Finite Group Databasebeta

← #35569522

Subgroups — #35569522

Order 21248.

2436 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128354C211yesmaximal, characteristic
2#24910608C214yesmaximal, complemented
3#24910523C211yesmaximal, characteristic, complemented
4#24910503C212yesmaximal, complemented
5#24910464C212yesmaximal, complemented
6#24910414C211yesmaximal, characteristic, complemented
7#24910363C211yesmaximal, characteristic, complemented
8#24910336C212yesmaximal, complemented
9#24910301C212yesmaximal, complemented
10#24910247C214yesmaximal, complemented
11#24910154C212yesmaximal, complemented
12#24910148C212yesmaximal, complemented
13#24910078C212yesmaximal, complemented
14#24910054C212yesmaximal, complemented
15#24909927C211yesmaximal, characteristic, complemented
16#24909927C211yesmaximal, characteristic, complemented
17C4×C4⋊Q8×C83C211yesmaximal, characteristic, complemented
18C22×#13050591C2212yes—
19#19128354C4116yescomplemented
20C2×#14581777C2214yes—
21C2×#14581768C2212yes—
22C2×#14581767C2212yes—
23C2×Q8×Dic83C2212yes—
24C2×C4×D332C2211yescharacteristic
25C2×C4×D332C2211yescharacteristic
26C2×#14581754C2212yes—
27C2×#14581750C2212yes—
28C2×#14581749C2212yes—
29C2×#14581749C2212yes—
30C2×C4⋊C4×D83C2212yes—
31C2×C4⋊C4×D83C2212yes—
32#19127608C2212yes—
33#19127603C2211yescharacteristic
34#19127603C2211yescharacteristic
35#19127603C2211yescharacteristic
36#19127603C2211yescharacteristic
37#19127603C2214yes—
38#19127602C2214yes—
39#19127602C2212yes—
40#19127600C2212yes—
41#19127599C2211yescharacteristic
42#19127599C2211yescharacteristic
43#19127599C2211yescharacteristic
44#19127599C2211yescharacteristic
45#19127598C2214yes—
46#19127597C2212yes—
47#19127596C2214yes—
48#19127593C2214yes—
49#19127592C2212yes—
50#19127592C2212yes—
51#19127592C2212yes—
52#19127592C2212yes—
53#19127591C2214yes—
54#19127590C2214yes—
55#19127587C2214yes—
56#19127585C2214yes—
57#19127583C2214yes—
58#19127579C2214yes—
59#19127579C2214yes—
60#19127572C2214yes—
61#19127572C2214yes—
62#19127560C2214yes—
63#19127560C2214yes—
64#19127558C2212yes—
65#19127558C2214yes—
66#19127558C2212yes—
67C4⋊C4×Dic83C2212yes—
68C4⋊C4×Dic83C2212yes—
69C4×C4⋊Dic83C2211yescharacteristic
70C4×C4⋊Dic83C2211yescharacteristic
71C4×(C2×D83)⋊C4C2212yes—
72C4×(C2×D83)⋊C4C2214yes—
73C4×(C2×D83)⋊C4C2212yes—
74C4×(C2×D83)⋊C4C2214yes—
75C2×C4⋊Q8×C83C2211yescharacteristic
76C2×C4×Q8×C83C2212yes—
77#391×C83C2212yes—
78#389×C83C2212yes—
79#389×C83C2212yes—
80#384×C83C2211yescharacteristic
81C4×C4⋊C4×C83C2212yes—
82C4×C4⋊C4×C83C2212yes—
83C43×C83C2211yescharacteristic
84C2×#13050591—44no—
85C2×#13050591—44no—
86C2×#13050591C2×C4116yescomplemented
87C22×D332C2311yescharacteristic
