Finite Group Databasebeta

← #7699862

Subgroups — #7699862

Order 512.

5427 conjugacy classes of subgroups.

The subgroup lattice has 1169 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60016C218yesmaximal, complemented
2#59821C211yesmaximal, characteristic, complemented
3#59487C214yesmaximal, complemented
4#59410C212yesmaximal, complemented
5#59276C214yesmaximal, complemented
6#59262C212yesmaximal, complemented
7#59237C214yesmaximal, complemented
8#59228C212yesmaximal, complemented
9#36563C211yesmaximal, characteristic, complemented
10#36504C212yesmaximal, complemented
11#36461C214yesmaximal, complemented
12#36460C212yesmaximal, complemented
13#36413C214yesmaximal, complemented
14#36410C212yesmaximal, complemented
15#36270C212yesmaximal, complemented
16#36269C214yesmaximal, complemented
17#36194C211yesmaximal, characteristic, complemented
18#36187C211yesmaximal, characteristic, complemented
19#36186C212yesmaximal, complemented
20#36174C212yesmaximal, complemented
21C4×#556C211yesmaximal, characteristic, complemented
22C4×#556C212yesmaximal, complemented
23C4×#550C211yesmaximal, characteristic, complemented
24C4×#547C211yesmaximal, characteristic, complemented
25#34129C212yesmaximal, complemented
26#34121C212yesmaximal, complemented
27C2×#556C2212yes—
28C2×#556C2211yescharacteristic
29C2×#555C2212yes—
30C2×#552C2214yes—
31C2×#550C2211yescharacteristic
32C2×#547C2211yescharacteristic
33C2×C4×#41C2212yes—
34C2×C4×#41C2212yes—
35#2868C2211yescharacteristic
36#2861C2218yes—
37#2860C2214yes—
38#2859C2212yes—
39#2857C2212yes—
40#2856C2212yes—
41#2854C2214yes—
42#2850C2214yes—
43#2769C2218yes—
44#2756C2218yes—
45#2737C2218yes—
46#2727C2214yes—
47#2705C2218yes—
48#2611C2218yes—
49#2610C2218yes—
50#2601C2218yes—
51#2593C2218yes—
52#2582C2212yes—
53#2574C2218yes—
54#2572C2218yes—
55#2571C2212yes—
56#2567C2212yes—
57#2563C2212yes—
58#2563C2212yes—
59#2562C2214yes—
60#2559C2218yes—
61#2558C2218yes—
62#2557C2218yes—
63#2554C2218yes—
64#2552C2212yes—
65#2550C2214yes—
66#2548C2212yes—
67#2542C2212yes—
68#2540C2214yes—
69#2538C2212yes—
70#2538C2212yes—
71#2537C2212yes—
72#2537C2212yes—
73#2536C2214yes—
74#2532C2218yes—
75#2526C2218yes—
76#2526C2218yes—
77#2521C2218yes—
78#2519C2218yes—
79#2518C2218yes—
80#2512C2214yes—
81#2512C2214yes—
82#2507C2214yes—
83#2506C2214yes—
84#2506C2214yes—
85#2500C2214yes—
86#2500C2214yes—
87#2498C2218yes—
88#2497C2214yes—
89#2495C2214yes—
90#2495C2214yes—
91#2492C2214yes—
92#2491C2214yes—
93#2491C2214yes—
94#2490C2214yes—
95#2489C2214yes—
96#2479C2218yes—
97#2476C2218yes—
98#2467C2218yes—
99#2464C2218yes—
100#2451C2214yes—
101#2448C2214yes—
102#2445C2214yes—
103#2439C2214yes—
104#2431C2214yes—
105#2426C2214yes—
106#2423C2214yes—
107#2423C2214yes—
108#2420C2214yes—
109#2417C2214yes—
110#2415C2214yes—
111#2414C2214yes—
112#2414C2214yes—
113#2407C2214yes—
114#2373C2214yes—
115#2373C2218yes—
116#2369C2212yes—
117#2369C2212yes—
118#2367C2214yes—
119#2367C2212yes—
120#2366C2212yes—
121#2366C2211yescharacteristic
122#2365C2211yescharacteristic
123#2365C2211yescharacteristic
124#2363C2214yes—
125#2363C2214yes—
126#2363C2212yes—
127#2363C2214yes—
128#2362C2212yes—
129#2362C2214yes—
130#2362C2212yes—
131#2361C2212yes—
132#2359C2214yes—
133#2357C2214yes—
134#2356C2214yes—
135#2356C2214yes—
136#2356C2212yes—
137#2355C2211yescharacteristic
138#2355C2212yes—
139#2355C2212yes—
140#2354C2212yes—
141#2354C2212yes—
142#2354C2212yes—
143#2354C2212yes—
144#2354C2211yescharacteristic
145#2354C2211yescharacteristic
146#2354C2214yes—
147#2354C2214yes—
148#2354C2212yes—
149#2354C2211yescharacteristic
150#2353C2218yes—
151#2352C2214yes—
152#2352C2214yes—
153Q8×C4⋊C4C2212yes—
154Q8×C4⋊C4C2212yes—
155Q8×C4⋊C4C2211yescharacteristic
156D4×C4⋊C4C2211yescharacteristic
157#2347C2214yes—
158#2347C2212yes—
159#2346C2214yes—
160#2346C2218yes—
161#2344C2212yes—
162#2341C2214yes—
163#2341C2212yes—
164#2339C2212yes—
165C4×C4⋊Q8C2212yes—
166C4×C4⋊Q8C2211yescharacteristic
167C4×C4⋊Q8C2211yescharacteristic
168C4×#127C2212yes—
