Finite Group Databasebeta

← #35569531

Subgroups — #35569531

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#24910610C214yesmaximal, complemented
3#24910500C212yesmaximal, complemented
4#24910473C212yesmaximal, complemented
5#24910410C211yesmaximal, characteristic, complemented
6C4⋊C4×D332C211yesmaximal, characteristic, complemented
7#24910336C212yesmaximal, complemented
8#24910301C212yesmaximal, complemented
9#24910259C214yesmaximal, complemented
10#24910157C212yesmaximal, complemented
11#24910139C212yesmaximal, complemented
12#24910078C212yesmaximal, complemented
13#24910054C212yesmaximal, complemented
14C4⋊Q8×Dic83C211yesmaximal, characteristic, complemented
15#24909924C211yesmaximal, characteristic, complemented
16#24909924C211yesmaximal, characteristic, complemented
17C83×#2365C211yesmaximal, characteristic, complemented
18C22×#13050591C2212yes—
19#19128354C4116yescomplemented
20C2×#14581777C2214yes—
21C2×#14581768C2212yes—
22C2×#14581767C2212yes—
23C2×Q8×Dic83C2212yes—
24C2×C4×D332C2212yes—
25C2×C4×D332C2211yescharacteristic
26C2×C4×D332C2211yescharacteristic
27C2×#14581750C2212yes—
28C2×#14581749C2212yes—
29C2×#14581749C2212yes—
30C2×C4⋊C4×D83C2212yes—
31C2×C4⋊C4×D83C2212yes—
32#19127608C2212yes—
33#19127603C2214yes—
34#19127603C2212yes—
35#19127602C2211yescharacteristic
36#19127602C2211yescharacteristic
37#19127602C2211yescharacteristic
38#19127602C2211yescharacteristic
39#19127602C2214yes—
40#19127600C2212yes—
41#19127600C2212yes—
42#19127599C2212yes—
43#19127598C2214yes—
44#19127597C2211yescharacteristic
45#19127597C2211yescharacteristic
46#19127597C2211yescharacteristic
47#19127597C2211yescharacteristic
48#19127596C2214yes—
49#19127593C2214yes—
50#19127592C2214yes—
51#19127591C2214yes—
52#19127590C2212yes—
53#19127590C2212yes—
54#19127590C2212yes—
55#19127590C2212yes—
56#19127585C2214yes—
57#19127583C2214yes—
58#19127579C2214yes—
59#19127579C2214yes—
60#19127575C2214yes—
61#19127575C2214yes—
62#19127571C2211yescharacteristic
63#19127560C2214yes—
64#19127560C2214yes—
65#19127558C2212yes—
66#19127558C2214yes—
67#19127558C2212yes—
68C4⋊C4×Dic83C2212yes—
69C4⋊C4×Dic83C2212yes—
70C4×C4⋊Dic83C2212yes—
71C4×(C2×D83)⋊C4C2212yes—
72C4×(C2×D83)⋊C4C2214yes—
73C4×(C2×D83)⋊C4C2212yes—
74#19127548C2214yes—
75C42×Dic83C2211yescharacteristic
76C2×C4⋊Q8×C83C2211yescharacteristic
77C2×C4×Q8×C83C2212yes—
78#391×C83C2212yes—
79#389×C83C2212yes—
80#387×C83C2214yes—
81C4×C4⋊C4×C83C2212yes—
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×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×D332—44no—
99C4×D332C2×C418yes—
100C4×D332C2×C418yescomplemented
101#14581750—44no—
102#14581749—44no—
103#14581749—44no—
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2312yes—
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2314yes—
108C2×C4⋊Dic83C2311yescharacteristic
109C2×C4⋊Dic83C2311yescharacteristic
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2312yes—
