Finite Group Databasebeta

← C2×#20252226 #27080382

Subgroups — C2×#20252226 #27080382

Order 12032.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094056C211yesmaximal, characteristic
2C2×#15689605C211yesmaximal, characteristic
3C2×#15689599C211yesmaximal, characteristic, complemented
4#20252226C2116yesmaximal, direct product factor
5C2×#15689230C211yesmaximal, characteristic, complemented
6C2×#15689228C211yesmaximal, characteristic, complemented
7C2×#15689222C211yesmaximal, characteristic, complemented
8C2×#15689221C211yesmaximal, characteristic, complemented
9C2×#15689215C211yesmaximal, characteristic, complemented
10C2×C4×#10625325C211yesmaximal, characteristic, complemented
11C2×#15689208C211yesmaximal, characteristic, complemented
12C2×#15689164C211yesmaximal, characteristic, complemented
13C2×#15689118C211yesmaximal, characteristic
14C2×#103×D47C211yesmaximal, characteristic, complemented
15C2×#15689077C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C2×#13094056C4116yescomplemented
20C2×#13094056C2218yes—
21C22×#10625337C2211yescharacteristic
22C22×#10625325C2211yescharacteristic
23C22×#10625336C2211yescharacteristic
24C22×#10625324C2211yescharacteristic
25C22×C8×D47C2211yescharacteristic
26#15689605—24no—
27#15689605C2218yes—
28#15689599—24no—
29#15689599C2218yescomplemented
30C2×Q8×Dic47C2211yescharacteristic
31C2×Q8×Dic47C2211yescharacteristic
32C2×C4×Dic94—21no—
33C2×C4×Dic94C2211yescharacteristic
34C2×#13093989—21no—
35C2×#13093989C2211yescharacteristic
36C2×C4×D188—21no—
37C2×C4×D188C2211yescharacteristic
38C2×#13093986—21no—
39C2×#13093986C2211yescharacteristic
40C2×#13093982—21no—
41C2×#13093982C2211yescharacteristic
42C2×#13093981—21no—
43C2×#13093981—21no—
44C2×#13093981C2211yescharacteristic
45C2×C4⋊C4×D47—21no—
46C2×C4⋊C4×D47C2211yescharacteristic
47#15689230C2218yescomplemented
48#15689228C2218yescomplemented
49#15689222C2218yescomplemented
50#15689221C2218yescomplemented
51#15689215C2218yescomplemented
52C4×#10625325C2218yescomplemented
53#15689208C2218yescomplemented
54#15689164C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#15689118C2218yes—
59C2×#13093949C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63#103×D47C2218yescomplemented
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66#15689077C2218yescomplemented
67C2×#13093935C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C2×C8×Dic47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C4×Q16×C47C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C2×C4×C8×C47C2211yescharacteristic
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354C2×C418yes—
81C2×#10625354C2314yes—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C2×Q8×D47—22no—
85C2×Q8×D47—24no—
86C2×Q8×D47C2×C418yescomplemented
87C2×Q8×D47C2314yes—
88C22×D188—21no—
89C22×D188C2311yescharacteristic
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47C2311yescharacteristic
96#13094056C2×C4164yescomplemented
97C2×#10625337C2×C418yescomplemented
98C2×#10625337C2314yes—
99C2×#10625325C2×C418yescomplemented
100C2×#10625325C2314yes—
101C2×#10625336C2×C418yescomplemented
102C2×#10625336C2314yes—
103C2×#10625324C2×C418yescomplemented
104C2×#10625324C2314yes—
105C22×C47⋊C8C2311yescharacteristic
106C22×C47⋊C8C2311yescharacteristic
107C2×C8×D47—24no—
108C2×C8×D47C2314yes—
109Q8×Dic47—22no—
110Q8×Dic47—22no—
111Q8×Dic47C2314yes—
112Q8×Dic47C2314yes—
113C4×Dic94—22no—
114C4×Dic94—28no—
115C4×Dic94C2314yes—
