Finite Group Databasebeta

← C2×#20255487 #27092935

Subgroups — C2×#20255487 #27092935

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×#15689808C211yesmaximal, characteristic, complemented
2C2×#15689775C211yesmaximal, characteristic
3#20255487C2116yesmaximal, direct product factor
4C2×#15689490C211yesmaximal, characteristic, complemented
5C2×#15689466C211yesmaximal, characteristic, complemented
6C2×#15689426C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689365C211yesmaximal, characteristic, complemented
9C2×#15689332C211yesmaximal, characteristic, complemented
10C2×#15689288C211yesmaximal, characteristic, complemented
11C2×#15689287C211yesmaximal, characteristic, complemented
12C2×#15689222C211yesmaximal, characteristic, complemented
13C2×#15689197C211yesmaximal, characteristic, complemented
14C2×#15689122C211yesmaximal, characteristic, complemented
15C2×#15689118C211yesmaximal, characteristic, complemented
16C2×C47×#484C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C22×Dic188C2211yescharacteristic
20C22×#10625337C2211yescharacteristic
21C22×#10625325C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23C22×C8×D47C2211yescharacteristic
24#15689808—24no—
25#15689808C2218yescomplemented
26#15689775—24no—
27#15689775C2218yes—
28C2×#13094022C2211yescharacteristic
29C2×#13094019—21no—
30C2×#13094015C2211yescharacteristic
31C2×#13094014—21no—
32C2×#13094009—21no—
33C2×#13094007—21no—
34C2×#13094006—21no—
35C2×#13094004C2211yescharacteristic
36C2×#13094004C2211yescharacteristic
37C2×#13094003C2211yescharacteristic
38C2×#13093997—21no—
39C2×#13093989C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×C4×C22⋊D47C2211yescharacteristic
42C2×#13093983—21no—
43C2×#13093982C2211yescharacteristic
44C2×C4⋊C4×D47—21no—
45#15689490C2218yescomplemented
46#15689466C2218yescomplemented
47#15689426C2218yescomplemented
48#15689379C2218yescomplemented
49#15689365C2218yescomplemented
50#15689332C2218yescomplemented
51#15689288C2218yescomplemented
52#15689287C2218yescomplemented
53#15689222C2218yescomplemented
54#15689197C2218yescomplemented
55C2×#13093955C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57#15689122C2218yescomplemented
58#15689118C2218yescomplemented
59C2×#13093949C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C47×#484C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—42no—
80C2×#10625354C2314yes—
81C2×#10625350—22no—
82C2×#10625350—24no—
83C2×#10625350—42no—
84C2×#10625350C2314yes—
85C22×Dic94C2311yescharacteristic
86C22×Dic94C2311yescharacteristic
87C22×D188—21no—
88C22×D188C2311yescharacteristic
89C22×C22⋊D47—21no—
90C22×C22⋊D47D411yescharacteristic
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C2×Dic188—42no—
96C2×Dic188C2314yes—
97C2×#10625337—42no—
98C2×#10625337C2314yes—
99C2×#10625325—24no—
100C2×#10625325C2314yes—
101C2×#10625329—42no—
102C2×#10625329C2314yes—
103C22×C47⋊C8C2311yescharacteristic
104C22×C47⋊C8C2311yescharacteristic
105C2×C8×D47—42no—
106C2×C8×D47C2314yes—
107#13094022—22no—
108#13094022C2314yes—
109#13094019—28no—
110#13094015—22no—
111#13094015C2314yes—
112#13094014—28no—
113#13094009—28no—
114#13094007—28no—
115#13094006—28no—
116#13094004—22no—
117#13094004—22no—
118#13094004C2314yes—
119#13094004C2314yes—
120#13094003—22no—
121#13094003C2314yes—
122#13093997—28no—
123#13093989—22no—
124#13093989C2314yes—
125#13093986—22no—
126#13093986C2314yes—
127C4×C22⋊D47D414yes—
128C4×C22⋊D47C2314yes—
129#13093983—28no—
130#13093982—22no—
131#13093982C2314yes—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47—21no—
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4D411yescharacteristic
142C4⋊C4×D47—28no—
143C2×C22⋊Dic47—21no—
144C2×C22⋊Dic47D411yescharacteristic
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4D411yescharacteristic
