Finite Group Databasebeta

← #9062270

Subgroups — #9062270

Order 512.

4382 conjugacy classes of subgroups.

The subgroup lattice has 1217 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60047C211yesmaximal, characteristic, complemented
2#60046C211yesmaximal, characteristic, complemented
3#60046C212yesmaximal, complemented
4#58589C212yesmaximal, complemented
5#55288C214yesmaximal, complemented
6#53487C212yesmaximal, complemented
7#50237C212yesmaximal, complemented
8#49680C214yesmaximal, complemented
9#47789C212yesmaximal, complemented
10#46675C214yesmaximal, complemented
11#46660C214yesmaximal, complemented
12#46358C212yesmaximal
13#45014C214yesmaximal, complemented
14#44189C214yesmaximal, complemented
15#44007C214yesmaximal, complemented
16#43827C214yesmaximal, complemented
17#43499C214yesmaximal, complemented
18#43289C212yesmaximal, complemented
19#43126C212yesmaximal, complemented
20#36021C212yesmaximal, complemented
21#35878C214yesmaximal, complemented
22#35555C212yesmaximal, complemented
23#35530C211yesmaximal, characteristic
24C2×#552C2212yes—
25C2×#539C2212yes—
26C2×#537C2211yescharacteristic
27C2×#520C2211yescharacteristic
28#2843C2212yes—
29#2839C2214yes—
30#2836C2214yes—
31#2817C2212yes—
32#2809C2211yescharacteristic
33#2807C2214yes—
34#2806C2214yes—
35#2806C2214yes—
36#2805C2214yes—
37#2805C2212yes—
38#2805C2212yes—
39#2805C2212yes—
40#2804C2212yes—
41#2802C2214yes—
42#2798C2214yes—
43#2794C2212yes—
44#2792C2214yes—
45#2792C2212yes—
46#2779C2214yes—
47#2777C2214yes—
48#2774C2214yes—
49#2773C2214yes—
50#2772C2214yes—
51#2770C2214yes—
52#2767C2214yes—
53#2767C2214yes—
54#2765C2214yes—
55#2763C2214yes—
56#2762C2214yes—
57#2762C2214yes—
58#2758C2214yes—
59#2757C2214yes—
60#2754C2214yes—
61#2745C2214yes—
62#2739C2214yes—
63#2734C2211yescharacteristic
64#2727C2212yes—
65#2724C2211yescharacteristic
66#2724C2212yes—
67#2720C2214yes—
68#2720C2214yes—
69#2720C2214yes—
70#2719C2214yes—
71#2717C2212yes—
72#2708C2214yes—
73#2708C2214yes—
74#2707C2214yes—
75#2702C2214yes—
76#2701C2214yes—
77#2690C2214yes—
78#2689C2214yes—
79#2689C2214yes—
80#2689C2214yes—
81#2683C2212yes—
82#2683C2211yescharacteristic
83#2680C2214yes—
84#2680C2214yes—
85#2672C2214yes—
86#2655C2214yes—
87#2654C2214yes—
88#2653C2214yes—
89#2638C2212yes—
90#2634C2212yes—
91#2627C2212yes—
92#2612C2214yes—
93#2611C2212yes—
94#2599C2214yes—
95#2599C2212yes—
96#2596C2214yes—
97#2593C2212yes—
98#2589C2214yes—
99#2589C2214yes—
100#2589C2214yes—
101#2587C2214yes—
102#2586C2212yes—
103#2586C2214yes—
104#2583C2212yes—
105#2583C2214yes—
106#2583C2212yes—
107#2582C2212yes—
108#2574C2214yes—
109#2573C2214yes—
110#2573C2214yes—
111#2573C2214yes—
112#2573C2214yes—
113#2570C2214yes—
114#2570C2214yes—
115#2570C2214yes—
116#2564C2212yes—
117#2560C2214yes—
118#2559C2214yes—
119#2558C2214yes—
120#2556C2214yes—
121#2553C2214yes—
122#2552C2214yes—
123#2552C2214yes—
124#2549C2214yes—
125#2530C2214yes—
126#2526C2214yes—
127#2518C2214yes—
128#2511C2214yes—
129#2511C2214yes—
130#2507C2214yes—
131#2507C2214yes—
132#2507C2214yes—
133#2506C2214yes—
134#2506C2214yes—
135#2502C2212yes—
136#2501C2212yes—
137#2500C2212yes—
138#2499C2214yes—
139#2499C2212yes—
140#2496C2214yes—
141#2489C2214yes—
142#2489C2214yes—
143#2488C2214yes—
144#2488C2214yes—
145#2486C2212yes—
146#2484C2212yes—
147#2479C2214yes—
148#2478C2214yes—
149#2478C2214yes—
150#2478C2214yes—
151#2477C2214yes—
152#2477C2214yes—