88C22×D332C2311yescharacteristic
89C22×D332C2314yes—
90C22×C4×D83C2312yes—
91C22×C4×D83C2312yes—
92C22×C4×D83C2314yes—
93C22×C4×D83C2314yes—
94#14581777C2×C4132yescomplemented
95#14581768C2×C4116yescomplemented
96#14581767C2×C4116yes—
97Q8×Dic83—44no—
98C4×D332C2×C418yes—
99C4×D332C2×C418yescomplemented
100#14581754—44no—
101#14581750—44no—
102#14581749—44no—
103#14581749—44no—
104C2×C4⋊Dic83C2311yescharacteristic
105C2×C4⋊Dic83C2311yescharacteristic
106C2×C4⋊Dic83C2311yescharacteristic
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2314yes—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2311yescharacteristic
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2312yes—
113C2×Dic83⋊C4C2312yes—
114C2×Dic83⋊C4C2312yes—
115C2×Dic83⋊C4C2312yes—
116C2×Dic83⋊C4C2314yes—
117C4⋊C4×D83—44no—
118C4⋊C4×D83C2×C4116yescomplemented
119C2×(C2×D83)⋊C4C2312yes—
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×(C2×D83)⋊C4C2312yes—
131C2×(C2×D83)⋊C4C2314yes—
132C2×(C2×D83)⋊C4C2312yes—
133C2×C4×Dic83C2312yes—
134C2×C4×Dic83C2312yes—
135C2×C4×Dic83C2314yes—
136C2×C4×Dic83C2314yes—
137C83⋊#95C2312yes—
138C83⋊#95C2312yes—
139C83⋊#95C2314yes—
140C83⋊#95C2314yes—
141C83⋊#95C2314yes—
142C83⋊#95C2312yes—
143C83⋊#95C2314yes—
144C83⋊#95C2312yes—
145C83⋊#95C2312yes—
146C83⋊#95C2312yes—
147C22×Q8×C83C2312yes—
148C4⋊Q8×C83C2×C418yescomplemented
149C4×Q8×C83—44no—
150C2×C4⋊C4×C83C2312yes—
151C2×C4⋊C4×C83C2312yes—
152C2×C4⋊C4×C83C2314yes—
153C2×C4⋊C4×C83C2312yes—
154C2×C4⋊C4×C83C2312yes—
155C2×C4⋊C4×C83C2312yes—
156C2×C42×C83C2311yescharacteristic
157C2×C42×C83C2311yescharacteristic
158C2×C42×C83C2311yescharacteristic
159C2×C42×C83C2311yescharacteristic
160C2×C42×C83C2311yescharacteristic
161C2×C42×C83C2314yes—
162C2×C42×C83C2311yescharacteristic
163C2×C42×C83C2311yescharacteristic
164#95×C83C2314yes—
165#95×C83C2314yes—
166C23×D83C2412yes—
167C23×D83C2412yes—
168#13050591—432no—
169C2×D332—22no—
170C2×D332—22no—
171C2×D332—22no—
172C2×D332—22no—
173C2×D332—44no—
174C2×D332—44no—
175C2×D332C22×C414yes—
176C2×D332C22×C414yes—
177C2×D332C22×C4116yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C2×C4×D83—24no—
185C2×C4×D83—24no—
186C2×C4×D83—24no—
187C2×C4×D83—24no—
188C2×C4×D83—44no—
189C2×C4×D83—44no—
190C2×C4×D83—44no—
191C2×C4×D83—44no—
192C2×C4×D83—44no—
193C2×C4×D83C22×C418yes—
194C2×C4×D83C22×C418yes—
195C2×C4×D83C22×C4116yes—
196C4⋊Dic83—22no—
197C4⋊Dic83—22no—
198C4⋊Dic83—22no—
199C4⋊Dic83—22no—
200C4⋊Dic83—44no—
201C4⋊Dic83C22×C414yes—
202C4⋊Dic83C22×C414yes—
203Dic83⋊C4—44no—
204Dic83⋊C4—42no—
205Dic83⋊C4—42no—
206Dic83⋊C4—42no—
207Dic83⋊C4—42no—
208Dic83⋊C4C22×C4116yes—
209(C2×D83)⋊C4—24no—
210(C2×D83)⋊C4—24no—