169C4×#127C2211yescharacteristic
170C4×#126C2214yes—
171C4×#126C2218yes—
172C4×#124C2212yes—
173C4×#124C2214yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2214yes—
176C4×C22⋊Q8C2212yes—
177C4×#123C2214yes—
178C4×#121C2212yes—
179C4×#121C2212yes—
180C4×#121C2214yes—
181#2298C2218yes—
182#2297C2214yes—
183#2293C2214yes—
184#2293C2218yes—
185#2285C2212yes—
186#2285C2214yes—
187#2285C2212yes—
188#2283C2214yes—
189C42×Q8C2214yes—
190C42×Q8C2211yescharacteristic
191C42×Q8C2212yes—
192C42×D4C2212yes—
193C42×D4C2211yescharacteristic
194C42×D4C2211yescharacteristic
195C4×#117C2214yes—
196C4×#117C2214yes—
197C4×#117C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C22×#41C2312yes—
201#556—216no—
202#556—28no—
203#555—48no—
204#552—416no—
205#550—28no—
206#547—28no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2312yes—
214C2×#126C2318yes—
215C2×#126C2314yes—
216C2×#126C2318yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#124C2318yes—
222C2×#123C2314yes—
223C2×#123C2318yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×#121C2312yes—
230C2×#121C2312yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C4×#41—216no—
237C4×#41—216no—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2312yes—
266C2×C4×D4C2311yescharacteristic
267C2×#117C2314yes—
268C2×#117C2312yes—
269C2×#117C2314yes—
270C2×#117C2312yes—
271C2×#117C2314yes—
272C2×#117C2312yes—
273C2×#117C2314yes—
274C2×#117C2318yes—
275C2×#117C2312yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C42C2314yes—
281C22×C42C2314yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#399C2318yes—
288#399C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#395C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#393C2318yes—
308#393C2318yes—
309#392C2318yes—
310#392C2318yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2314yes—
315#391C2318yes—
316#391C2318yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#390C2312yes—
322#390C2314yes—
323#390C2312yes—
324#390C2312yes—
325#390C2312yes—
326#390C2312yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2318yes—
331#390C2312yes—
332#390C2318yes—
333#390C2318yes—
334#390C2314yes—
335#390C2312yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2318yes—
341#390C2314yes—
342#390C2312yes—
343#389C2314yes—
344#389C2312yes—
345#389C2314yes—
346#389C2312yes—
347#389C2312yes—
348#389C2312yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2314yes—
360#389C2318yes—
361#389C2314yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#388C2314yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2314yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2318yes—
395#388C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2318yes—
404#387C2314yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#386C2314yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2314yes—
414#386C2314yes—
415#386C2318yes—
416#386C2318yes—
417#386C2314yes—
418#386C2314yes—
419#385C2318yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#384C2311yescharacteristic
424#384C2312yes—
425#384C2311yescharacteristic
426#384C2312yes—
427#384C2311yescharacteristic
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#384C2314yes—
432#384C2312yes—
433#383C2314yes—
434#383C2318yes—
435#383C2318yes—
436#382C2314yes—
437#382C2314yes—
438#382C2314yes—
439#382C2318yes—
440#382C2314yes—
441#382C2312yes—
442#381C2314yes—
443#381C2318yes—
444#380C2312yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2312yes—
453#380C2318yes—
454#380C2314yes—
455#380C2312yes—
456#380C2314yes—
457#380C2312yes—
458#380C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2318yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2318yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520#376C2318yes—
521#376C2318yes—
522C2×#95C2314yes—
523C43C2314yes—
524C43C2318yes—
525C43C2311yescharacteristic
526C43C2312yes—
527C2×#41—28no—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—28no—
531C2×#41—44no—
532C2×#41—44no—
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2414yes—
