Finite Group Databasebeta

← #7687928

Subgroups — #7687928

Order 512.

5543 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59679C212yesmaximal, complemented
3#59545C214yesmaximal, complemented
4#59466C212yesmaximal, complemented
5#59078C212yesmaximal, complemented
6#59068C214yesmaximal, complemented
7#45393C214yesmaximal, complemented
8#44329C218yesmaximal, complemented
9#40174C214yesmaximal, complemented
10#40141C214yesmaximal, complemented
11#39736C212yesmaximal, complemented
12#38952C212yesmaximal, complemented
13#36595C211yesmaximal, characteristic, complemented
14#36595C211yesmaximal, characteristic, complemented
15#36463C212yesmaximal, complemented
16#36300C212yesmaximal, complemented
17#36300C212yesmaximal, complemented
18#36128C211yesmaximal, characteristic
19#36117C212yesmaximal, complemented
20#35778C214yesmaximal, complemented
21#34941C211yesmaximal, characteristic, complemented
22#34934C212yesmaximal, complemented
23#34313C212yesmaximal, complemented
24#34206C212yesmaximal, complemented
25C4×#557C211yesmaximal, characteristic, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27C2×#559C2212yes—
28C2×#559C2212yes—
29C2×#557C2211yescharacteristic
30C2×#554C2211yescharacteristic
31C2×#550C2212yes—
32C2×#532C2212yes—
33C2×#529C2214yes—
34C2×#520C2214yes—
35#2867C2211yescharacteristic
36#2860C2214yes—
37#2858C2212yes—
38#2858C2212yes—
39#2856C2212yes—
40#2854C2214yes—
41#2806C2214yes—
42#2800C2218yes—
43#2761C2218yes—
44#2748C2218yes—
45#2741C2218yes—
46#2711C2218yes—
47#2706C2218yes—
48#2705C2218yes—
49#2691C2218yes—
50#2672C2218yes—
51#2672C2218yes—
52#2630C2218yes—
53#2620C2214yes—
54#2584C2214yes—
55#2582C2214yes—
56#2579C2218yes—
57#2574C2214yes—
58#2567C2212yes—
59#2567C2211yescharacteristic
60#2566C2214yes—
61#2566C2214yes—
62#2563C2211yescharacteristic
63#2557C2218yes—
64#2554C2218yes—
65#2553C2218yes—
66#2552C2212yes—
67#2552C2211yescharacteristic
68#2552C2212yes—
69#2548C2212yes—
70#2548C2212yes—
71#2548C2212yes—
72#2548C2212yes—
73#2548C2212yes—
74#2548C2212yes—
75#2548C2212yes—
76#2545C2214yes—
77#2544C2214yes—
78#2544C2214yes—
79#2541C2212yes—
80#2541C2212yes—
81#2538C2211yescharacteristic
82#2521C2218yes—
83#2521C2218yes—
84#2513C2214yes—
85#2513C2214yes—
86#2512C2214yes—
87#2512C2214yes—
88#2512C2214yes—
89#2512C2214yes—
90#2508C2212yes—
91#2507C2214yes—
92#2501C2214yes—
93#2497C2212yes—
94#2490C2214yes—
95#2490C2214yes—
96#2479C2218yes—
97#2474C2218yes—
98#2474C2218yes—
99#2470C2218yes—
100#2466C2218yes—
101#2460C2218yes—
102#2459C2218yes—
103#2455C2218yes—
104#2454C2214yes—
105#2454C2214yes—
106#2454C2214yes—
107#2454C2214yes—
108#2454C2214yes—
109#2454C2212yes—
110#2448C2214yes—
111#2448C2214yes—
112#2447C2214yes—
113#2445C2214yes—
114#2445C2214yes—
115#2445C2214yes—
116#2445C2214yes—
117#2445C2214yes—
118#2445C2214yes—
119#2432C2214yes—
120#2431C2214yes—
121#2428C2214yes—
122#2428C2214yes—
123#2426C2214yes—
124#2425C2218yes—
125#2423C2212yes—
126#2420C2214yes—
127#2413C2218yes—
128#2396C2214yes—
129#2392C2218yes—
130#2370C2214yes—
131#2370C2212yes—
132#2370C2212yes—
133#2369C2212yes—
134#2369C2211yescharacteristic
135#2368C2214yes—
136#2367C2214yes—
137#2367C2214yes—
138#2367C2214yes—
139#2366C2214yes—
140#2366C2212yes—
141#2366C2212yes—
142#2366C2212yes—
143#2366C2212yes—
144#2366C2212yes—
145#2366C2212yes—
146#2365C2211yescharacteristic
147#2365C2212yes—
148#2365C2212yes—
149#2361C2214yes—
150#2361C2218yes—
151#2360C2212yes—
152#2357C2214yes—
153#2355C2211yescharacteristic
154#2355C2211yescharacteristic
155#2355C2212yes—
156#2354C2214yes—
157#2354C2214yes—
158#2352C2218yes—
159#2351C2212yes—
