteristic
492C2×Q16—474no—
493C2×Q16—474no—
494C2×Q16—1882no—
495C2×Q16—1882no—
496C2×SD16—474no—
497C2×SD16—944no—
498C2×M16—474no—
499C2×M16—1882no—
500C22×C8—471no—
501C22×C8—471no—
502C22×C8—471no—
503C22×C8—471no—
504C22×C8—474no—
505C22×C8—1882no—
506C4⋊Q8—22no—
507C4⋊Q8C22×D4714yes—
508#126—948no—
509#125—474no—
510#125—948no—
511#125—942no—
512#123—28no—
513#123—28no—
514#123—948no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—474no—
518C22⋊Q8—474no—
519C22⋊Q8—942no—
520C22⋊Q8—942no—
521C22⋊Q8C22×D4714yes—
522C22⋊Q8C22×D4714yes—
523#121—28no—
524C4×Q8—474no—
525C4×Q8—942no—
526C4×D4—22no—
527C4×D4C22⋊D4714yes—
528C4×D4C22×D4714yes—
529C4×D4C22×D4714yes—
530#117—474no—
531#117—942no—
532#117—948no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—28no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—471no—
540C2×C4⋊C4—474no—
541C2×C4⋊C4—471no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—942no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4C22⋊D4711yescharacteristic
550C2×C4⋊C4C22×D4711yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4C22⋊D4711yescharacteristic
558C2×C22⋊C4C22⋊D4711yescharacteristic
559C2×C42—941no—
560C2×C42—941no—
561C2×C42C22×D4711yescharacteristic
562#107—474no—
563#107—474no—
564#106—474no—
565C4⋊C8—474no—
566#103—474no—
567#103—474no—
568#103—474no—
569#103—474no—
570#103—474no—
571#103—474no—
572#103—474no—
573#102—474no—
574#102—474no—
575#102—474no—
576C22⋊C8—474no—
577C22⋊C8—474no—
578#97—474no—
579C24—21no—
580C24C2×C22⋊D4711yescharacteristic
581C24C2×C22⋊D4711yescharacteristic
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—472no—
595C2×Q8—941no—
596C2×Q8—942no—
597C2×Q8—942no—
598C2×Q8C23×D4712yes—
599C2×Q8C23×D4712yes—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—42no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4#1062535214yes—
608C2×D4C2×C22⋊D4714yes—
609C2×D4C23×D4712yes—
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—944no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—1884no—
629C22×C4C2×C22⋊D4712yes—
630C22×C4C2×C22⋊D4712yes—
631C22×C4C2×C22⋊D4711yescharacteristic
632C22×C4C2×C22⋊D4711yescharacteristic
633C22×C4C2×C22⋊D4711yescharacteristic
634C22×C4C2×C22⋊D4711yescharacteristic
635C22×C4C23×D4712yes—
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638Q16—1884no—
639Q16—1884no—
640SD16—948no—
641M16—1884no—
642C2×C8—472no—
643C2×C8—472no—
644C2×C8—472no—
645C2×C8—472no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8—942no—
649C2×C8—942no—
650C2×C8—1884no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—472no—
657C4⋊C4—472no—
658C4⋊C4—472no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—944no—
662C4⋊C4—944no—
663C4⋊C4—944no—
664C4⋊C4—941no—
665C4⋊C4—941no—
666C4⋊C4—944no—
667C4⋊C4—941no—
668C4⋊C4C2×C22⋊D4714yes—
669C4⋊C4C23×D4712yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4C2×C22⋊D4714yes—
677C22⋊C4C2×C22⋊D4714yes—
678C42—944no—
679C42—944no—
680C42C2×C22⋊D4712yes—
681C42C23×D4712yes—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊D4712yes—
693C23C22×C22⋊D4712yes—
694C23C22×C22⋊D4711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—942no—
702Q8—942no—
703Q8—1882no—
704D4—24no—
705D4—22no—
706D4—44no—
707D4—48no—
708D4—48no—
709D4C2×#1062535214yes—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
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—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—1888no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4—1882no—
738C2×C4C22×C22⋊D4712yes—
739C2×C4C22×C22⋊D4712yes—
740C2×C4C22×C22⋊D4712yes—
741C2×C4C22×C22⋊D4712yes—
742C2×C4C22×C22⋊D4711yescharacteristic
743C2×C4C2×#1062535212yes—
744C2×C4#1309406912yes—
745C2×C4C24×D4711yescharacteristic
746C8—942no—
747C8—942no—
748C8—942no—
749C8—942no—
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#1568976712yes—
763C22#1568992112yes—
764C22#1568993812yes—
765C22C23×C22⋊D4711yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—1882no—
774C4—1882no—
775C4—1882no—
776C4—1882no—
777C4#1568976712yes—
778C4C22×#1062535211yescharacteristic
779C4C2×#1309406911yescharacteristic
780C2—42no—
781C2—42no—
782C2—44no—
783C2#2025548414yesdirect product factor
784C2C2×#1568976711yescharacteristic
785C2C2×#1568992111yescharacteristic
786C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
Fitting, prime radicalC2×C47×#547C2
socleC23×C47C22×D4
hypercenterC2×#547D47
hypocenterC47C2×#3315
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#15689813C2semidirect
2. #20255484C2direct (N × H)
3. C2×#15689491C2semidirect
4. C2×#15689456C2semidirect
5. C2×#15689461C2semidirect
6. C2×#15689423C2semidirect
7. C2×#15689379C2semidirect
8. C2×#15689362C2semidirect
9. C2×#15689330C2semidirect
10. C2×#15689285C2semidirect
11. C2×#15689285C2semidirect
12. C2×#15689223C2semidirect
13. C2×#15689195C2semidirect
14. C2×#15689124C2semidirect
15. C2×#15689119C2semidirect
23. #15689813C22semidirect
34. #15689491C22semidirect
35. #15689461C22semidirect
36. #15689456C22semidirect
37. #15689423C22semidirect
38. #15689379C22semidirect
39. #15689362C22semidirect
40. #15689330C22semidirect
41. #15689285C22semidirect
42. #15689285C22semidirect
43. #15689223C22semidirect
44. #15689195C22semidirect
49. #15689124C22semidirect
50. #15689119C22semidirect
406. C2×C47#3315semidirect
470. C47C2×#3315semidirect
783. C2#20255484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898132
#202554842
C2×#156894912
C2×#156894562
C2×#156894612
C2×#156894232
C2×#156893792
C2×#156893622
C2×#156893302
C2×#156892852
C2×#156892232
C2×#156891952
C2×#156891242
C2×#156891192
C2×C47×#5472
C2×#331547