Finite Group Databasebeta

← #8429308

Subgroups — #8429308

Order 512.

5137 conjugacy classes of subgroups.

The subgroup lattice has 1153 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59823C212yesmaximal, complemented
3#59458C212yesmaximal, complemented
4#59070C212yesmaximal, complemented
5#55278C218yesmaximal, complemented
6#53112C214yesmaximal, complemented
7#53108C214yesmaximal, complemented
8#52964C214yesmaximal, complemented
9#42556C214yesmaximal, complemented
10#42479C214yesmaximal, complemented
11#42441C214yesmaximal, complemented
12#39726C212yesmaximal, complemented
13#39387C212yesmaximal, complemented
14#39351C212yesmaximal, complemented
15#39201C212yesmaximal, complemented
16#38987C212yesmaximal, complemented
17#38985C212yesmaximal, complemented
18#37640C212yesmaximal, complemented
19#37625C212yesmaximal, complemented
20#37625C212yesmaximal, complemented
21#36595C211yesmaximal, characteristic, complemented
22#36595C211yesmaximal, characteristic, complemented
23#36128C211yesmaximal, characteristic
24#34950C211yesmaximal, characteristic, complemented
25#34941C211yesmaximal, characteristic, complemented
26#34929C211yesmaximal, characteristic, complemented
27C2×#559C2212yes—
28C2×#559C2212yes—
29C2×#554C2214yes—
30C2×#550C2212yes—
31C2×#542C2214yes—
32C2×#533C2212yes—
33C2×#532C2212yes—
34#2867C2211yescharacteristic
35#2858C2212yes—
36#2858C2212yes—
37#2856C2212yes—
38#2837C2218yes—
39#2829C2218yes—
40#2829C2218yes—
41#2827C2218yes—
42#2820C2218yes—
43#2816C2218yes—
44#2814C2218yes—
45#2806C2214yes—
46#2786C2218yes—
47#2740C2218yes—
48#2732C2218yes—
49#2730C2218yes—
50#2723C2218yes—
51#2717C2218yes—
52#2715C2218yes—
53#2712C2218yes—
54#2710C2218yes—
55#2707C2218yes—
56#2705C2218yes—
57#2700C2218yes—
58#2695C2218yes—
59#2692C2218yes—
60#2681C2218yes—
61#2681C2218yes—
62#2672C2218yes—
63#2672C2218yes—
64#2644C2214yes—
65#2644C2214yes—
66#2641C2214yes—
67#2630C2218yes—
68#2630C2218yes—
69#2624C2214yes—
70#2624C2214yes—
71#2624C2214yes—
72#2620C2214yes—
73#2620C2214yes—
74#2620C2214yes—
75#2618C2218yes—
76#2616C2218yes—
77#2592C2214yes—
78#2586C2214yes—
79#2584C2214yes—
80#2582C2211yescharacteristic
81#2582C2214yes—
82#2580C2214yes—
83#2574C2214yes—
84#2567C2211yescharacteristic
85#2567C2212yes—
86#2567C2211yescharacteristic
87#2567C2211yescharacteristic
88#2563C2211yescharacteristic
89#2556C2214yes—
90#2552C2212yes—
91#2552C2211yescharacteristic
92#2552C2212yes—
93#2551C2211yescharacteristic
94#2551C2211yescharacteristic
95#2548C2212yes—
96#2548C2212yes—
97#2548C2212yes—
98#2548C2214yes—
99#2548C2212yes—
100#2548C2212yes—
101#2548C2212yes—
102#2548C2212yes—
103#2547C2214yes—
104#2546C2211yescharacteristic
105#2545C2214yes—
106#2544C2214yes—
107#2544C2214yes—
108#2542C2214yes—
109#2542C2211yescharacteristic
110#2542C2214yes—
111#2541C2212yes—
112#2541C2212yes—
113#2538C2214yes—
114#2538C2214yes—
115#2538C2214yes—
116#2538C2211yescharacteristic
117#2538C2214yes—
118#2538C2211yescharacteristic
119#2513C2214yes—
120#2512C2214yes—
121#2512C2214yes—
122#2508C2212yes—
123#2507C2212yes—
124#2507C2214yes—
125#2507C2212yes—
126#2506C2212yes—
127#2497C2212yes—
128#2492C2212yes—
129#2491C2214yes—
130#2454C2214yes—
131#2454C2214yes—
132#2454C2214yes—
133#2454C2212yes—
134#2452C2214yes—
135#2452C2214yes—
136#2452C2214yes—
137#2452C2212yes—
138#2451C2212yes—
139#2451C2212yes—
140#2449C2218yes—
141#2448C2214yes—
142#2447C2214yes—