116#13093989—28no—
117#13093989—22no—
118#13093989C2314yes—
119C4×D188—22no—
120C4×D188—28no—
121C4×D188C2314yes—
122#13093986—28no—
123#13093986—22no—
124#13093986C2314yes—
125#13093982—22no—
126#13093982—28no—
127#13093982C2314yes—
128#13093981—28no—
129#13093981—28no—
130#13093981D414yes—
131#13093981C2314yes—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4D411yescharacteristic
140C2×Dic47⋊C4D411yescharacteristic
141C4⋊C4×D47—22no—
142C4⋊C4×D47—28no—
143C4⋊C4×D47C2314yes—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4D411yescharacteristic
148C2×(C2×D47)⋊C4D411yescharacteristic
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151C2×C4×Dic47—21no—
152C2×C4×Dic47—21no—
153C2×C4×Dic47—21no—
154C2×C4×Dic47C2311yescharacteristic
155#13093957C2314yes—
156#13093956C2314yes—
157#13093955C2314yes—
158#13093949C2314yes—
159#13093948C2314yes—
160#13093948C2314yes—
161#13093947C2314yes—
162#13093946C2314yes—
163#13093944C2314yes—
164#13093935C2314yes—
165#13093934C2314yes—
166C8×Dic47C2314yes—
167C22×Q8×C47C2311yescharacteristic
168C22×Q8×C47C2311yescharacteristic
169C2×Q16×C47C2×C418yescomplemented
170C2×Q16×C47C2314yes—
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C4×Q8×C47—22no—
174C4×Q8×C47—22no—
175C4×Q8×C47C2314yes—
176C4×Q8×C47C2314yes—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C42×C47—21no—
182C2×C42×C47—21no—
183C2×C42×C47C2311yescharacteristic
184#107×C47C2314yes—
185#103×C47C2314yes—
186#103×C47C2314yes—
187C4×C8×C47C2314yes—
188C23×D47—21no—
189C23×D47C2×D411yescharacteristic
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47C22×C414yes—
195C2×Q8×C47C22×C414yes—
196C2×Q8×C47C2412yes—
197C2×Q8×C47C2412yes—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2411yescharacteristic
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211#10625354—216no—
212#10625354—28no—
213#10625354C22×C4116yes—
214Q8×D47—216no—
215Q8×D47—28no—
216Q8×D47C22×C4116yescomplemented
217C2×D188—28no—
218C2×D188—24no—
219C2×D188—21no—
220C2×D188—22no—
221C2×D188C22×C414yes—
222C2×D188C2412yes—
223C2×C4×D47—28no—
224C2×C4×D47—24no—
225C2×C4×D47—28no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—24no—
229C2×C4×D47—24no—
230C2×C4×D47—82no—
231C2×C4×D47—82no—
232C2×C4×D47—82no—
233C2×C4×D47C22×C414yes—
234C2×C4×D47C2×D412yes—
235C2×C4×D47#4114yes—
236C2×C4×D47C2412yes—
237C2×Dic94—21no—
238C2×Dic94—22no—
239C2×Dic94—28no—
240C2×Dic94—24no—
241C2×Dic94C22×C414yes—
242C2×Dic94C2412yes—
243Q16×C47C22×C4116yescomplemented
244C2×C8×C47—22no—
245C2×C8×C47C22×C414yes—
246C2×C8×C47C2412yes—
247C2×C8×C47C2412yes—
248C4⋊C4×C47—24no—
249C4⋊C4×C47—24no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47C2412yes—
253C4⋊C4×C47C2412yes—
254C42×C47—24no—
255C42×C47—24no—
256C42×C47C2×D412yes—
257C42×C47C2412yes—
258#10625337C22×C4116yescomplemented
259#10625336C22×C4116yescomplemented
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4C2×D414yes—
264(C2×D47)⋊C4C2×D414yes—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—24no—
268C4⋊Dic47—24no—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4C2×D414yes—
275Dic47⋊C4C2×D414yes—
276C4×Dic47—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47C2×D412yes—
282C4×Dic47C2412yes—
283C2×C47⋊C8—22no—
284C2×C47⋊C8C22×C414yes—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287#10625325C22×C4116yescomplemented
288#10625324C22×C4116yescomplemented
289C8×D47—28no—
290C23×C47C22×D411yescharacteristic
