Finite Group Databasebeta

← #35567425

Subgroups — #35567425

Order 21248.

2190 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128238C211yesmaximal, characteristic
2#24910608C214yesmaximal, complemented
3#24910558C212yesmaximal, complemented
4#24910530C212yesmaximal, complemented
5#24910420C211yesmaximal, characteristic, complemented
6#24910414C212yesmaximal, complemented
7#24910410C211yesmaximal, characteristic, complemented
8#24910395C212yesmaximal, complemented
9#24910363C211yesmaximal, characteristic, complemented
10#24910231C214yesmaximal, complemented
11#24910154C212yesmaximal
12#24910139C212yesmaximal, complemented
13#24910084C212yesmaximal, complemented
14#24910068C212yesmaximal, complemented
15#24909868C211yesmaximal, characteristic, complemented
16#24909867C211yesmaximal, characteristic, complemented
17Q8×C4⋊C4×C83C211yesmaximal, characteristic, complemented
18#19128238C4116yescomplemented
19C2×#14581787C2212yes—
20C2×#14581783C2211yescharacteristic
21C2×#14581781C2211yescharacteristic
22C2×#14581777C2212yes—
23C2×#14581768C2211yescharacteristic
24C2×#14581767C2211yescharacteristic
25C2×C4×D332C2211yescharacteristic
26C2×C4×D332C2212yes—
27C2×#14581754C2212yes—
28C2×#14581750C2212yes—
29C2×#14581750C2212yes—
30C2×#14581749C2212yes—
31C2×#14581749C2212yes—
32C2×C4⋊C4×D83C2212yes—
33C2×C42×D83C2211yescharacteristic
34#19127608C2212yes—
35#19127603C2212yes—
36#19127602C2214yes—
37#19127597C2212yes—
38#19127596C2214yes—
39#19127596C2214yes—
40#19127593C2214yes—
41#19127592C2214yes—
42#19127592C2214yes—
43#19127591C2214yes—
44#19127591C2214yes—
45#19127590C2214yes—
46#19127587C2214yes—
47#19127586C2214yes—
48#19127585C2214yes—
49#19127583C2214yes—
50#19127579C2214yes—
51#19127572C2214yes—
52#19127572C2214yes—
53#19127572C2214yes—
54#19127571C2211yescharacteristic
55#19127570C2211yescharacteristic
56#19127570C2211yescharacteristic
57#19127567C2212yes—
58#19127566C2212yes—
59#19127565C2212yes—
60#19127560C2212yes—
61#19127558C2212yes—
62#19127558C2212yes—
63#19127558C2211yescharacteristic
64#19127558C2211yescharacteristic
65#19127558C2212yes—
66#19127558C2212yes—
67C4⋊C4×Dic83C2212yes—
68C4⋊C4×Dic83C2212yes—
69C4⋊C4×Dic83C2212yes—
70C4⋊C4×Dic83C2214yes—
71C4×Dic83⋊C4C2212yes—
72C4×C4⋊Dic83C2211yescharacteristic
73C4×C4⋊Dic83C2212yes—
74C4×C4⋊Dic83C2212yes—
75C4×(C2×D83)⋊C4C2214yes—
76C2×C4×Q8×C83C2212yes—
77C2×C4×Q8×C83C2211yescharacteristic
78#389×C83C2214yes—
79#389×C83C2212yes—
80#384×C83C2212yes—
81#384×C83C2211yescharacteristic
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C22×D332C2311yescharacteristic
85C22×D332C2312yes—
86C22×C4×D83C2311yescharacteristic
87C22×C4×D83C2311yescharacteristic
88C22×C4×D83C2312yes—
89C22×C4×D83C2314yes—
90C22×C4×D83C2311yescharacteristic
91#14581787C2×C4116yescomplemented