143#2447C2214yes—
144#2445C2214yes—
145#2445C2214yes—
146#2445C2214yes—
147#2445C2214yes—
148#2445C2214yes—
149#2445C2214yes—
150#2431C2214yes—
151#2429C2212yes—
152#2428C2214yes—
153#2428C2214yes—
154#2427C2214yes—
155#2427C2214yes—
156#2427C2214yes—
157#2426C2214yes—
158#2423C2212yes—
159#2422C2214yes—
160#2422C2214yes—
161#2422C2214yes—
162#2417C2218yes—
163#2406C2218yes—
164#2399C2214yes—
165#2396C2214yes—
166#2396C2214yes—
167#2369C2212yes—
168#2366C2212yes—
169#2366C2212yes—
170#2366C2212yes—
171#2366C2212yes—
172#2366C2212yes—
173#2366C2212yes—
174#2365C2212yes—
175Q8×C4⋊C4C2212yes—
176D4×C4⋊C4C2214yes—
177D4×C4⋊C4C2214yes—
178#2324C2214yes—
179#2319C2214yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2211yescharacteristic
186C4×#127C2212yes—
187C4×#127C2212yes—
188C4×#125C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194#2293C2212yes—
195#2285C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C22×#41C2314yes—
200#559—48no—
201#559—48no—
202#554—416no—
203#550—48no—
204#542—416no—
205#533—48no—
206#532—48no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2312yes—
220C2×#127C2312yes—
221C2×#127C2314yes—
222C2×#127C2312yes—
223C2×#126C2318yes—
224C2×#125C2312yes—
225C2×#125C2314yes—
226C2×#125C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#124C2318yes—
234C2×#124C2314yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×#123C2318yes—
238C2×#123C2318yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2318yes—
246C2×C22⋊Q8C2318yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2318yes—
249C2×#121C2318yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2314yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×#117C2314yes—
282C2×#117C2314yes—
283C22×C4⋊C4C2318yes—
284C22×C42C2312yes—
285#400C2314yes—
286#400C2314yes—
287#399C2314yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2314yes—
293#398C2314yes—
294#398C2318yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2314yes—
319#396C2314yes—
320#396C2318yes—
321#396C2314yes—
322#396C2314yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#395C2314yes—
327#395C2318yes—
328#395C2314yes—
329#395C2314yes—
330#395C2314yes—
331#395C2314yes—
332#395C2314yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#393C2314yes—
351#393C2318yes—
352#393C2314yes—
353#393C2318yes—
354#392C2318yes—
355#392C2318yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2314yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#391C2312yes—
366#391C2312yes—
367#391C2318yes—
368#391C2312yes—
369#391C2312yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2314yes—
375#390C2314yes—
376#390C2312yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#390C2318yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2314yes—
386#390C2314yes—
387#390C2314yes—
388#390C2314yes—
389#390C2314yes—
390#390C2314yes—
391#390C2314yes—
392#390C2314yes—
393#390C2314yes—
394#390C2314yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2312yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2314yes—
416#389C2312yes—
417#389C2314yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2318yes—
423#389C2314yes—
424#389C2318yes—
425#389C2314yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2318yes—
449#387C2314yes—
450#386C2318yes—
451#386C2318yes—
452#386C2318yes—
453#386C2318yes—
454#386C2318yes—
455#386C2318yes—
456#386C2318yes—