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—24no—
294C22×D47—22no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47C4×D414yes—
298C22×D47C22×D412yes—
299Q8×C47—24no—
300Q8×C47—24no—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47C23×C414yes—
304Q8×C47C23×C414yes—
305C2×C4×C47—24no—
306C2×C4×C47—24no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47C23×C412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C2×#4112yes—
320C2×C4×C47C2511yescharacteristic
321C2×Dic47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47C4×D414yes—
330C2×Dic47C22×D412yes—
331C2×Dic47C22×D412yes—
332C2×Dic47C22×D412yes—
333D188—216no—
334D188—24no—
335D188—22no—
336D188C23×C414yes—
337C4×D47—216no—
338C4×D47—216no—
339C4×D47—84no—
340C4×D47—84no—
341C4×D47—84no—
342C4×D47C4×D418yes—
343C4×D47C23×C414yes—
344C4×D47C2×#4114yes—
345Dic94—24no—
346Dic94—22no—
347Dic94—216no—
348Dic94C23×C414yes—
349C8×C47—22no—
350C8×C47C23×C414yes—
351C47⋊C8—22no—
352C47⋊C8C23×C414yes—
353C2×#2947—471nomaximal, Sylow
354C22×C47C2×C4×D412yes—
355C22×C47#57712yes—
356C22×C47#57812yes—
357C22×C47C23×D411yescharacteristic
358C2×D47—28no—
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—24no—
362C2×D47—48no—
363C2×D47—42no—
364C2×D47—42no—
365C2×D47C2×C4×D414yes—
366C4×C47—24no—
367C4×C47—24no—
368C4×C47—22no—
369C4×C47—22no—
370C4×C47—42no—
371C4×C47—42no—
372C4×C47C2×C4×D412yes—
373C4×C47C24×C411yescharacteristic
374C4×C47C22×#4111yescharacteristic
375Dic47—24no—
376Dic47—22no—
377Dic47—22no—
378Dic47—42no—
379Dic47—42no—
380Dic47C2×C4×D414yes—
381C22×#137—471no—
382C2×#520—471no—
383C2×#519—471no—
384#2947—4716no—
385C2×#441—471no—
386C2×#441—471no—
387C2×#440—471no—
388C2×#440—471no—
389C2×C4×Q16—471no—
390C2×C4×Q16D4711yescharacteristic, complemented
391C2×C4×SD16—471no—
392C2×C4×SD16—471no—
393C2×#428—471no—
394C2×#416—471no—
395C22×#103—471no—
396C2×#405—471no—
397C2×C47#294714yescomplemented
398C2×C47C22×C4×D411yescharacteristic
399C2×C47C2×#57711yescharacteristic
400C2×C47C2×#57811yescharacteristic
401D47—24no—
402D47—44no—
403C22×#41—471no—
404C23×Q8—471no—
405C2×#137—4716no—
406C2×#137—478no—
407C22×Q16—471no—
408C22×Q16C2×D4711yescharacteristic
409C22×SD16—471no—
410C22×SD16—471no—
411C22×M16—471no—
412C23×C8—471no—
413#520—478no—
414#520—944no—
415#519—478no—
416#519—944no—
417C2×C4×Q8—471no—
418C2×C4×Q8—471no—
419C2×C4×Q8—471no—
420C2×C4×Q8—471no—
421C2×C4×Q8—941no—
422C2×C4×Q8—941no—
423C2×C4×Q8C2×D4711yescharacteristic
424C2×C4×Q8C2×D4711yescharacteristic
425C2×C4×D4—471no—
426C2×C4×D4—471no—
427C2×C4×D4—941no—
428C2×C4×D4—941no—
429C2×#117—471no—
430C2×#117—471no—
431C2×#117—941no—
432C2×#117—941no—
433C2×#117—941no—
434C22×C4⋊C4—471no—
435C22×C4⋊C4—941no—
436#441—478no—
437#441—478no—
438#440—478no—
439#440—478no—
440C4×Q16—478no—
441C4×Q16C2×D4718yescomplemented
442C4×SD16—478no—
443C4×SD16—478no—
444#428—478no—
445C2×#107—471no—
446C2×#107C2×D4711yescharacteristic
447C2×#106—471no—
448C2×#106—471no—
449#416—478no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#103—471no—
454C2×#103—478no—
455C2×#103C2×D4711yescharacteristic
456C2×#103C2×D4711yescharacteristic
457C2×#102—471no—
458C2×#102—471no—
459#405—478no—
460C2×#97—471no—
461C2×#97—471no—
462C2×C4×C8—471no—
463C2×C4×C8C2×D4711yescharacteristic
464C47C2×#294711yescharacteristic, complemented, Sylow
465C2×#41—478no—
466C2×#41—474no—
467C2×#41—942no—
468C2×#41—944no—
469C22×Q8—478no—
470C22×Q8—474no—
471C22×Q8—471no—
472C22×Q8—941no—