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2211yescharacteristic
162#2349C2212yes—
163D4×C4⋊C4C2211yescharacteristic
164D4×C4⋊C4C2214yes—
165D4×C4⋊C4C2214yes—
166#2345C2212yes—
167#2341C2214yes—
168#2325C2218yes—
169#2324C2218yes—
170#2324C2214yes—
171#2311C2214yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×#127C2212yes—
177C4×#127C2214yes—
178C4×#127C2212yes—
179C4×#125C2212yes—
180C4×#125C2212yes—
181C4×#125C2212yes—
182C4×#125C2214yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2214yes—
186C4×#121C2214yes—
187C4×#121C2214yes—
188#2293C2212yes—
189#2293C2214yes—
190#2293C2214yes—
191#2285C2212yes—
192C42×Q8C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2314yes—
200#559—48no—
201#559—48no—
202#557—28no—
203#554—28no—
204#550—216no—
205#532—216no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2312yes—
211C2×#127C2312yes—
212C2×#127C2314yes—
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218#529—416no—
219C2×#126C2318yes—
220C2×#126C2318yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2312yes—
225C2×#125C2314yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#123C2318yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×#121C2314yes—
241C2×#121C2318yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246#520—416no—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2318yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2318yes—
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×#117C2314yes—
281C2×#117C2318yes—
282C2×#117C2318yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2318yes—
286C22×C42C2312yes—
287C22×C42C2314yes—
288#400C2314yes—
289#399C2314yes—
290#399C2318yes—
291#399C2318yes—
292#399C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2314yes—
308#396C2318yes—
309#396C2314yes—
310#396C2318yes—
311#395C2314yes—
312#395C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#393C2314yes—
325#392C2318yes—
326#392C2318yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2314yes—
333#391C2312yes—
334#391C2318yes—
335#391C2312yes—
336#391C2314yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2318yes—
342#390C2314yes—
343#390C2318yes—
344#390C2314yes—
345#390C2314yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2318yes—
353#390C2314yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2312yes—
384#389C2314yes—
385#389C2318yes—
386#389C2318yes—
387#389C2314yes—
388#389C2314yes—
389#389C2312yes—
390#389C2312yes—
391#389C2314yes—
392#389C2312yes—
393#388C2314yes—
394#388C2314yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#385C2318yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2314yes—
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2312yes—
451#384C2314yes—
452#384C2312yes—
453#382C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2314yes—
457#382C2314yes—
458#381C2318yes—
459#380C2312yes—
460#380C2312yes—
461#380C2318yes—
462#380C2318yes—
463#380C2314yes—
464#380C2318yes—
465#380C2312yes—
466#380C2318yes—
467#380C2314yes—
468#380C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2311yescharacteristic
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C2×#95C2314yes—
523C43C2312yes—
524C43C2312yes—
525C43C2314yes—
526C43C2311yescharacteristic
527C2×#41—216no—
528C2×#41—216no—
529C2×#41—48no—
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×D4C2414yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2418yes—
539C22×D4C2411yescharacteristic
540C22×D4C2418yes—
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C23×C4C2412yes—
546C23×C4C2418yes—
547C23×C4C2412yes—
548C23×C4C2418yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2418yes—