92#14581783C2×C418yescomplemented
93#14581781C2×C418yes—
94#14581777C2×C4116yescomplemented
95#14581768C2×C418yescomplemented
96#14581767C2×C418yes—
97C4×D332C2×C418yes—
98C4×D332C2×C4116yescomplemented
99#14581754—44no—
100#14581750—44no—
101#14581750—44no—
102#14581749—44no—
103#14581749C2×C4116yescomplemented
104C2×C4⋊Dic83C2311yescharacteristic
105C2×C4⋊Dic83C2312yes—
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2312yes—
111C2×Dic83⋊C4C2312yes—
112C2×Dic83⋊C4C2312yes—
113C2×Dic83⋊C4C2312yes—
114C2×Dic83⋊C4C2312yes—
115C2×Dic83⋊C4C2314yes—
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2312yes—
118C4⋊C4×D83—44no—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2312yes—
121C2×(C2×D83)⋊C4C2312yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2314yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×(C2×D83)⋊C4C2312yes—
128C2×(C2×D83)⋊C4C2312yes—
129C2×(C2×D83)⋊C4C2312yes—
130C2×C4×Dic83C2312yes—
131C2×C4×Dic83C2314yes—
132C2×C4×Dic83C2314yes—
133C2×C4×Dic83C2314yes—
134C2×C4×Dic83C2311yescharacteristic
135C2×C4×Dic83C2311yescharacteristic
136C2×C4×Dic83C2311yescharacteristic
137C42×D83C2×C418yescomplemented
138C83⋊#95C2314yes—
139C83⋊#95C2312yes—
140C83⋊#95C2314yes—
141C83⋊#95C2312yes—
142C83⋊#95C2312yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C83⋊#95C2314yes—
147C83⋊#95C2314yes—
148C22×Q8×C83C2311yescharacteristic
149C4×Q8×C83—44no—
150C4×Q8×C83C2×C418yescomplemented
151C2×C4⋊C4×C83C2312yes—
152C2×C4⋊C4×C83C2311yescharacteristic
153C2×C4⋊C4×C83C2312yes—
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2314yes—
157C2×C4⋊C4×C83C2314yes—
158C2×C4⋊C4×C83C2311yescharacteristic
159C2×C4⋊C4×C83C2312yes—
160C2×C42×C83C2312yes—
161C2×C42×C83C2314yes—
162C2×C42×C83C2312yes—
163C2×C42×C83C2311yescharacteristic
164#95×C83C2312yes—
165#95×C83C2314yes—
166C23×D83C2411yescharacteristic
167C23×D83C2412yes—
168C2×D332—22no—
169C2×D332—22no—
170C2×D332—42no—
171C2×D332—42no—
172C2×D332C22×C414yes—
173C2×D332C22×C418yes—
174C22×Dic83C2412yes—
175C22×Dic83C2412yes—
176C22×Dic83C2414yes—
177C22×Dic83C2411yescharacteristic
178C22×Dic83C2411yescharacteristic
179C22×Dic83C2411yescharacteristic
180C22×Dic83C2412yes—
181C2×C4×D83—24no—
182C2×C4×D83—22no—
183C2×C4×D83—22no—
184C2×C4×D83—22no—
185C2×C4×D83—24no—
186C2×C4×D83—22no—
187C2×C4×D83—41no—
188C2×C4×D83—41no—
189C2×C4×D83—44no—
190C2×C4×D83—44no—
191C2×C4×D83—44no—
192C2×C4×D83C22×C414yes—
193C2×C4×D83C22×C414yes—
194C2×C4×D83C22×C418yes—
195C2×C4×D83C22×C414yes—
196C4⋊Dic83—22no—
197C4⋊Dic83—24no—
198C4⋊Dic83—22no—
199C4⋊Dic83—24no—
200C4⋊Dic83—42no—
201C4⋊Dic83C22×C414yes—
202C4⋊Dic83C22×C418yes—
203Dic83⋊C4—44no—
204Dic83⋊C4—42no—
205Dic83⋊C4—42no—
206Dic83⋊C4—42no—
207Dic83⋊C4—42no—
208Dic83⋊C4C22×C418yes—
209Dic83⋊C4C22×C418yes—
210(C2×D83)⋊C4—44no—