112C2×Dic83⋊C4C2312yes—
113C2×Dic83⋊C4C2312yes—
114C2×Dic83⋊C4C2312yes—
115C2×Dic83⋊C4C2314yes—
116C4⋊C4×D83—44no—
117C4⋊C4×D83C2×C4116yescomplemented
118C2×(C2×D83)⋊C4C2312yes—
119C2×(C2×D83)⋊C4C2312yes—
120C2×(C2×D83)⋊C4C2312yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×(C2×D83)⋊C4C2312yes—
128C2×(C2×D83)⋊C4C2312yes—
129C2×(C2×D83)⋊C4C2312yes—
130C2×(C2×D83)⋊C4C2314yes—
131C2×(C2×D83)⋊C4C2312yes—
132C2×C4×Dic83C2311yescharacteristic
133C2×C4×Dic83C2311yescharacteristic
134C2×C4×Dic83C2311yescharacteristic
135C2×C4×Dic83C2311yescharacteristic
136C2×C4×Dic83C2311yescharacteristic
137C2×C4×Dic83C2314yes—
138C2×C4×Dic83C2314yes—
139C2×C4×Dic83C2311yescharacteristic
140C83⋊#95C2314yes—
141C83⋊#95C2314yes—
142C83⋊#95C2314yes—
143C83⋊#95C2314yes—
144C83⋊#95C2312yes—
145C83⋊#95C2312yes—
146C83⋊#95C2312yes—
147C83⋊#95C2312yes—
148C22×Q8×C83C2312yes—
149C4⋊Q8×C83C2×C418yescomplemented
150C4×Q8×C83—44no—
151C2×C4⋊C4×C83C2311yescharacteristic
152C2×C4⋊C4×C83C2311yescharacteristic
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2314yes—
156C2×C4⋊C4×C83C2312yes—
157C2×C4⋊C4×C83C2312yes—
158C2×C42×C83C2312yes—
159C2×C42×C83C2312yes—
160C2×C42×C83C2314yes—
161C2×C42×C83C2311yescharacteristic
162#95×C83C2314yes—
163#95×C83C2314yes—
164#95×C83C2312yes—
165#95×C83C2312yes—
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×Dic83C2414yes—
179C22×Dic83C2411yescharacteristic
180C22×Dic83C2411yescharacteristic
181C22×Dic83C2411yescharacteristic
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2411yescharacteristic
185C2×C4×D83—24no—
186C2×C4×D83—24no—
187C2×C4×D83—24no—
188C2×C4×D83—24no—
189C2×C4×D83—44no—
190C2×C4×D83—44no—
191C2×C4×D83—44no—
192C2×C4×D83—44no—
193C2×C4×D83—44no—
194C2×C4×D83C22×C418yes—
195C2×C4×D83C22×C418yes—
196C2×C4×D83C22×C4116yes—
197C4⋊Dic83—24no—
198C4⋊Dic83—24no—
199C4⋊Dic83—42no—
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—42no—
213(C2×D83)⋊C4—44no—
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—22no—
224C4×Dic83—22no—
225C4×Dic83—22no—
226C4×Dic83—22no—
227C4×Dic83—22no—
228C4×Dic83—41no—
229C4×Dic83—44no—
230C4×Dic83—44no—
231C2×Q8×C83—24no—
232C2×Q8×C83—24no—
233C2×Q8×C83C22×C418yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2414yes—
239C22×C4×C83C2411yescharacteristic
240C22×C4×C83C2411yescharacteristic
241C22×C4×C83C2411yescharacteristic
242C4⋊C4×C83—22no—
243C4⋊C4×C83—22no—
244C4⋊C4×C83—22no—
245C4⋊C4×C83—22no—
246C4⋊C4×C83—44no—
247C4⋊C4×C83C22×C418yes—
248C4⋊C4×C83C22×C418yes—
249C42×C83—24no—
250C42×C83—24no—
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—24no—
270C2×C4×C83—24no—
271C2×C4×C83—21no—
272C2×C4×C83—21no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83C23×C412yes—
286C2×C4×C83C23×C418yes—
287C2×C4×C83C23×C412yes—
288C2×C4×C83C23×C412yes—
289C2×C4×C83H(5,𝔽2)12yes—
290C2×C4×C83H(5,𝔽2)12yes—
291C2×C4×C83H(5,𝔽2)12yes—
292C2×C4×C832−1+412yes—
293C2×Dic83—21no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—21no—