553C4⋊Q8—28no—
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8#4118yes—
557#127—216no—
558#127—28no—
559#127—28no—
560#127—28no—
561#127—44no—
562#127—44no—
563#127—44no—
564#127—82no—
565#126—416no—
566#126—88no—
567#125—28no—
568#125—216no—
569#125—28no—
570#125—44no—
571#125—48no—
572#124—216no—
573#124—216no—
574#124—48no—
575#124—48no—
576#124—48no—
577#124—84no—
578#124—84no—
579#123—416no—
580#123—416no—
581#123—416no—
582#123—88no—
583C22⋊Q8—28no—
584C22⋊Q8—28no—
585C22⋊Q8—216no—
586#121—216no—
587#121—216no—
588#121—216no—
589#121—232no—
590#121—48no—
591#121—84no—
592C4×Q8—28no—
593C4×Q8—28no—
594C4×Q8—24no—
595C4×Q8—28no—
596C4×Q8—28no—
597C4×Q8—24no—
598C4×Q8—28no—
599C4×Q8—24no—
600C4×Q8—24no—
601C4×Q8—24no—
602C4×Q8—24no—
603C4×Q8—44no—
604C4×Q8—44no—
605C4×Q8—48no—
606C4×D4—28no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—216no—
611C4×D4—24no—
612C4×D4—416no—
613C4×D4—48no—
614C4×D4—44no—
615C4×D4—48no—
616C4×D4—48no—
617C4×D4—42no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—416no—
622C4×D4—48no—
623C4×D4—416no—
624C4×D4#4118yes—
625#117—48no—
626#117—416no—
627#117—416no—
628C2×C4⋊C4—28no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—416no—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2411yescharacteristic
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2412yes—
712C2×C42—28no—
713C2×C42—48no—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2412yes—
727C2×C42C2414yes—
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2412yes—
732C2×C42C2414yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2414yes—
737C2×C42C2418yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746#95C2412yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2412yes—
757#95C2412yes—
758#95C2414yes—
759#95C2412yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2412yes—
764#95C2412yes—
765#95C2412yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2412yes—
770#95C2414yes—
771#95C2412yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777#95C2418yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782C24C2518yes—
783C24C2512yes—
784#41—464no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—42no—
798C2×Q8C2×#4118yes—
799C2×Q8H(5,𝔽2)14yes—
800C2×D4—216no—
801C2×D4—216no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—216no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—22no—
812C2×D4—28no—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—22no—
816C2×D4—28no—
817C2×D4—48no—
818C2×D4—48no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—48no—
822C2×D4—44no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4C2×#4114yes—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—216no—
835C22×C4—216no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—28no—
840C22×C4—216no—
841C22×C4—48no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—48no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—44no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4C2×#4118yes—
854C22×C4C2512yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2511yescharacteristic
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2514yes—
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2514yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C4⋊C4—22no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—22no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—22no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—22no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4C2×#4114yes—
928C4⋊C4C2×#4118yes—
929C4⋊C4C2×#4118yes—
930C4⋊C4H(5,𝔽2)14yes—
931C22⋊C4—28no—