537C22×D4C2411yescharacteristic
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2414yes—
542C22×D4C2411yescharacteristic
543C22×D4C2412yes—
544C22×D4C2414yes—
545C22×D4C2418yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2414yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2414yes—
557C4⋊Q8—24no—
558C4⋊Q8—44no—
559C4⋊Q8—44no—
560C4⋊Q8—44no—
561C4⋊Q8#4118yescomplemented
562#127—28no—
563#127—24no—
564#126—232no—
565#126—216no—
566#126—416no—
567#125—416no—
568#125—48no—
569#124—216no—
570#124—28no—
571#124—416no—
572#123—216no—
573#123—416no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—216no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579#121—28no—
580#121—28no—
581#121—216no—
582#121—48no—
583#121—48no—
584#121—48no—
585#121—48no—
586C4×Q8—28no—
587C4×Q8—216no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—28no—
591C4×Q8—24no—
592C4×Q8—28no—
593C4×Q8—28no—
594C4×Q8—48no—
595C4×Q8—42no—
596C4×Q8#4118yescomplemented
597C4×D4—28no—
598C4×D4—216no—
599C4×D4—28no—
600C4×D4—216no—
601C4×D4—28no—
602C4×D4—24no—
603C4×D4—216no—
604C4×D4—28no—
605C4×D4—216no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—24no—
609C4×D4—28no—
610C4×D4—44no—
611C4×D4—42no—
612C4×D4—48no—
613C4×D4—44no—
614C4×D4#4118yes—
615#117—28no—
616#117—28no—
617#117—216no—
618#117—216no—
619#117—28no—
620#117—216no—
621#117—216no—
622#117—416no—
623#117—48no—
624#117—44no—
625#117—48no—
626C2×C4⋊C4—28no—
627C2×C4⋊C4—28no—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2412yes—
707C2×C42—216no—
708C2×C42—28no—
709C2×C42—216no—
710C2×C42—28no—
711C2×C42C2418yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2418yes—
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2412yes—
727C2×C42C2414yes—
728C2×C42C2411yescharacteristic
729C2×C42C2414yes—
730C2×C42C2411yescharacteristic
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2418yes—
734C2×C42C2414yes—
735C2×C42C2418yes—
736C2×C42C2412yes—
737C2×C42C2414yes—
738C2×C42C2411yescharacteristic
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2412yes—
743C2×C42C2411yescharacteristic
744#95C2412yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2412yes—
751#95C2418yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2412yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2412yes—
763#95C2412yes—
764#95C2412yes—
765#95C2414yes—
766#95C2412yes—
767#95C2418yes—
768#95C2414yes—
769#95C2418yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773#95C2414yes—
774#95C2412yes—
775#95C2412yes—
776#95C2418yes—
777#95C2414yes—
778#95C2418yes—
779#95C2414yes—
780C24C2512yes—
781C24C2514yes—
782C24C2512yes—
783#41—432no—
784#41—432no—
785C2×Q8—24no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—44no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8C2×#4114yes—
796C2×Q8C2×#4118yes—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—22no—
801C2×D4—28no—
802C2×D4—24no—
803C2×D4—22no—
804C2×D4—24no—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—28no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—44no—
820C2×D4—48no—
821C2×D4—48no—
822C2×D4—48no—
823C2×D4C2×#4114yes—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—28no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—24no—
835C22×C4—28no—
836C22×C4—24no—
837C22×C4—28no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—28no—
847C22×C4—24no—
848C22×C4—42no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—42no—
854C22×C4—44no—
855C22×C4—42no—
856C22×C4C2×#4118yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2511yescharacteristic
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2518yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2512yes—
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C4⋊C4—22no—
881C4⋊C4—28no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—28no—
895C4⋊C4—216no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—22no—
904C4⋊C4—28no—
905C4⋊C4—22no—
906C4⋊C4—28no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—42no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4C2×#4118yes—