211(C2×D83)⋊C4—42no—
212(C2×D83)⋊C4—42no—
213(C2×D83)⋊C4—44no—
214(C2×D83)⋊C4—44no—
215(C2×D83)⋊C4—44no—
216(C2×D83)⋊C4C22×C418yes—
217(C2×D83)⋊C4C22×C418yes—
218(C2×D83)⋊C4C22×C418yes—
219(C2×D83)⋊C4C22×C418yes—
220(C2×D83)⋊C4C22×C418yes—
221C4×Dic83—24no—
222C4×Dic83—44no—
223C4×Dic83—44no—
224C4×Dic83—44no—
225C4×Dic83C22×C414yes—
226C4×Dic83C22×C414yes—
227C4×Dic83C22×C414yes—
228C2×Q8×C83—22no—
229C2×Q8×C83—22no—
230C2×Q8×C83C22×C414yes—
231C22×C4×C83C2414yes—
232C22×C4×C83C2412yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2411yescharacteristic
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2411yescharacteristic
238C22×C4×C83C2411yescharacteristic
239C4⋊C4×C83—24no—
240C4⋊C4×C83—24no—
241C4⋊C4×C83—22no—
242C4⋊C4×C83—22no—
243C4⋊C4×C83—42no—
244C4⋊C4×C83—44no—
245C4⋊C4×C83—44no—
246C4⋊C4×C83C22×C414yes—
247C4⋊C4×C83C22×C418yes—
248C42×C83—24no—
249C42×C83—44no—
250C42×C83C22×C414yes—
251C42×C83C22×C418yes—
252C23×C83C2511yescharacteristic
253C22×D83—21no—
254C22×D83—21no—
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—21no—
258C22×D83—22no—
259C22×D83—21no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—21no—
264C22×D83—21no—
265C22×D83C23×C414yes—
266C22×D83C23×C412yes—
267Q8×C83—28no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—21no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—21no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—24no—
277C2×C4×C83—22no—
278C2×C4×C83—24no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—24no—
282C2×C4×C83—22no—
283C2×C4×C83C23×C412yes—
284C2×C4×C83C23×C414yes—
285C2×C4×C83C23×C414yes—
286C2×C4×C83C23×C412yes—
287C2×C4×C83C23×C412yes—
288C2×C4×C83H(5,𝔽2)12yes—
289C2×C4×C83H(5,𝔽2)12yes—
290C2×C4×C832−1+412yes—
291C2×C4×C832−1+412yes—
292C2×Dic83—21no—
293C2×Dic83—22no—
294C2×Dic83—21no—
295C2×Dic83—21no—
296C2×Dic83—22no—
297C2×Dic83—21no—
298C2×Dic83—21no—
299C2×Dic83—21no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—24no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—24no—
306C2×Dic83—22no—
307C2×Dic83—24no—
308C2×Dic83—22no—
309C2×Dic83C23×C412yes—
310C2×Dic83C23×C412yes—
311C2×Dic83C23×C412yes—
312C2×Dic83C23×C414yes—
313D332—28no—
314D332—48no—
315C4×D83—28no—
316C4×D83—216no—
317C4×D83—28no—
318C4×D83—44no—
319C4×D83—88no—
320C22×C83C24×C411yescharacteristic
321C22×C83C2×H(5,𝔽2)11yescharacteristic
322C22×C83C2×H(5,𝔽2)11yescharacteristic
323C22×C83C2×2−1+411yescharacteristic
324C22×C83C2×2−1+411yescharacteristic
325C22×C83#58511yescharacteristic
326C22×C83#58511yescharacteristic
327C2×D83—22no—
328C2×D83—22no—
329C2×D83—24no—
330C2×D83—24no—
331C2×D83—22no—
332C2×D83—24no—
333C2×D83—42no—
334C2×D83—41no—
335C2×D83—41no—
336C2×D83—42no—
337C2×D83—41no—
338C2×D83—42no—
339C2×D83—41no—
340C2×D83—42no—
341C4×C83—24no—