211(C2×D83)⋊C4—42no—
212(C2×D83)⋊C4—44no—
213(C2×D83)⋊C4—42no—
214(C2×D83)⋊C4—42no—
215(C2×D83)⋊C4—42no—
216(C2×D83)⋊C4—42no—
217(C2×D83)⋊C4—42no—
218(C2×D83)⋊C4—44no—
219(C2×D83)⋊C4—44no—
220(C2×D83)⋊C4C22×C4116yes—
221(C2×D83)⋊C4C22×C418yes—
222(C2×D83)⋊C4C22×C418yes—
223C4×Dic83—24no—
224C4×Dic83—24no—
225C4×Dic83—44no—
226C4×Dic83—44no—
227C2×Q8×C83—24no—
228C2×Q8×C83—24no—
229C2×Q8×C83C22×C418yes—
230C22×C4×C83C2414yes—
231C22×C4×C83C2411yescharacteristic
232C22×C4×C83C2411yescharacteristic
233C22×C4×C83C2411yescharacteristic
234C22×C4×C83C2414yes—
235C22×C4×C83C2411yescharacteristic
236C22×C4×C83C2411yescharacteristic
237C22×C4×C83C2411yescharacteristic
238C22×C4×C83C2411yescharacteristic
239C4⋊C4×C83—24no—
240C4⋊C4×C83—24no—
241C4⋊C4×C83—42no—
242C4⋊C4×C83—44no—
243C4⋊C4×C83C22×C418yes—
244C4⋊C4×C83C22×C418yes—
245C42×C83—22no—
246C42×C83—22no—
247C42×C83—22no—
248C42×C83—22no—
249C42×C83—22no—
250C42×C83—41no—
251C42×C83—44no—
252C42×C83C22×C414yes—
253C23×C83C2511yescharacteristic
254C22×D83—22no—
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83C23×C414yes—
267C22×D83C23×C414yes—
268Q8×C83—216no—
269C2×C4×C83—21no—
270C2×C4×C83—24no—
271C2×C4×C83—24no—
272C2×C4×C83—21no—
273C2×C4×C83—21no—
274C2×C4×C83—21no—
275C2×C4×C83—21no—
276C2×C4×C83—21no—
277C2×C4×C83—21no—
278C2×C4×C83—21no—
279C2×C4×C83—21no—
280C2×C4×C83—24no—
281C2×C4×C83—24no—
282C2×C4×C83—21no—
283C2×C4×C83—21no—
284C2×C4×C83—21no—
285C2×C4×C83—21no—
286C2×C4×C83—24no—
287C2×C4×C83C23×C412yes—
288C2×C4×C83C23×C418yes—
289C2×C4×C83C23×C412yes—
290C2×C4×C83C23×C412yes—
291C2×C4×C83H(5,𝔽2)12yes—
292C2×C4×C83H(5,𝔽2)12yes—
293C2×C4×C83H(5,𝔽2)12yes—
294C2×C4×C832−1+412yes—
295C2×C4×C832−1+412yes—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83C23×C414yes—
313C2×Dic83C23×C414yes—
314D332—28no—
315D332—28no—
316D332—416no—
317C4×D83—216no—
318C4×D83—216no—
319C4×D83—416no—
320C4×D83—88no—
321C22×C83C24×C411yescharacteristic
322C22×C83C2×H(5,𝔽2)11yescharacteristic
323C22×C83C2×H(5,𝔽2)11yescharacteristic
324C22×C83C2×H(5,𝔽2)11yescharacteristic
325C22×C83C2×2−1+411yescharacteristic
326C22×C83C2×2−1+411yescharacteristic
327C22×C83#58511yescharacteristic
328C2×D83—24no—
329C2×D83—24no—
330C2×D83—24no—
331C2×D83—24no—
332C2×D83—24no—
333C2×D83—24no—
334C2×D83—42no—
335C2×D83—42no—
336C2×D83—42no—
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—42no—
340C2×D83—42no—
341C2×D83—42no—
342C4×C83—28no—
343C4×C83—22no—
344C4×C83—22no—
345C4×C83—44no—
346C4×C83—41no—
347C4×C83—41no—
348C4×C83—41no—
349C4×C83#51814yes—
350C4×C83#52014yes—
351Dic83—24no—
352Dic83—24no—
353Dic83—42no—
354Dic83—42no—
355Dic83—42no—
356Dic83—42no—
357#34480—831nomaximal, Sylow