153#2477C2214yes—
154#2474C2214yes—
155#2473C2214yes—
156#2473C2214yes—
157#2473C2214yes—
158#2473C2214yes—
159#2473C2214yes—
160#2470C2214yes—
161#2470C2214yes—
162#2470C2214yes—
163#2470C2214yes—
164#2468C2214yes—
165#2466C2214yes—
166#2462C2214yes—
167#2462C2214yes—
168#2458C2214yes—
169#2451C2214yes—
170#2443C2214yes—
171#2443C2214yes—
172#2443C2214yes—
173#2440C2214yes—
174#2432C2212yes—
175#2423C2214yes—
176#2422C2214yes—
177#2422C2214yes—
178#2419C2214yes—
179#2406C2212yes—
180#2406C2214yes—
181#2401C2214yes—
182#2399C2212yes—
183#2395C2212yes—
184#2395C2214yes—
185C2×#398C2212yes—
186#2379C2212yes—
187#2374C2212yes—
188#2374C2214yes—
189#2374C2212yes—
190#2373C2214yes—
191#2373C2214yes—
192#2370C2214yes—
193#2369C2212yes—
194#2368C2214yes—
195#2360C2214yes—
196#2360C2214yes—
197#2360C2214yes—
198#2359C2214yes—
199#2359C2214yes—
200#2353C2212yes—
201#2344C2214yes—
202#2334C2214yes—
203#2333C2212yes—
204#2330C2214yes—
205#2329C2214yes—
206#2322C2214yes—
207#2320C2214yes—
208#2317C2212yes—
209#2317C2212yes—
210#2317C2211yescharacteristic
211#2316C2212yes—
212#2311C2211yescharacteristic
213#2297C2211yescharacteristic
214#2297C2211yescharacteristic
215#2296C2212yes—
216#2296C2212yes—
217C2×#384C2211yescharacteristic
218#2274C2212yes—
219C22×#41C2311yescharacteristic
220C22×#41C2311yescharacteristic
221#552—48no—
222#539—48no—
223#537—44no—
224C2×C4⋊Q8C2312yes—
225C2×#126C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#125C2314yes—
229C2×#125C2312yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#125C2314yes—
233C2×#124C2312yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×#123C2314yes—
237C2×#123C2314yes—
238C2×#123C2312yes—
239C2×#123C2312yes—
240C2×#123C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×#121C2312yes—
251C2×#121C2314yes—
252C2×#121C2312yes—
253#520—44no—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×#117C2312yes—
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2311yescharacteristic
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C42C2311yescharacteristic
279#401C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2312yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#400C2312yes—
298#400C2314yes—
299#400C2314yes—
300#400C2312yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#399C2312yes—
306#399C2314yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2312yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2312yes—
322#398C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2312yes—
338#398C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2312yes—
349#397C2314yes—
350#397C2312yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2312yes—
365#395C2314yes—
366#395C2312yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2312yes—
373#395C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#393C2314yes—
384#393C2312yes—
385#393C2314yes—
386#393C2314yes—
387#391C2314yes—
388#391C2312yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2312yes—
394#391C2311yescharacteristic
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2311yescharacteristic
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#390C2314yes—
404#390C2312yes—
405#390C2311yescharacteristic
406#390C2312yes—
407#390C2311yescharacteristic
408#390C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2312yes—
423#389C2312yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2314yes—