342C4×C83—22no—
343C4×C83—24no—
344C4×C83—44no—
345C4×C83—42no—
346C4×C83—42no—
347C4×C83#52014yes—
348C4×C83#52014yes—
349Dic83—22no—
350Dic83—22no—
351Dic83—24no—
352Dic83—22no—
353Dic83—42no—
354Dic83—42no—
355Dic83—44no—
356#34383—831nomaximal, Sylow
357C2×C83C2×#52011yescharacteristic
358C2×C83C2×#52011yescharacteristic
359C2×C83#342811yescharacteristic
360C2×C83#354611yescharacteristic
361C2×C83#354711yescharacteristic
362C2×C83#355411yescharacteristic
363C2×C83#355511yescharacteristic
364D83—42no—
365D83—44no—
366C2×#529—831no—
367#2376—834no—
368#2370—832no—
369#2367—832no—
370#2355—831no—
371#2354—832no—
372#2354—831no—
373#2352—832no—
374Q8×C4⋊C4D8311yescharacteristic, complemented
375D4×C4⋊C4—831no—
376#2334—834no—
377#2324—832no—
378#2323—832no—
379#2317—832no—
380#2314—832no—
381#2285—831no—
382#2285—831no—
383C83#3438311yescharacteristic, complemented, Sylow
384#529—8316no—
385C2×#126—832no—
386C2×#125—831no—
387C2×#124—831no—
388C2×#123—832no—
389C2×C22⋊Q8—831no—
390C2×#121—831no—
391C2×C4×Q8C2×D8312yes—
392C2×C4×Q8C2×D8311yescharacteristic
393C2×C4×D4—832no—
394C2×C4×D4—831no—
395C2×C4×D4—832no—
396C2×#117—832no—
397C2×#117—832no—
398C2×#117—832no—
399C2×#117—832no—
400C22×C4⋊C4—832no—
401C22×C42—831no—
402#391—832no—
403#390—834no—
404#390—832no—
405#389—834no—
406#389—834no—
407#389—832no—
408#389C2×D8312yes—
409#389C2×D8314yes—
410#388—834no—
411#388—834no—
412#388—834no—
413#388—834no—
414#388—834no—
415#388—834no—
416#387—834no—
417#387—834no—
418#387—834no—
419#387—834no—
420#386—834no—
421#385—834no—
422#385—834no—
423#385—834no—
424#384—831no—
425#384—831no—
426#384—831no—
427#384C2×D8312yes—
428#384C2×D8311yescharacteristic
429#382—832no—
430#382—832no—
431#382—832no—
432#380—832no—
433#380—832no—
434#380—832no—
435#380—831no—
436#380—831no—
437#380—832no—
438#380—832no—
439C4×C4⋊C4—832no—
440C4×C4⋊C4—832no—
441C4×C4⋊C4—834no—
442C4×C4⋊C4—832no—
443C4×C4⋊C4—832no—
444C4×C4⋊C4—832no—
445C4×C4⋊C4—831no—
446C4×C4⋊C4—832no—
447C4×C4⋊C4C2×D8312yes—
448C4×C4⋊C4C2×D8311yescharacteristic
449C4×C22⋊C4—834no—
450C22×Q8C22×D8311yescharacteristic
451C22×D4—832no—
452C22×D4—831no—
453C23×C4—834no—
454C23×C4—831no—
455C23×C4—832no—
456C23×C4—831no—
457C23×C4—831no—
458#126—8316no—
459#125—838no—
460#124—838no—
461#123—8316no—
462C22⋊Q8—838no—
463#121—838no—
464C4×Q8—44no—
465C4×Q8C4×D8318yescomplemented
466C4×D4—3324no—
467C4×D4—838no—
468C4×D4—8316no—
469#117—3324no—
470#117—3324no—
471#117—3324no—
472#117—8316no—
473C2×C4⋊C4—3324no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—832no—
476C2×C4⋊C4—832no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—832no—
479C2×C4⋊C4—832no—
480C2×C4⋊C4—832no—
481C2×C4⋊C4—832no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—832no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—832no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—832no—