358C2×C83C2×#51811yescharacteristic
359C2×C83C2×#52011yescharacteristic
360C2×C83C4×2−1+411yescharacteristic
361C2×C83#354611yescharacteristic
362C2×C83#354711yescharacteristic
363C2×C83#354811yescharacteristic
364C2×C83#355211yescharacteristic
365D83—44no—
366D83—44no—
367C2×#547—831no—
368#2376—834no—
369#2365—831no—
370#2363—832no—
371#2360—832no—
372#2354—831no—
373D4×C4⋊C4—831no—
374#2345—832no—
375#2341—832no—
376#2335—834no—
377#2324—832no—
378#2323—832no—
379#2316—832no—
380#2311—832no—
381C4×C4⋊Q8D8311yescharacteristic, complemented
382#2293—831no—
383#2293—831no—
384C83#3448011yescharacteristic, complemented, Sylow
385C22×#41—832no—
386#547—8316no—
387C2×C4⋊Q8C2×D8311yescharacteristic
388C2×#123—834no—
389C2×C22⋊Q8—832no—
390C2×#121—832no—
391C2×C4×Q8—832no—
392C2×C4×Q8C2×D8312yes—
393C2×C4×D4—832no—
394C2×C4×D4—831no—
395C2×C4×D4—831no—
396C2×#117—832no—
397C2×#117—832no—
398C2×#117—832no—
399C22×C4⋊C4—832no—
400C22×C4⋊C4—832no—
401#391—832no—
402#391C2×D8312yes—
403#390—832no—
404#390—834no—
405#390—831no—
406#390—831no—
407#390—834no—
408#390—831no—
409#390—831no—
410#389—832no—
411#389—834no—
412#389—832no—
413#389—831no—
414#389—831no—
415#389—831no—
416#389—831no—
417#389—834no—
418#389C2×D8312yes—
419#389C2×D8312yes—
420#388—834no—
421#388—832no—
422#388—832no—
423#388—832no—
424#388—832no—
425#388—834no—
426#388—834no—
427#387—834no—
428#387—834no—
429#387—834no—
430#386—834no—
431#386—834no—
432#385—834no—
433#385—834no—
434#384C2×D8311yescharacteristic
435#380—834no—
436#380—832no—
437#380—832no—
438#380—834no—
439#380—834no—
440C4×C4⋊C4—832no—
441C4×C4⋊C4—832no—
442C4×C4⋊C4—831no—
443C4×C4⋊C4—831no—
444C4×C4⋊C4C2×D8312yes—
445C4×C4⋊C4C2×D8312yes—
446C4×C22⋊C4—834no—
447C4×C22⋊C4—834no—
448C4×C22⋊C4—832no—
449C4×C22⋊C4—832no—
450C43C2×D8311yescharacteristic
451C2×#41—3324no—
452C2×#41—3324no—
453C2×#41—8316no—
454C22×Q8C22×D8312yes—
455C22×D4—834no—
456C22×D4—831no—
457C22×D4—831no—
458C23×C4—834no—
459C23×C4—834no—
460C23×C4—832no—
461C23×C4—832no—
462C4⋊Q8C4×D8318yescomplemented
463#123—8332no—
464C22⋊Q8—8316no—
465#121—8316no—
466C4×Q8—44no—
467C4×Q8—3324no—
468C4×D4—3324no—
469C4×D4—838no—
470C4×D4—838no—
471#117—3324no—
472#117—3324no—
473#117—3324no—
474C2×C4⋊C4—3324no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—832no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—832no—
479C2×C4⋊C4—832no—
480C2×C4⋊C4—834no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4—834no—
483C2×C4⋊C4—831no—
484C2×C4⋊C4—8316no—
485C2×C4⋊C4—831no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4C22×D8312yes—
490C2×C4⋊C4C22×D8312yes—
491C2×C4⋊C4C22×D8314yes—
492C2×C4⋊C4C22×D8312yes—
493C2×C4⋊C4C22×D8312yes—