473C22×Q8—942no—
474C22×Q8—944no—
475C22×Q8C22×D4711yescharacteristic
476C22×Q8C22×D4711yescharacteristic
477C22×D4—471no—
478C22×D4—941no—
479C23×C4—471no—
480C23×C4—941no—
481C23×C4—941no—
482C23×C4—941no—
483C23×C4—941no—
484C23×C4—941no—
485#137—4764no—
486C2×Q16—478no—
487C2×Q16—474no—
488C2×Q16C4×D4718yescomplemented
489C2×Q16C22×D4714yes—
490C2×SD16—478no—
491C2×SD16—474no—
492C2×SD16—478no—
493C2×SD16—474no—
494C2×M16—478no—
495C2×M16—474no—
496C22×C8—471no—
497C22×C8—471no—
498C22×C8—474no—
499C22×C8—944no—
500C22×C8C22×D4711yescharacteristic
501C22×C8C22×D4711yescharacteristic
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—474no—
505C4×Q8—474no—
506C4×Q8—474no—
507C4×Q8—474no—
508C4×Q8—948no—
509C4×Q8—942no—
510C4×Q8—942no—
511C4×Q8—942no—
512C4×Q8—948no—
513C4×Q8—942no—
514C4×Q8C22×D4714yes—
515C4×Q8C22×D4714yes—
516C4×D4—474no—
517C4×D4—474no—
518C4×D4—948no—
519C4×D4—942no—
520C4×D4—948no—
521C4×D4—942no—
522#117—474no—
523#117—474no—
524#117—474no—
525#117—948no—
526#117—948no—
527#117—948no—
528#117—942no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—471no—
532C2×C4⋊C4—471no—
533C2×C4⋊C4—471no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—474no—
536C2×C4⋊C4—948no—
537C2×C4⋊C4—942no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4C22×D4711yescharacteristic
544C2×C4⋊C4C22×D4711yescharacteristic
545C2×C22⋊C4—471no—
546C2×C22⋊C4—471no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—471no—
553C2×C42—941no—
554C2×C42—941no—
555C2×C42—941no—
556C2×C42—941no—
557C2×C42—941no—
558C2×C42C22×D4711yescharacteristic
559#107—474no—
560#107C22×D4714yes—
561#106—474no—
562#106—474no—
563#103—474no—
564#103—474no—
565#103—474no—
566#103—474no—
567#103C22×D4714yes—
568#103C22×D4714yes—
569#102—474no—
570#102—474no—
571#97—474no—
572#97—474no—
573C4×C8—474no—
574C4×C8C22×D4714yes—
575C24—471no—
576C24—941no—
577#41—4716no—
578#41—9416no—
579#41—948no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—4716no—
585C2×Q8—474no—
586C2×Q8—472no—
587C2×Q8—944no—
588C2×Q8—948no—
589C2×Q8—9416no—
590C2×Q8—948no—
591C2×Q8—941no—
592C2×Q8—942no—
593C2×Q8C2×C4×D4714yes—
594C2×Q8C2×C4×D4714yes—
595C2×Q8C23×D4712yes—
596C2×Q8C23×D4712yes—
597C2×D4—474no—
598C2×D4—472no—
599C2×D4—944no—
600C2×D4—948no—
601C2×D4—941no—
602C2×D4—942no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—471no—
608C22×C4—474no—
609C22×C4—472no—
610C22×C4—474no—
611C22×C4—472no—
612C22×C4—471no—
613C22×C4—471no—
614C22×C4—944no—
615C22×C4—948no—
616C22×C4—944no—
617C22×C4—944no—
618C22×C4—948no—
619C22×C4—944no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—944no—
624C22×C4—3762no—
625C22×C4—3762no—
626C22×C4—3762no—
627C22×C4D4×D4711yescharacteristic
628C22×C4D4×D4711yescharacteristic
629C22×C4C23×D4711yescharacteristic
630Q16—4716no—
631Q16C2×C4×D47116yescomplemented
632SD16—4716no—
633SD16—4716no—
634M16—4716no—
635C2×C8—22no—
636C2×C8—474no—
637C2×C8—472no—
638C2×C8—472no—
639C2×C8—948no—
640C2×C8—942no—
641C2×C8C2×C4×D4714yes—
642C2×C8C23×D4712yes—
643C2×C8C23×D4712yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—474no—
649C4⋊C4—474no—
650C4⋊C4—472no—
651C4⋊C4—472no—
652C4⋊C4—944no—
653C4⋊C4—944no—
654C4⋊C4—944no—
655C4⋊C4—944no—
656C4⋊C4—944no—
657C4⋊C4—941no—
658C4⋊C4—941no—
659C4⋊C4C23×D4712yes—
660C4⋊C4C23×D4712yes—
661C22⋊C4—474no—
662C22⋊C4—474no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C42—24no—
667C42—24no—
668C42—472no—
669C42—472no—
670C42—944no—