488C2×C4⋊C4C22×D8312yes—
489C2×C4⋊C4C22×D8311yescharacteristic
490C2×C4⋊C4C22×D8312yes—
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8314yes—
493C2×C4⋊C4C22×D8312yes—
494C2×C4⋊C4C22×D8314yes—
495C2×C4⋊C4C22×D8311yescharacteristic
496C2×C4⋊C4C22×D8312yes—
497C2×C22⋊C4—832no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—834no—
502C2×C22⋊C4—834no—
503C2×C22⋊C4—832no—
504C2×C22⋊C4—832no—
505C2×C22⋊C4—832no—
506C2×C22⋊C4—832no—
507C2×C22⋊C4—832no—
508C2×C42—834no—
509C2×C42—834no—
510C2×C42—834no—
511C2×C42—831no—
512C2×C42—831no—
513C2×C42—831no—
514C2×C42—838no—
515C2×C42—832no—
516C2×C42C22×D8312yes—
517C2×C42C22×D8314yes—
518C2×C42C22×D8312yes—
519C2×C42C22×D8311yescharacteristic
520#95—832no—
521#95—834no—
522#95—832no—
523#95—832no—
524#95—834no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95—834no—
530#95C22×D8312yes—
531#95C22×D8314yes—
532C24—832no—
533C24—831no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8C2×C4×D8314yes—
537C2×D4—3322no—
538C2×D4—3322no—
539C2×D4—838no—
540C2×D4—834no—
541C2×D4—1662no—
542C2×D4—1662no—
543C22×C4—3321no—
544C22×C4—3321no—
545C22×C4—3324no—
546C22×C4—3324no—
547C22×C4—3324no—
548C22×C4—834no—
549C22×C4—831no—
550C22×C4—831no—
551C22×C4—831no—
552C22×C4—832no—
553C22×C4—834no—
554C22×C4—834no—
555C22×C4—838no—
556C22×C4—832no—
557C22×C4—834no—
558C22×C4—832no—
559C22×C4—1662no—
560C22×C4—1664no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1664no—
564C22×C4—1662no—
565C22×C4C23×D8312yes—
566C22×C4C23×D8314yes—
567C22×C4C23×D8312yes—
568C22×C4C23×D8312yes—
569C22×C4C23×D8312yes—
570C22×C4C23×D8311yescharacteristic
571C22×C4C23×D8311yescharacteristic
572C22×C4C23×D8311yescharacteristic
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—3324no—
581C4⋊C4—3322no—
582C4⋊C4—3322no—
583C4⋊C4—3322no—
584C4⋊C4—3322no—
585C4⋊C4—3322no—
586C4⋊C4—838no—
587C4⋊C4—838no—
588C4⋊C4—834no—
589C4⋊C4—838no—
590C4⋊C4—1662no—
591C4⋊C4—1664no—
592C4⋊C4—1664no—
593C4⋊C4—1662no—
594C4⋊C4C2×C4×D8314yes—
595C4⋊C4C2×C4×D8318yes—
596C22⋊C4—3322no—
597C22⋊C4—3322no—
598C22⋊C4—3324no—
599C22⋊C4—3324no—
600C22⋊C4—3324no—
601C22⋊C4—3324no—
602C22⋊C4—838no—
603C22⋊C4—838no—
604C22⋊C4—838no—
605C22⋊C4—838no—
606C22⋊C4—838no—
607C42—24no—
608C42—44no—
609C42—3324no—
610C42—3324no—
611C42—3324no—
612C42—834no—
613C42—834no—
614C42—834no—
615C42—1664no—
616C42C2×C4×D8314yes—
617C42C2×C4×D8318yes—
618C23—834no—
619C23—832no—
620C23—1661no—
621C23—1662no—
622C23—1661no—
623C23—1662no—
624C23—1661no—
625C23—1661no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23—1661no—
630C23—1662no—
631C23—1661no—
632C23C24×D8311yescharacteristic
633Q8—28no—
634D4—3328no—
635D4—1668no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—3324no—