494C2×C4⋊C4C22×D8312yes—
495C2×C22⋊C4—832no—
496C2×C22⋊C4—834no—
497C2×C22⋊C4—832no—
498C2×C22⋊C4—832no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—832no—
502C2×C22⋊C4—834no—
503C2×C22⋊C4—832no—
504C2×C22⋊C4—832no—
505C2×C22⋊C4—832no—
506C2×C22⋊C4—834no—
507C2×C22⋊C4—832no—
508C2×C22⋊C4—832no—
509C2×C42—834no—
510C2×C42—834no—
511C2×C42—832no—
512C2×C42—832no—
513C2×C42C22×D8311yescharacteristic
514C2×C42C22×D8311yescharacteristic
515C2×C42C22×D8311yescharacteristic
516C2×C42C22×D8311yescharacteristic
517C2×C42C22×D8311yescharacteristic
518C2×C42C22×D8314yes—
519C2×C42C22×D8311yescharacteristic
520C2×C42C22×D8311yescharacteristic
521#95—832no—
522#95—832no—
523#95—834no—
524#95—832no—
525#95—834no—
526#95—832no—
527#95—834no—
528#95—834no—
529#95—832no—
530#95—832no—
531#95C22×D8314yes—
532#95C22×D8314yes—
533C24—832no—
534C24—832no—
535#41—33232no—
536C2×Q8—24no—
537C2×Q8—24no—
538C2×Q8C2×C4×D8318yes—
539C2×D4—3324no—
540C2×D4—3324no—
541C2×D4—8316no—
542C2×D4—834no—
543C2×D4—834no—
544C2×D4—1662no—
545C2×D4—1662no—
546C2×D4—1662no—
547C2×D4—1662no—
548C22×C4—3324no—
549C22×C4—3324no—
550C22×C4—3324no—
551C22×C4—3324no—
552C22×C4—3324no—
553C22×C4—8316no—
554C22×C4—832no—
555C22×C4—832no—
556C22×C4—838no—
557C22×C4—838no—
558C22×C4—832no—
559C22×C4—832no—
560C22×C4—832no—
561C22×C4—832no—
562C22×C4—1664no—
563C22×C4—1664no—
564C22×C4—1664no—
565C22×C4—1664no—
566C22×C4C23×D8311yescharacteristic
567C22×C4C23×D8314yes—
568C22×C4C23×D8311yescharacteristic
569C22×C4C23×D8311yescharacteristic
570C22×C4C23×D8311yescharacteristic
571C22×C4C23×D8314yes—
572C22×C4C23×D8311yescharacteristic
573C22×C4C23×D8311yescharacteristic
574C22×C4C23×D8311yescharacteristic
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—3324no—
580C4⋊C4—3322no—
581C4⋊C4—3322no—
582C4⋊C4—3322no—
583C4⋊C4—3322no—
584C4⋊C4—3324no—
585C4⋊C4—834no—
586C4⋊C4—8316no—
587C4⋊C4—834no—
588C4⋊C4—1662no—
589C4⋊C4—1662no—
590C4⋊C4—1662no—
591C4⋊C4—1662no—
592C4⋊C4C2×C4×D8318yes—
593C4⋊C4C2×C4×D8318yes—
594C22⋊C4—3322no—
595C22⋊C4—3322no—
596C22⋊C4—3322no—
597C22⋊C4—3322no—
598C22⋊C4—3324no—
599C22⋊C4—3324no—
600C22⋊C4—3322no—
601C22⋊C4—3322no—
602C22⋊C4—3324no—
603C22⋊C4—838no—
604C22⋊C4—838no—
605C22⋊C4—8316no—
606C22⋊C4—1664no—
607C22⋊C4—1664no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—44no—
614C42—41no—
615C42—3324no—
616C42—3324no—
617C42—1664no—
618C42—1664no—
619C42C2×C4×D8314yes—
620C23—834no—
621C23—834no—
622C23—1662no—
623C23—1662no—
624C23—1662no—
625C23—1662no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23—1662no—
630C23—1662no—
631C23—1662no—
632C23—1662no—
633C23—1662no—
634C23C24×D8311yescharacteristic
635Q8—216no—