671C42—944no—
672C42—944no—
673C42—944no—
674C42—944no—
675C42D4×D4712yes—
676C42C23×D4712yes—
677C23—474no—
678C23—472no—
679C23—942no—
680C23—942no—
681C23—944no—
682C23—942no—
683C23—1882no—
684C23—1882no—
685C23C2×D4×D4711yescharacteristic
686Q8—24no—
687Q8—24no—
688Q8—22no—
689Q8—22no—
690Q8—474no—
691Q8—9416no—
692Q8—944no—
693Q8—942no—
694Q8C22×C4×D4714yes—
695Q8C22×C4×D4714yes—
696D4—474no—
697D4—9416no—
698D4—944no—
699D4—942no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—474no—
711C2×C4—472no—
712C2×C4—478no—
713C2×C4—474no—
714C2×C4—474no—
715C2×C4—472no—
716C2×C4—472no—
717C2×C4—9416no—
718C2×C4—9416no—
719C2×C4—944no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—3764no—
726C2×C4—3764no—
727C2×C4—3764no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4C22×C4×D4712yes—
731C2×C4C2×D4×D4712yes—
732C2×C4C2×D4×D4712yes—
733C2×C4C2×D4×D4711yescharacteristic
734C2×C4#41×D4712yes—
735C2×C4C24×D4711yescharacteristic
736C8—22no—
737C8—474no—
738C8—942no—
739C8C22×C4×D4714yes—
740C22—474no—
741C22—948no—
742C22—942no—
743C22—942no—
744C22—944no—
745C22—1888no—
746C22—1882no—
747C22—1882no—
748C22C4×D4×D4712yes—
749C22#1568993012yes—
750C22#1568993612yes—
751C22C22×D4×D4711yescharacteristic
752C4—24no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—474no—
759C4—944no—
760C4—942no—
761C4—942no—
762C4—1882no—
763C4—1882no—
764C4C4×D4×D4712yes—
765C4C23×C4×D4711yescharacteristic
766C4C2×#41×D4711yescharacteristic
767C2—944no—
768C2—1884no—
769C2#2025222614yesdirect product factor
770C2C2×C4×D4×D4711yescharacteristic
771C2C2×#1568993011yescharacteristic
772C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C4×Q16×C47C2
socleC23×C47C22×D4
prime radicalC22×#10625354C22
cosocleC2×C4×C47C25
hypercenterC2×C4×Q16D47
hypocenterC47C2×#2947
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×#15689599C2semidirect
4. #20252226C2direct (N × H)
5. C2×#15689230C2semidirect
6. C2×#15689228C2semidirect
7. C2×#15689222C2semidirect
8. C2×#15689221C2semidirect
9. C2×#15689215C2semidirect
10. C2×C4×#10625325C2semidirect
11. C2×#15689208C2semidirect
12. C2×#15689164C2semidirect
14. C2×#103×D47C2semidirect
15. C2×#15689077C2semidirect
16. C2×C4×Q16×C47C2semidirect
19. C2×#13094056C4semidirect
29. #15689599C22semidirect
47. #15689230C22semidirect
48. #15689228C22semidirect
49. #15689222C22semidirect
50. #15689221C22semidirect
51. #15689215C22semidirect
52. C4×#10625325C22semidirect
53. #15689208C22semidirect
54. #15689164C22semidirect
63. #103×D47C22semidirect
66. #15689077C22semidirect
73. C4×Q16×C47C22semidirect
86. C2×Q8×D47C2×C4semidirect
96. #13094056C2×C4semidirect
97. C2×#10625337C2×C4semidirect
99. C2×#10625325C2×C4semidirect
101. C2×#10625336C2×C4semidirect
103. C2×#10625324C2×C4semidirect
169. C2×Q16×C47C2×C4semidirect
216. Q8×D47C22×C4semidirect
243. Q16×C47C22×C4semidirect
258. #10625337C22×C4semidirect
259. #10625336C22×C4semidirect
287. #10625325C22×C4semidirect
288. #10625324C22×C4semidirect
390. C2×C4×Q16D47semidirect
397. C2×C47#2947semidirect
441. C4×Q16C2×D47semidirect
464. C47C2×#2947semidirect
488. C2×Q16C4×D47semidirect
631. Q16C2×C4×D47semidirect
769. C2#20252226direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940562
C2×#156896052
C2×#156895992
#202522262
C2×#156892302
C2×#156892282
C2×#156892222
C2×#156892212
C2×#156892152
C2×C4×#106253252
C2×#156892082
C2×#156891642
C2×#156891182
C2×#103×D472
C2×#156890772
C2×C4×Q16×C472
C2×#294747