446#389C2312yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2312yes—
522#386C2312yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2312yes—
527#386C2312yes—
528#386C2314yes—
529#386C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#384C2312yes—
557#384C2314yes—
558#384C2314yes—
559#384C2312yes—
560#384C2314yes—
561#384C2314yes—
562#384C2312yes—
563#383C2314yes—
564#383C2312yes—
565#383C2314yes—
566#382C2314yes—
567#382C2314yes—
568#382C2314yes—
569#382C2314yes—
570#382C2312yes—
571#382C2314yes—
572#381C2312yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2312yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614#376C2314yes—
615#376C2312yes—
616C2×#95C2312yes—
617C2×#95C2314yes—
618C2×#41—24no—
619C2×#41—42no—
620C2×#41—42no—
621C2×#41—42no—
622C2×#41—42no—
623C2×#41—42no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2414yes—
626C22×Q8C2411yescharacteristic
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×D4C2412yes—
630C22×D4C2414yes—
631C22×D4C2411yescharacteristic
632C22×D4C2412yes—
633C22×D4C2411yescharacteristic
634C23×C4C2412yes—
635C23×C4C2411yescharacteristic
636C23×C4C2412yes—
637C23×C4C2414yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2414yes—
642C23×C4C2411yescharacteristic
643C23×C4C2411yescharacteristic
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C4⋊Q8—44no—
648#126—216no—
649#126—48no—
650#126—48no—
651#125—44no—
652#125—48no—
653#125—48no—
654#125—48no—
655#125—48no—
656#124—44no—
657#123—216no—
658#123—48no—
659#123—48no—
660#123—44no—
661#123—48no—
662#123—48no—
663#123—44no—
664C22⋊Q8—216no—
665C22⋊Q8—44no—
666C22⋊Q8—48no—
667C22⋊Q8—44no—
668C22⋊Q8—44no—
669C22⋊Q8—48no—
670C22⋊Q8—48no—
671C22⋊Q8—44no—
672C22⋊Q8—44no—
673#121—28no—
674#121—48no—
675#121—44no—
676C4×Q8—48no—
677C4×Q8—44no—
678C4×Q8—44no—
679C4×D4—28no—
680C4×D4—44no—
681C4×D4—44no—
682C4×D4—48no—
683#117—28no—
684#117—42no—
685#117—42no—
686#117—44no—
687#117—44no—
688#117—44no—
689#117—44no—
690#117—48no—
691#117—44no—
692C2×C4⋊C4—48no—
693C2×C4⋊C4—44no—
694C2×C4⋊C4—44no—
695C2×C4⋊C4—42no—
696C2×C4⋊C4—42no—
697C2×C4⋊C4—44no—
698C2×C4⋊C4—44no—
699C2×C4⋊C4—44no—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C42—42no—
792C2×C42C2412yes—
793C2×C42C2412yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2412yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813#95C2412yes—
814#95C2414yes—
815#95C2412yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2412yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2412yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873C24C2512yes—
874C24C2512yes—
875C24C2511yescharacteristic
876#41—416no—
877#41—88no—
878C2×Q8—22no—
879C2×Q8—28no—
880C2×Q8—22no—
881C2×Q8—41no—
882C2×Q8—41no—
883C2×Q8—42no—
884C2×Q8—44no—
885C2×Q8—41no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—41no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—28no—
895C2×D4—24no—
896C2×D4—22no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—41no—
901C2×D4—42no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—41no—
905C2×D4—42no—
906C2×D4H(5,𝔽2)14yes—
907C22×C4—24no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—28no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—41no—
932C22×C4—42no—
933C22×C4—41no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4C2514yes—
942C22×C4C2514yes—
943C22×C4C2512yes—