921C4⋊C4C2×#4114yes—
922C4⋊C4C2×#4114yes—
923C4⋊C4C2×#4118yes—
924C4⋊C4C2×#4118yes—
925C4⋊C4H(5,𝔽2)14yes—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—216no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—216no—
941C22⋊C4—216no—
942C22⋊C4—24no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—42no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4C2×#4118yes—
959C42—24no—
960C42—24no—
961C42—28no—
962C42—24no—
963C42—28no—
964C42—24no—
965C42—28no—
966C42—24no—
967C42—28no—
968C42—28no—
969C42—24no—
970C42—216no—
971C42—28no—
972C42—24no—
973C42—28no—
974C42—216no—
975C42—28no—
976C42—22no—
977C42—24no—
978C42—24no—
979C42—22no—
980C42—22no—
981C42—42no—
982C42—41no—
983C42—44no—
984C42—48no—
985C42—44no—
986C42—48no—
987C42—42no—
988C42C2×#4114yes—
989C42C2×#4118yes—
990C42C2×#4114yes—
991C42C2×#4114yes—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—24no—
1007C23—22no—
1008C23—24no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23C22×#4114yes—
1013C23C2611yescharacteristic
1014Q8—216no—
1015Q8—28no—
1016Q8—48no—
1017Q8—164no—
1018D4—28no—
1019D4—416no—
1020D4—416no—
1021D4—48no—
1022D4—48no—
1023D4—44no—
1024D4—84no—
1025D4—88no—
1026D4—168no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—216no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—21no—
1061C2×C4—28no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—28no—
1073C2×C4—28no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—48no—
1081C2×C4—416no—
1082C2×C4—416no—
1083C2×C4—416no—
1084C2×C4—48no—
1085C2×C4—48no—
1086C2×C4—48no—
1087C2×C4—416no—
1088C2×C4—84no—
1089C2×C4—88no—
1090C2×C4C22×#4114yes—
1091C2×C4C22×#4114yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4114yes—
1094C2×C4C22×#4112yes—
1095C2×C4C22×#4118yes—
1096C2×C4C22×#4112yes—
1097C2×C4C22×#4112yes—
1098C2×C4C22×#4112yes—
1099C2×C4C22×#4112yes—
1100C2×C4C22×#4112yes—
1101C2×C4C22×#4112yes—
1102C2×C4C22×#4112yes—
1103C2×C4C2×H(5,𝔽2)14yes—
1104C2×C4C2×H(5,𝔽2)12yes—
1105C2×C4#58512yes—
1106C2×C4#58512yes—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—44no—
1116C22—44no—
1117C22—42no—
1118C22—44no—
1119C22—42no—
1120C22—42no—
1121C22—44no—
1122C22—44no—
1123C22—42no—
1124C22—42no—
1125C22—44no—
1126C22—44no—
1127C22—42no—
1128C22C23×#4111yescharacteristic
1129C22C23×#4111yescharacteristic
1130C22C23×#4111yescharacteristic
1131C22C22×H(5,𝔽2)11yescharacteristic
1132C22C2×#58511yescharacteristic
1133C22C2×#58511yescharacteristic
1134C222−1+611yescharacteristic
1135C4—24no—
1136C4—22no—
1137C4—22no—
1138C4—24no—
1139C4—22no—
1140C4—24no—
1141C4—24no—
1142C4—28no—
1143C4—44no—
1144C4—42no—
1145C4—44no—
1146C4—42no—
1147C4—42no—
1148C4—48no—
1149C4—41no—
1150C4—42no—
1151C4—42no—
1152C4—44no—
1153C4—42no—
1154C4—44no—
1155C4#347514yes—
1156C4#347514yes—
1157C4#348314yes—
1158C2—44no—
1159C2—82no—
1160C2—84no—
1161C2C2×#347511yescharacteristic
1162C2C2×#347511yescharacteristic
1163C2C2×#348311yescharacteristic
1164C2#6298511yescharacteristic
1165C2#6300711yescharacteristic
1166C2#6300911yescharacteristic
1167C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60016C2semidirect
2. #59821C2semidirect
3. #59487C2semidirect
4. #59410C2semidirect
5. #59276C2semidirect
6. #59262C2semidirect
7. #59237C2semidirect
8. #59228C2semidirect
9. #36563C2semidirect
10. #36504C2semidirect
11. #36461C2semidirect
12. #36460C2semidirect
13. #36413C2semidirect
14. #36410C2semidirect
15. #36270C2semidirect
16. #36269C2semidirect
17. #36194C2semidirect
18. #36187C2semidirect
19. #36186C2semidirect
20. #36174C2semidirect
21. C4×#556C2semidirect
22. C4×#556C2semidirect
23. C4×#550C2semidirect
24. C4×#547C2semidirect
25. #34129C2semidirect
26. #34121C2semidirect
561. C4⋊Q8#41semidirect
596. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#600162
#598212
#594872
#594102
#592762
#592622
#592372
#592282
#365632
#365042
#364612
#364602
#364132
#364102
#362702
#362692
#361942
#361872
#361862
#361742
C4×#5562
C4×#5502
C4×#5472
#341292
#341212