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47C2311yescharacteristic
153#13093955C2314yes—
154Dic47⋊C8C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159#13093947C2314yes—
160#13093946C2314yes—
161#13093944C2314yes—
162#13093944C2314yes—
163(C2×D47)⋊C8C2314yes—
164#13093934C2314yes—
165C22×Q8×C47C2311yescharacteristic
166C23×C4×C47—21no—
167C23×C4×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22⋊Q8×C47—22no—
171C22⋊Q8×C47C2314yes—
172C2×C4⋊C4×C47—22no—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47C2314yes—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C22⋊C4×C47—21no—
180#107×C47C2314yes—
181#107×C47C2314yes—
182#103×C47C2314yes—
183#103×C47C2314yes—
184C22⋊C8×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C23×D47—21no—
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47C2412yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—24no—
199C22×C4×C47—44no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2412yes—
203C22×C4×C47C2411yescharacteristic
204C2×C22⋊D47—24no—
205C2×C22⋊D47—42no—
206C2×C22⋊D47—44no—
207C2×C22⋊D47C2×D414yes—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47C2×D411yescharacteristic
212C22×Dic47C2×D411yescharacteristic
213C22×Dic47C2×D411yescharacteristic
214#10625354—28no—
215#10625354—44no—
216#10625354—48no—
217#10625350—28no—
218#10625350—44no—
219#10625350—48no—
220C2×D188—21no—
221C2×D188—22no—
222C2×D188—24no—
223C2×D188—44no—
224C2×D188#4114yes—
225C2×D188C2412yes—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—24no—
229C2×C4×D47—24no—
230C2×C4×D47—24no—
231C2×C4×D47—44no—
232C2×C4×D47—44no—
233C2×C4×D47—44no—
234C2×C4×D47C2×D412yes—
235C2×C4×D47C2412yes—
236C2×Dic94—22no—
237C2×Dic94—22no—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—21no—
241C2×Dic94—21no—
242C2×Dic94C2412yes—
243C2×Dic94C2412yes—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C2×C8×C47C2412yes—
247C2×C8×C47C2412yes—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47C2412yes—
254C4⋊C4×C47C2412yes—
255C4⋊C4×C47C2412yes—
256C22⋊C4×C47—24no—
257C22⋊Dic47—24no—
258C22⋊Dic47C2×D414yes—
259#10625337—44no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4C2×D414yes—
265C4⋊Dic47—21no—
266C4⋊Dic47—24no—
267C4⋊Dic47—24no—
268C4⋊Dic47—24no—
269C4⋊Dic47C2412yes—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4C2×D414yes—
276C4×Dic47—24no—
277C4×Dic47—24no—
278C4×Dic47C2×D412yes—
279C4×Dic47C2412yes—
280#10625329—44no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8C2412yes—
284C2×C47⋊C8C2412yes—
285Dic188—44no—
286#10625325—28no—
287C8×D47—44no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47C22×D412yes—
292C23×C47C22×D411yescharacteristic
293C22×D47—22no—
294C22×D47—24no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47C22×D412yes—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—42no—
304C2×C4×C47—22no—
305C2×C4×C47—24no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—48no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4112yes—
320C2×C4×C47H(5,𝔽2)12yes—
321C2×C4×C47C2511yescharacteristic
322C22⋊D47—44no—
323C22⋊D47—48no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47C22×D412yes—
334C2×Dic47C22×D412yes—
335C2×Dic47C22×D412yes—
336D188—24no—
337D188—22no—
338D188—48no—
339D188C2×#4114yes—
340C4×D47—24no—
341C4×D47—22no—
342C4×D47—22no—
343C4×D47—48no—
344C4×D47—48no—
345C4×D47—48no—
346Dic94—22no—
347Dic94—22no—
348Dic94—22no—
349Dic94—22no—
350Dic94—42no—
351Dic94—42no—
352C8×C47—22no—
353C8×C47—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3315—471nomaximal, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—44no—
361C22×C47#54612yes—
362C22×C47#57512yes—
363C22×C47#57812yes—
364C22×C47C23×D411yescharacteristic
365C2×D47—22no—
366C2×D47—24no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—44no—
370C2×D47—48no—
371C2×D47—42no—