944C22×C4C2514yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2512yes—
948C22×C4C2512yes—
949C22×C4C2512yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2512yes—
956C22×C4C2511yescharacteristic
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2511yescharacteristic
961C4⋊C4—24no—
962C4⋊C4—28no—
963C4⋊C4—24no—
964C4⋊C4—28no—
965C4⋊C4—24no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—41no—
979C4⋊C4—42no—
980C4⋊C4—44no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—41no—
997C4⋊C4—42no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—42no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C42−1+418yes—
1022C22⋊C4—24no—
1023C22⋊C4—24no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—42no—
1039C22⋊C4—44no—
1040C22⋊C4—42no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C42—24no—
1053C42—28no—
1054C42—28no—
1055C42—24no—
1056C42—41no—
1057C42—42no—
1058C42—41no—
1059C42—44no—
1060C42—44no—
1061C42—44no—
1062C42—44no—
1063C42—42no—
1064C42—42no—
1065C42—44no—
1066C42—44no—
1067C42—44no—
1068C42—44no—
1069C42—42no—
1070C42—44no—
1071C42—44no—
1072C42—42no—
1073C23—21no—
1074C23—24no—
1075C23—22no—
1076C23—24no—
1077C23—22no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—24no—
1083C23—24no—
1084C23—22no—
1085C23—22no—
1086C23C2×H(5,𝔽2)14yes—
1087C23#58512yes—
1088C23C2611yescharacteristic
1089Q8—44no—
1090Q8—88no—
1091Q8—82no—
1092Q8—84no—
1093Q8—162no—
1094D4—44no—
1095D4—48no—
1096D4—82no—
1097D4—88no—
1098D4—84no—
1099C2×C4—216no—
1100C2×C4—28no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—48no—
1153C2×C4—88no—
1154C2×C4—84no—
1155C2×C4—84no—
1156C2×C4—84no—
1157C2×C4—88no—
1158C2×C4—84no—
1159C2×C4—161no—
1160C2×C4—161no—
1161C2×C4—162no—
1162C2×C4—162no—
1163C2×C4C2×H(5,𝔽2)12yes—
1164C2×C4C2×2−1+418yes—
1165C2×C4C2×2−1+414yes—
1166C2×C4#58512yes—
1167C2×C4#58514yes—
1168C22—24no—
1169C22—24no—
1170C22—22no—
1171C22—24no—
1172C22—24no—
1173C22—41no—
1174C22—44no—
1175C22—42no—
1176C22—41no—
1177C22—44no—
1178C22—42no—
1179C22—44no—
1180C22—42no—
1181C22—42no—
1182C22—44no—
1183C22C22×H(5,𝔽2)11yescharacteristic
1184C22C22×2−1+412yes—
1185C22C2×#58512yes—
1186C22C2×#58511yescharacteristic
1187C22C2×#58511yescharacteristic
1188C4—28no—
1189C4—22no—
1190C4—22no—
1191C4—24no—
1192C4—24no—
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—44no—
1197C4—44no—
1198C4—44no—
1199C4—44no—
1200C4—42no—
1201C4—44no—
1202C4—42no—
1203C4—44no—
1204C4—42no—
1205C4—44no—
1206C4—44no—
1207C4—44no—
1208C2—44no—
1209C2—42no—
1210C2—82no—
1211C2#6282011yescharacteristic
1212C2#6282512yes—
1213C2#6302111yescharacteristic
1214C2#6302512yes—
1215C2#6303711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60047C2semidirect
2. #60046C2semidirect
3. #60046C2semidirect
4. #58589C2semidirect
5. #55288C2semidirect
6. #53487C2semidirect
7. #50237C2semidirect
8. #49680C2semidirect
9. #47789C2semidirect
10. #46675C2semidirect
11. #46660C2semidirect
13. #45014C2semidirect
14. #44189C2semidirect
15. #44007C2semidirect
16. #43827C2semidirect
17. #43499C2semidirect
18. #43289C2semidirect
19. #43126C2semidirect
20. #36021C2semidirect
21. #35878C2semidirect
22. #35555C2semidirect

Maximal subgroups

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

subgroupindex
#600472
#600462
#585892
#552882
#534872
#502372
#496802
#477892
#466752
#466602
#463582
#450142
#441892
#440072
#438272
#434992
#432892
#431262
#360212
#358782
#355552
#355302