457#386C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2314yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2314yes—
466#384C2311yescharacteristic
467#384C2311yescharacteristic
468#384C2312yes—
469#384C2312yes—
470#384C2311yescharacteristic
471#384C2312yes—
472#384C2314yes—
473#384C2312yes—
474#384C2314yes—
475#384C2312yes—
476#382C2312yes—
477#382C2314yes—
478#381C2318yes—
479#380C2312yes—
480#380C2312yes—
481#380C2314yes—
482#380C2318yes—
483#380C2318yes—
484#380C2318yes—
485#380C2318yes—
486#380C2312yes—
487#380C2312yes—
488#380C2318yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2311yescharacteristic
516C4×C4⋊C4C2311yescharacteristic
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522#376C2314yes—
523C43C2312yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C2×#41—48no—
527C2×#41—48no—
528C2×#41—84no—
529C22×Q8C2411yescharacteristic
530C22×Q8C2412yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2414yes—
533C22×Q8C2414yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2411yescharacteristic
540C22×D4C2414yes—
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2418yes—
544C22×D4C2418yes—
545C22×D4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2418yes—
550C23×C4C2418yes—
551C23×C4C2418yes—
552C4⋊Q8—28no—
553C4⋊Q8—28no—
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—44no—
558C4⋊Q8—44no—
559C4⋊Q8—44no—
560#127—28no—
561#127—28no—
562#127—28no—
563#127—44no—
564#127—48no—
565#127—44no—
566#127—44no—
567#127—82no—
568#126—416no—
569#125—28no—
570#125—48no—
571#125—48no—
572#124—48no—
573#124—48no—
574#124—48no—
575#124—48no—
576#124—48no—
577#124—48no—
578#124—416no—
579#124—84no—
580#123—416no—
581#123—416no—
582#123—416no—
583#123—88no—
584C22⋊Q8—28no—
585C22⋊Q8—416no—
586C22⋊Q8—416no—
587C22⋊Q8—48no—
588C22⋊Q8—44no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—416no—
592C22⋊Q8—416no—
593C22⋊Q8—88no—
594#121—416no—
595#121—48no—
596#121—48no—
597#121—48no—
598#121—48no—
599#121—48no—
600C4×Q8—24no—
601C4×Q8—24no—
602C4×Q8—28no—
603C4×Q8—24no—
604C4×Q8—24no—
605C4×Q8—24no—
606C4×Q8—48no—
607C4×Q8—44no—
608C4×Q8—48no—
609C4×Q8—44no—
610C4×Q8—42no—
611C4×Q8—48no—
612C4×D4—216no—
613C4×D4—24no—
614C4×D4—216no—
615C4×D4—24no—
616C4×D4—24no—
617C4×D4—48no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—48no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—48no—
625C4×D4—84no—
626#117—48no—
627#117—48no—
628C2×C4⋊C4—416no—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2418yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2418yes—
716C2×C42—28no—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2418yes—
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2418yes—
779C24C2512yes—
780C24C2518yes—
781#41—832no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—28no—
789C2×Q8—28no—
790C2×Q8—22no—
791C2×Q8—22no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—22no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—42no—
800C2×Q8—44no—
801C2×Q8—42no—
802C2×Q8—44no—
803C2×D4—28no—
804C2×D4—28no—
805C2×D4—22no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—28no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—48no—
821C2×D4—44no—
822C2×D4—48no—
823C2×D4—48no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—44no—
827C2×D4—48no—
828C2×D4—44no—
829C2×D4—48no—
830C2×D4—48no—
831C2×D4—44no—
832C2×D4—44no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—216no—
842C22×C4—216no—