636D4—33216no—
637D4—1668no—
638D4—1668no—
639C2×C4—21no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—24no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—24no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—24no—
657C2×C4—33216no—
658C2×C4—834no—
659C2×C4—834no—
660C2×C4—6648no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4—16616no—
678C2×C4—16616no—
679C2×C4C22×C4×D8312yes—
680C2×C4C22×C4×D8318yes—
681C2×C4C22×C4×D8312yes—
682C2×C4C22×C4×D8312yes—
683C2×C4#1458183712yes—
684C2×C4#1458183812yes—
685C2×C4#1458183812yes—
686C2×C4#1458184012yes—
687C2×C4#1458184012yes—
688C22—3322no—
689C22—3322no—
690C22—3322no—
691C22—3322no—
692C22—3322no—
693C22—3322no—
694C22—3322no—
695C22—3322no—
696C22—1664no—
697C22—1664no—
698C22—1664no—
699C22—1664no—
700C22—1664no—
701C22—1664no—
702C22C23×C4×D8311yescharacteristic
703C22C2×#1458183711yescharacteristic
704C22C2×#1458183811yescharacteristic
705C22C2×#1458183811yescharacteristic
706C22C2×#1458184011yescharacteristic
707C22C2×#1458184011yescharacteristic
708C22#1912853711yescharacteristic
709C4—22no—
710C4—28no—
711C4—22no—
712C4—41no—
713C4—44no—
714C4—41no—
715C4—41no—
716C4—3322no—
717C4—3322no—
718C4—3322no—
719C4—3322no—
720C4—1664no—
721C4—1664no—
722C4#1912817314yes—
723C4#1912818314yes—
724C2—3324no—
725C2—3324no—
726C2C2×#1912817311yescharacteristic
727C2C2×#1912818311yescharacteristic
728C2C4×#1458184011yescharacteristic
729C2#2492182911yescharacteristic
730C2#2492184611yescharacteristic
731C2#2492186311yescharacteristic
732C2#2492190411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC4×C4⋊Q8×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#19128354C2
hypercenterC4×C4⋊Q8D83
hypocenterC83#34480
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #24910608C2semidirect
3. #24910523C2semidirect
4. #24910503C2semidirect
5. #24910464C2semidirect
6. #24910414C2semidirect
7. #24910363C2semidirect
8. #24910336C2semidirect
9. #24910301C2semidirect
10. #24910247C2semidirect
11. #24910154C2semidirect
12. #24910148C2semidirect
13. #24910078C2semidirect
14. #24910054C2semidirect
15. #24909927C2semidirect
16. #24909927C2semidirect
17. C4×C4⋊Q8×C83C2semidirect
19. #19128354C4semidirect
86. C2×#13050591C2×C4semidirect
94. #14581777C2×C4semidirect
95. #14581768C2×C4semidirect
99. C4×D332C2×C4semidirect
118. C4⋊C4×D83C2×C4semidirect
148. C4⋊Q8×C83C2×C4semidirect
381. C4×C4⋊Q8D83semidirect
384. C83#34480semidirect
462. C4⋊Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283542
#249106082
#249105232
#249105032
#249104642
#249104142
#249103632
#249103362
#249103012
#249102472
#249101542
#249101482
#249100782
#249100542
#249099272
C4×C4⋊Q8×C832
#3448083