298C2×Dic83—22no—
299C2×Dic83—21no—
300C2×Dic83—21no—
301C2×Dic83—21no—
302C2×Dic83—21no—
303C2×Dic83—21no—
304C2×Dic83—24no—
305C2×Dic83—24no—
306C2×Dic83—21no—
307C2×Dic83—21no—
308C2×Dic83—21no—
309C2×Dic83—21no—
310C2×Dic83—24no—
311C2×Dic83C23×C414yes—
312C2×Dic83C23×C414yes—
313C2×Dic832−1+412yes—
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—42no—
345C4×C83—42no—
346C4×C83—42no—
347C4×C83—42no—
348C4×C83#51814yes—
349C4×C83#52014yes—
350Dic83—24no—
351Dic83—24no—
352Dic83—22no—
353Dic83—44no—
354Dic83—41no—
355Dic83—41no—
356Dic83—41no—
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#2365D8311yescharacteristic, complemented
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⋊Q8—831no—
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—831no—
404#390—831no—
405#390—834no—
406#390—831no—
407#390—831no—
408#390—832no—
409#390—834no—
410#389—832no—
411#389—832no—
412#389—831no—
413#389—834no—
414#389—831no—
415#389—831no—
416#389—831no—
417#389—832no—
418#389—834no—
419#389C2×D8312yes—
420#388—834no—
421#388—834no—
422#388—832no—
423#388—832no—
424#388—834no—
425#388—832no—
426#388—832no—
427#387—834no—
428#387—834no—
429#387C2×D8314yes—
430#386—834no—
431#386—834no—
432#385—834no—
433#385—834no—
434#384—831no—
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—832no—
443C4×C4⋊C4C2×D8312yes—
444C4×C4⋊C4C2×D8311yescharacteristic
445C4×C4⋊C4C2×D8311yescharacteristic
446C4×C22⋊C4—834no—
447C4×C22⋊C4—832no—
448C4×C22⋊C4—832no—
449C4×C22⋊C4—834no—
450C43—831no—
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—832no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—834no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—8316no—
486C2×C4⋊C4—832no—
487C2×C4⋊C4—832no—
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C4⋊C4C22×D8311yescharacteristic
490C2×C4⋊C4C22×D8311yescharacteristic
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8314yes—
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—831no—
512C2×C42—831no—
513C2×C42—831no—
514C2×C42—831no—
515C2×C42—831no—
516C2×C42—831no—
517C2×C42C22×D8312yes—
518C2×C42C22×D8312yes—
519C2×C42C22×D8314yes—
520C2×C42C22×D8311yescharacteristic
521#95—832no—
522#95—832no—
523#95—834no—
524#95—832no—
525#95—832no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95C22×D8314yes—
530#95C22×D8314yes—
531#95C22×D8312yes—
532#95C22×D8312yes—
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—831no—
555C22×C4—832no—
556C22×C4—832no—
557C22×C4—838no—
558C22×C4—838no—
559C22×C4—831no—
560C22×C4—831no—
561C22×C4—834no—
562C22×C4—831no—
563C22×C4—1664no—
564C22×C4—1664no—
565C22×C4—1664no—
566C22×C4—1664no—
567C22×C4C23×D8312yes—
568C22×C4C23×D8312yes—
569C22×C4C23×D8312yes—
570C22×C4C23×D8312yes—
571C22×C4C23×D8314yes—
572C22×C4C23×D8311yescharacteristic
573C22×C4C23×D8311yescharacteristic
574C22×C4C23×D8311yescharacteristic
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—44no—
580C4⋊C4—3324no—