843C22×C4—42no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2511yescharacteristic
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4H(5,𝔽2)14yes—
931C4⋊C4H(5,𝔽2)14yes—
932C22⋊C4—24no—
933C22⋊C4—216no—
934C22⋊C4—216no—
935C22⋊C4—28no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
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⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—48no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—28no—
968C42—28no—
969C42—28no—
970C42—22no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—24no—
975C42—22no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—22no—
980C42—42no—
981C42—42no—
982C42—48no—
983C42—42no—
984C42—41no—
985C42H(5,𝔽2)14yes—
986C422−1+414yes—
987C422−1+414yes—
988C23—22no—
989C23—28no—
990C23—28no—
991C23—22no—
992C23—28no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—28no—
997C23—28no—
998C23—22no—
999C23—28no—
1000C23—22no—
1001C23—28no—
1002C23C2611yescharacteristic
1003Q8—48no—
1004Q8—44no—
1005Q8—48no—
1006Q8—44no—
1007Q8—88no—
1008Q8—88no—
1009Q8—84no—
1010D4—416no—
1011D4—416no—
1012D4—44no—
1013D4—416no—
1014D4—88no—
1015D4—88no—
1016D4—88no—
1017D4—816no—
1018D4—164no—
1019D4—168no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—816no—
1082C2×C4—816no—
1083C2×C4—168no—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×H(5,𝔽2)14yes—
1086C2×C4C2×H(5,𝔽2)14yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×H(5,𝔽2)12yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4C2×2−1+412yes—
1094C2×C4C2×2−1+412yes—
1095C2×C4C2×2−1+412yes—
1096C2×C4C2×2−1+412yes—
1097C2×C4#58512yes—
1098C22—42no—
1099C22—48no—
1100C22—42no—
1101C22—48no—
1102C22—48no—
1103C22—42no—
1104C22—48no—
1105C22—42no—
1106C22—42no—
1107C22—48no—
1108C22—48no—
1109C22—42no—
1110C22—48no—
1111C22—42no—
1112C22C22×H(5,𝔽2)11yescharacteristic
1113C22C22×H(5,𝔽2)11yescharacteristic
1114C22C22×H(5,𝔽2)11yescharacteristic
1115C22C22×2−1+411yescharacteristic
1116C22C22×2−1+411yescharacteristic
1117C22C2×#58511yescharacteristic
1118C22H(7,𝔽2)11yescharacteristic
1119C4—24no—
1120C4—22no—
1121C4—24no—
1122C4—22no—
1123C4—22no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—44no—
1129C4—44no—
1130C4—41no—
1131C4—44no—
1132C4—42no—
1133C4—44no—
1134C4—42no—
1135C4—44no—
1136C4—42no—
1137C4—42no—
1138C4—44no—
1139C4—42no—
1140C4#354814yes—
1141C4#355014yes—
1142C4#355414yes—
1143C2—82no—
1144C2—88no—
1145C2C2×#355411yescharacteristic
1146C2C2×#354811yescharacteristic
1147C2C2×#355011yescharacteristic
1148C2#6291211yescharacteristic
1149C2#6291711yescharacteristic
1150C2#6296211yescharacteristic
1151C2#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. #59823C2semidirect
3. #59458C2semidirect
4. #59070C2semidirect
5. #55278C2semidirect
6. #53112C2semidirect
7. #53108C2semidirect
8. #52964C2semidirect
9. #42556C2semidirect
10. #42479C2semidirect
11. #42441C2semidirect
12. #39726C2semidirect
13. #39387C2semidirect
14. #39351C2semidirect
15. #39201C2semidirect
16. #38987C2semidirect
17. #38985C2semidirect
18. #37640C2semidirect
19. #37625C2semidirect
20. #37625C2semidirect
21. #36595C2semidirect
22. #36595C2semidirect
24. #34950C2semidirect
25. #34941C2semidirect
26. #34929C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598232
#594582
#590702
#552782
#531122
#531082
#529642
#425562
#424792
#424412
#397262
#393872
#393512
#392012
#389872
#389852
#376402
#376252
#365952
#361282
#349502
#349412
#349292