652C2×C4—832no—
653C2×C4—832no—
654C2×C4—832no—
655C2×C4—834no—
656C2×C4—6648no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1664no—
660C2×C4—1662no—
661C2×C4—1664no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1664no—
666C2×C4—1661no—
667C2×C4—1661no—
668C2×C4—1662no—
669C2×C4—1661no—
670C2×C4—1661no—
671C2×C4—1662no—
672C2×C4—1661no—
673C2×C4—1661no—
674C2×C4—1668no—
675C2×C4—1668no—
676C2×C4—16616no—
677C2×C4C22×C4×D8312yes—
678C2×C4C22×C4×D8314yes—
679C2×C4C22×C4×D8314yes—
680C2×C4C22×C4×D8312yes—
681C2×C4C22×C4×D8312yes—
682C2×C4#1458183712yes—
683C2×C4#1458183812yes—
684C2×C4#1458184012yes—
685C2×C4#1458184012yes—
686C22—3321no—
687C22—3322no—
688C22—3321no—
689C22—3322no—
690C22—3322no—
691C22—3321no—
692C22—3321no—
693C22—3322no—
694C22—1662no—
695C22—1664no—
696C22—1664no—
697C22—1662no—
698C22—1662no—
699C22—1664no—
700C22C23×C4×D8311yescharacteristic
701C22C2×#1458183711yescharacteristic
702C22C2×#1458183811yescharacteristic
703C22C2×#1458184011yescharacteristic
704C22C2×#1458184011yescharacteristic
705C22#1912853611yescharacteristic
706C22#1912853811yescharacteristic
707C4—24no—
708C4—22no—
709C4—24no—
710C4—44no—
711C4—42no—
712C4—42no—
713C4—3324no—
714C4—3322no—
715C4—3322no—
716C4—1662no—
717C4—1662no—
718C4—1664no—
719C4—1662no—
720C4#1912818214yes—
721C4#1912818314yes—
722C2—3324no—
723C2—3322no—
724C2C2×#1912818211yescharacteristic
725C2C2×#1912818311yescharacteristic
726C2#2492066311yescharacteristic
727C2#2492182311yescharacteristic
728C2#2492184811yescharacteristic
729C2#2492193711yescharacteristic
730C2#2492195211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingQ8×C4⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#14581767C22
hypercenterQ8×C4⋊C4D83
hypocenterC83#34383
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #24910608C2semidirect
3. #24910558C2semidirect
4. #24910530C2semidirect
5. #24910420C2semidirect
6. #24910414C2semidirect
7. #24910410C2semidirect
8. #24910395C2semidirect
9. #24910363C2semidirect
10. #24910231C2semidirect
12. #24910139C2semidirect
13. #24910084C2semidirect
14. #24910068C2semidirect
15. #24909868C2semidirect
16. #24909867C2semidirect
17. Q8×C4⋊C4×C83C2semidirect
18. #19128238C4semidirect
91. #14581787C2×C4semidirect
92. #14581783C2×C4semidirect
94. #14581777C2×C4semidirect
95. #14581768C2×C4semidirect
98. C4×D332C2×C4semidirect
103. #14581749C2×C4semidirect
137. C42×D83C2×C4semidirect
150. C4×Q8×C83C2×C4semidirect
374. Q8×C4⋊C4D83semidirect
383. C83#34383semidirect
465. C4×Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282382
#249106082
#249105582
#249105302
#249104202
#249104142
#249104102
#249103952
#249103632
#249102312
#249101542
#249101392
#249100842
#249100682
#249098682
#249098672
Q8×C4⋊C4×C832
#3438383