581C4⋊C4—3322no—
582C4⋊C4—3322no—
583C4⋊C4—3322no—
584C4⋊C4—3322no—
585C4⋊C4—3324no—
586C4⋊C4—3322no—
587C4⋊C4—834no—
588C4⋊C4—8316no—
589C4⋊C4—834no—
590C4⋊C4—1664no—
591C4⋊C4—1664no—
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—3324no—
602C22⋊C4—3322no—
603C22⋊C4—838no—
604C22⋊C4—838no—
605C22⋊C4—8316no—
606C22⋊C4—1664no—
607C22⋊C4—1664no—
608C42—24no—
609C42—24no—
610C42—44no—
611C42—3324no—
612C42—3324no—
613C42—3321no—
614C42—1662no—
615C42—1662no—
616C42—1662no—
617C42—1662no—
618C42—1662no—
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—24no—
640C2×C4—24no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—33216no—
656C2×C4—834no—
657C2×C4—834no—
658C2×C4—832no—
659C2×C4—6648no—
660C2×C4—1661no—
661C2×C4—1661no—
662C2×C4—1664no—
663C2×C4—1664no—
664C2×C4—1661no—
665C2×C4—1661no—
666C2×C4—1661no—
667C2×C4—1661no—
668C2×C4—1661no—
669C2×C4—1661no—
670C2×C4—1661no—
671C2×C4—1664no—
672C2×C4—1662no—
673C2×C4—1661no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1661no—
677C2×C4—1662no—
678C2×C4—16616no—
679C2×C4—16616no—
680C2×C4C22×C4×D8312yes—
681C2×C4C22×C4×D8318yes—
682C2×C4C22×C4×D8312yes—
683C2×C4C22×C4×D8312yes—
684C2×C4#1458183712yes—
685C2×C4#1458183812yes—
686C2×C4#1458183812yes—
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
706C222−1+4×D8311yescharacteristic
707C22C2×#1458184011yescharacteristic
708C22#1912853811yescharacteristic
709C4—28no—
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—3321no—
716C4—3324no—
717C4—3321no—
718C4—3321no—
719C4—1662no—
720C4—1664no—
721C4—1664no—
722C4#1912817314yes—
723C4#1912818314yes—
724C2—3324no—
725C2—3324no—
726C2C2×#1912817311yescharacteristic
727C2C2×#1912818311yescharacteristic
728C2#2492067211yescharacteristic
729C2#2492183811yescharacteristic
730C2#2492184811yescharacteristic
731C2#2492186011yescharacteristic
732C2#2492190911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2365C2
socle, cosocleC23×C83C25
prime radicalC2×#19128354C2
hypercenter#2365D83
hypocenterC83#34480
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #24910610C2semidirect
3. #24910500C2semidirect
4. #24910473C2semidirect
5. #24910410C2semidirect
6. C4⋊C4×D332C2semidirect
7. #24910336C2semidirect
8. #24910301C2semidirect
9. #24910259C2semidirect
10. #24910157C2semidirect
11. #24910139C2semidirect
12. #24910078C2semidirect
13. #24910054C2semidirect
14. C4⋊Q8×Dic83C2semidirect
15. #24909924C2semidirect
16. #24909924C2semidirect
17. C83×#2365C2semidirect
19. #19128354C4semidirect
86. C2×#13050591C2×C4semidirect
94. #14581777C2×C4semidirect
95. #14581768C2×C4semidirect
100. C4×D332C2×C4semidirect
117. C4⋊C4×D83C2×C4semidirect
149. C4⋊Q8×C83C2×C4semidirect
369. #2365D83semidirect
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
#249106102
#249105002
#249104732
#249104102
C4⋊C4×D3322
#249103362
#249103012
#249102592
#249101572
#249101392
#249100782
#249100542
C4⋊Q8×Dic832
#249099242
C83×#23652
#3448083