372C2×D47—42no—
373C4×C47—22no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47—42no—
377C4×C47—42no—
378C4×C47#54612yes—
379C4×C47C22×#4111yescharacteristic
380C4×C47C2×H(5,𝔽2)11yescharacteristic
381Dic47—22no—
382Dic47—22no—
383Dic47—22no—
384Dic47—42no—
385Dic47—42no—
386Dic47—42no—
387C2×#552—471no—
388C2×#547—471no—
389#3315—4716no—
390C2×#491—471no—
391C2×#484D4711yescharacteristic, complemented
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#331514yescomplemented
405C2×C47C2×#54611yescharacteristic
406C2×C47C2×#57511yescharacteristic
407C2×C47C2×#57811yescharacteristic
408D47—42no—
409D47—44no—
410C22×#41—471no—
411C22×#41—471no—
412C22×Q16—471no—
413C22×Q16—471no—
414C22×SD16—471no—
415C22×M16—471no—
416C23×C8—471no—
417#552—478no—
418#552—944no—
419#547—478no—
420#547—944no—
421C2×C4⋊Q8—471no—
422C2×#126—941no—
423C2×#125—471no—
424C2×#125—941no—
425C2×#123—941no—
426C2×#123—941no—
427C2×#123—941no—
428C2×C22⋊Q8—471no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8C2×D4711yescharacteristic
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×#117—471no—
437C2×#117—941no—
438C22×C4⋊C4—941no—
439C22×C4⋊C4C2×D4711yescharacteristic
440#491—478no—
441#485—478no—
442#484C2×D4718yescomplemented
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×#107C2×D4711yescharacteristic
452C2×#107C2×D4711yescharacteristic
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×#103C2×D4711yescharacteristic
463C2×#103C2×D4711yescharacteristic
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×C22⋊C8—471no—
468C2×C22⋊C8C2×D4711yescharacteristic
469C2×#97—471no—
470C47C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—474no—
472C2×#41—474no—
473C2×#41—944no—
474C2×#41—942no—
475C2×#41—942no—
476C2×#41—944no—
477C2×#41—1882no—
478C2×#41—1882no—
479C22×Q8—471no—
480C22×Q8—471no—
481C22×Q8C22×D4711yescharacteristic
482C22×D4—471no—
483C22×D4—471no—
484C22×D4—941no—
485C22×D4—941no—
486C23×C4—21no—
487C23×C4—471no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
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—474no—
503C22×C8—1882no—
504C22×C8C22×D4711yescharacteristic
505C22×C8C22×D4711yescharacteristic
506C4⋊Q8—474no—
507C4⋊Q8—942no—
508#126—948no—
509#125—474no—
510#125—942no—
511#125—948no—
512#123—948no—
513#123—948no—
514#123—948no—
515C22⋊Q8—22no—
516C22⋊Q8—474no—
517C22⋊Q8—474no—
518C22⋊Q8—474no—
519C22⋊Q8—942no—
520C22⋊Q8—942no—
521C22⋊Q8—942no—
522C22⋊Q8C22×D4714yes—
523#121—948no—
524C4×Q8—474no—
525C4×Q8—942no—
526C4×D4—474no—
527C4×D4—474no—
528C4×D4—474no—
529C4×D4—942no—
530#117—474no—
531#117—948no—
532#117—942no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—948no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C4⋊C4C22×D4711yescharacteristic
549C2×C4⋊C4C22×D4714yes—
550C2×C4⋊C4C22×D4711yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—471no—
553C2×C22⋊C4—471no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C22⋊C4—941no—
559C2×C42—471no—
560C2×C42—941no—
561C2×C42—941no—
562#107C22×D4714yes—
563#107C22×D4714yes—
564#106—474no—
565C4⋊C8—474no—
566#103—474no—
567#103—474no—
568#103—474no—
569#103—474no—
570#103—474no—
571#103C22×D4714yes—
572#103C22×D4714yes—
573#102—474no—
574#102—474no—
575#102—474no—
576C22⋊C8—474no—
577C22⋊C8C22×D4714yes—
578#97—474no—
579C24—471no—
580C24—941no—
581C24D4×D4711yescharacteristic
582#41—948no—
583#41—948no—
584#41—1884no—
585#41—1888no—
586#41—1884no—
587#41—1888no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—472no—
592C2×Q8—472no—
593C2×Q8—941no—
594C2×Q8—941no—
595C2×Q8—942no—
596C2×Q8—942no—
597C2×Q8—942no—
598C2×Q8—942no—
599C2×Q8C23×D4712yes—
600C2×D4—474no—
601C2×D4—474no—
602C2×D4—472no—
603C2×D4—944no—
604C2×D4—944no—
605C2×D4—941no—
606C2×D4—942no—
607C2×D4—1884no—
608C2×D4—1882no—