932C22⋊C4—216no—
933C22⋊C4—216no—
934C22⋊C4—216no—
935C22⋊C4—216no—
936C22⋊C4—216no—
937C22⋊C4—28no—
938C22⋊C4—216no—
939C22⋊C4—24no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—42no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4C2×#4118yes—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—28no—
964C42—28no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—28no—
969C42—28no—
970C42—28no—
971C42—24no—
972C42—28no—
973C42—24no—
974C42—24no—
975C42—22no—
976C42—22no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—22no—
981C42—44no—
982C42—44no—
983C42—48no—
984C42—42no—
985C42—42no—
986C42—44no—
987C42—41no—
988C42C2×#4114yes—
989C42C2×#4114yes—
990C422−1+414yes—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—28no—
998C23—28no—
999C23—28no—
1000C23—28no—
1001C23—28no—
1002C23—28no—
1003C23—28no—
1004C23C22×#4114yes—
1005C23C2611yescharacteristic
1006Q8—216no—
1007Q8—28no—
1008Q8—44no—
1009Q8—84no—
1010Q8—84no—
1011D4—28no—
1012D4—432no—
1013D4—416no—
1014D4—416no—
1015D4—416no—
1016D4—88no—
1017D4—88no—
1018D4—88no—
1019D4—816no—
1020D4—164no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—216no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—432no—
1079C2×C4—48no—
1080C2×C4—84no—
1081C2×C4—816no—
1082C2×C4—88no—
1083C2×C4—88no—
1084C2×C4—168no—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4118yes—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4114yes—
1089C2×C4C22×#4112yes—
1090C2×C4C22×#4112yes—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C2×H(5,𝔽2)14yes—
1094C2×C4C2×H(5,𝔽2)14yes—
1095C2×C4C2×H(5,𝔽2)12yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C2×C4C2×2−1+412yes—
1098C2×C4C2×2−1+412yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4#58512yes—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—48no—
1109C22—48no—
1110C22—48no—
1111C22—48no—
1112C22—48no—
1113C22—48no—
1114C22—48no—
1115C22C23×#4111yescharacteristic
1116C22C23×#4111yescharacteristic
1117C22C22×H(5,𝔽2)11yescharacteristic
1118C22C22×H(5,𝔽2)11yescharacteristic
1119C22C22×2−1+411yescharacteristic
1120C22C2×#58511yescharacteristic
1121C22H(7,𝔽2)11yescharacteristic
1122C4—22no—
1123C4—22no—
1124C4—24no—
1125C4—24no—
1126C4—22no—
1127C4—24no—
1128C4—28no—
1129C4—42no—
1130C4—44no—
1131C4—44no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—44no—
1136C4—44no—
1137C4—42no—
1138C4—41no—
1139C4—42no—
1140C4—42no—
1141C4—44no—
1142C4—42no—
1143C4#348114yes—
1144C4#350714yes—
1145C4#352214yes—
1146C2—44no—
1147C2—88no—
1148C2C2×#348111yescharacteristic
1149C2C2×#350711yescharacteristic
1150C2C2×#352211yescharacteristic
1151C2#6291711yescharacteristic
1152C2#6298611yescharacteristic
1153C2#6300611yescharacteristic
1154C2#6301411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36128C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59679C2semidirect
3. #59545C2semidirect
4. #59466C2semidirect
5. #59078C2semidirect
6. #59068C2semidirect
7. #45393C2semidirect
8. #44329C2semidirect
9. #40174C2semidirect
10. #40141C2semidirect
11. #39736C2semidirect
12. #38952C2semidirect
13. #36595C2semidirect
14. #36595C2semidirect
15. #36463C2semidirect
16. #36300C2semidirect
17. #36300C2semidirect
19. #36117C2semidirect
20. #35778C2semidirect
21. #34941C2semidirect
22. #34934C2semidirect
23. #34313C2semidirect
24. #34206C2semidirect
25. C4×#557C2semidirect
26. C4×#554C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#596792
#595452
#594662
#590782
#590682
#453932
#443292
#401742
#401412
#397362
#389522
#365952
#364632
#363002
#361282
#361172
#357782
#349412
#349342
#343132
#342062
C4×#5572
C4×#5542