609C2×D4—1884no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—44no—
618C22×C4—471no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—472no—
622C22×C4—472no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—944no—
631C22×C4—1884no—
632C22×C4—1884no—
633C22×C4—1884no—
634C22×C4D4×D4712yes—
635C22×C4D4×D4711yescharacteristic
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638Q16—1884no—
639Q16—1884no—
640SD16—948no—
641M16—1884no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—472no—
645C2×C8—472no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8—1884no—
649C2×C8C23×D4712yes—
650C2×C8C23×D4712yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—474no—
657C4⋊C4—472no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—944no—
662C4⋊C4—944no—
663C4⋊C4—944no—
664C4⋊C4—944no—
665C4⋊C4—944no—
666C4⋊C4—941no—
667C4⋊C4C23×D4712yes—
668C4⋊C4C23×D4712yes—
669C4⋊C4C23×D4712yes—
670C22⋊C4—24no—
671C22⋊C4—474no—
672C22⋊C4—474no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C42—472no—
679C42—472no—
680C42—944no—
681C42—944no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—472no—
686C23—942no—
687C23—944no—
688C23—942no—
689C23—942no—
690C23—942no—
691C23—1882no—
692C23—1882no—
693C23C2×D4×D4712yes—
694C23C2×D4×D4711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—942no—
699Q8—942no—
700Q8—942no—
701Q8—942no—
702Q8—1882no—
703Q8—1882no—
704D4—474no—
705D4—944no—
706D4—942no—
707D4—1888no—
708D4—1884no—
709D4—1888no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—472no—
724C2×C4—472no—
725C2×C4—472no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—944no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—1888no—
736C2×C4—1888no—
737C2×C4—1888no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4#41×D4712yes—
744C2×C4#1309407012yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—942no—
755C22—944no—
756C22—942no—
757C22—942no—
758C22—1882no—
759C22—1882no—
760C22—1884no—
761C22—1888no—
762C22#1568976512yes—
763C22#1568991912yes—
764C22#1568993612yes—
765C22C22×D4×D4711yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—942no—
772C4—942no—
773C4—942no—
774C4—1882no—
775C4—1882no—
776C4—1882no—
777C4#1568976512yes—
778C4C2×#41×D4711yescharacteristic
779C4C2×#1309407011yescharacteristic
780C2—42no—
781C2—1882no—
782C2—1884no—
783C2#2025548714yesdirect product factor
784C2C2×#1568976511yescharacteristic
785C2C2×#1568991911yescharacteristic
786C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#484C2
socleC23×C47C22×D4
prime radicalC2×#15689775C2
hypercenterC2×#484D47
hypocenterC47C2×#3315
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#15689808C2semidirect
3. #20255487C2direct (N × H)
4. C2×#15689490C2semidirect
5. C2×#15689466C2semidirect
6. C2×#15689426C2semidirect
7. C2×#15689379C2semidirect
8. C2×#15689365C2semidirect
9. C2×#15689332C2semidirect
10. C2×#15689288C2semidirect
11. C2×#15689287C2semidirect
12. C2×#15689222C2semidirect
13. C2×#15689197C2semidirect
14. C2×#15689122C2semidirect
15. C2×#15689118C2semidirect
16. C2×C47×#484C2semidirect
25. #15689808C22semidirect
45. #15689490C22semidirect
46. #15689466C22semidirect
47. #15689426C22semidirect
48. #15689379C22semidirect
49. #15689365C22semidirect
50. #15689332C22semidirect
51. #15689288C22semidirect
52. #15689287C22semidirect
53. #15689222C22semidirect
54. #15689197C22semidirect
57. #15689122C22semidirect
58. #15689118C22semidirect
71. C47×#484C22semidirect
391. C2×#484D47semidirect
404. C2×C47#3315semidirect
442. #484C2×D47semidirect
470. C47C2×#3315semidirect
783. C2#20255487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898082
C2×#156897752
#202554872
C2×#156894902
C2×#156894662
C2×#156894262
C2×#156893792
C2×#156893652
C2×#156893322
C2×#156892882
C2×#156892872
C2×#156892222
C2×#156891972
C2×#156891222
C2×#156891182
C2×C47×#4842
C2×#331547