Finite Group Databasebeta

← #8901168

Subgroups — #8901168

Order 512.

4174 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58666C214yesmaximal, complemented
2#54744C214yesmaximal, complemented
3#54475C214yesmaximal, complemented
4#51668C212yesmaximal, complemented
5#51668C212yesmaximal, complemented
6#50996C214yesmaximal, complemented
7#50982C214yesmaximal, complemented
8#47732C214yesmaximal, complemented
9#47211C212yesmaximal, complemented
10#46913C214yesmaximal, complemented
11#46882C212yesmaximal
12#46882C212yesmaximal
13#46855C212yesmaximal, complemented
14#46815C212yesmaximal
15#40096C214yesmaximal, complemented
16#39699C214yesmaximal, complemented
17#38389C214yesmaximal
18#37392C212yesmaximal, complemented
19#36708C211yesmaximal, characteristic
20#35644C211yesmaximal, characteristic
21#35496C212yesmaximal, complemented
22#35488C212yesmaximal
23#35391C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C2×#543C2211yescharacteristic
27C2×#541C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29#2862C2212yescomplemented
30#2859C2212yescomplemented
31#2848C2212yes—
32#2844C2214yescomplemented
33#2839C2214yescomplemented
34#2839C2214yescomplemented
35#2835C2212yes—
36#2835C2212yes—
37#2817C2212yes—
38#2809C2212yescomplemented
39#2809C2212yescomplemented
40#2806C2214yescomplemented
41#2802C2214yescomplemented
42#2794C2214yescomplemented
43#2788C2214yes—
44#2788C2214yes—
45#2774C2214yescomplemented
46#2774C2214yescomplemented
47#2774C2214yescomplemented
48#2770C2214yes—
49#2770C2214yes—
50#2769C2214yescomplemented
51#2767C2214yescomplemented
52#2767C2214yescomplemented
53#2763C2212yes—
54#2763C2212yes—
55#2758C2214yescomplemented
56#2758C2214yescomplemented
57#2758C2214yescomplemented
58#2758C2214yescomplemented
59#2758C2214yescomplemented
60#2755C2214yescomplemented
61#2755C2214yescomplemented
62#2747C2214yes—
63#2747C2214yes—
64#2747C2214yes—
65#2744C2214yes—
66#2739C2214yes—
67#2734C2214yescomplemented
68#2734C2212yescomplemented
69#2734C2212yescomplemented
70#2729C2214yes—
71#2722C2212yes—
72#2722C2212yes—
73#2722C2214yes—
74#2720C2214yes—
75#2719C2214yescomplemented
76#2719C2214yescomplemented
77#2719C2214yescomplemented
78#2719C2214yescomplemented
79#2713C2214yescomplemented
80#2713C2214yescomplemented
81#2713C2214yescomplemented
82#2713C2214yescomplemented
83#2713C2214yescomplemented
84#2704C2214yes—
85#2698C2214yes—
86#2698C2214yes—
87#2698C2214yes—
88#2698C2214yes—
89#2690C2214yes—
90#2690C2214yes—
91#2690C2214yes—
92#2690C2214yes—
93#2690C2214yes—
94#2689C2214yes—
95#2689C2214yes—
96#2689C2214yes—
97#2689C2214yes—
98#2677C2214yes—
99#2677C2214yes—
100#2666C2214yescomplemented
101#2666C2214yescomplemented
102#2666C2214yescomplemented
103#2666C2214yescomplemented
104#2660C2212yescomplemented
105#2652C2214yes—
106#2652C2214yes—
107#2642C2212yescomplemented
108#2627C2212yes—
109#2608C2212yes—
110#2590C2214yescomplemented
111#2589C2214yes—
112#2588C2214yescomplemented
113#2588C2214yescomplemented
114#2588C2214yescomplemented
115#2586C2214yescomplemented
116#2583C2214yes—
117#2583C2212yes—
118#2583C2212yes—
119#2577C2214yes—
120#2574C2214yes—
121#2574C2214yes—
122#2573C2214yes—
123#2573C2214yes—
124#2573C2214yes—
125#2570C2214yescomplemented
126#2569C2214yes—
127#2569C2214yes—
128#2568C2212yescomplemented
129#2567C2212yescomplemented
130#2565C2212yescomplemented
131#2565C2212yescomplemented
132#2561C2212yes—
133#2561C2211yescharacteristic
134#2561C2211yescharacteristic
135#2561C2212yes—
136#2556C2214yes—
137#2550C2214yescomplemented
138#2550C2214yescomplemented
139#2550C2214yescomplemented
140#2549C2214yes—
141#2549C2214yes—
142#2533C2214yescomplemented
143#2530C2214yes—
144#2524C2214yescomplemented
145#2524C2214yescomplemented
146#2523C2212yes—
147#2523C2212yes—
148#2523C2214yes—
149#2520C2214yescomplemented
150#2520C2214yescomplemented
151#2520C2214yescomplemented
152#2517C2214yes—
153#2515C2214yes—
154#2515C2214yes—
155#2515C2214yes—
156#2508C2214yescomplemented
157#2508C2214yescomplemented
158#2506C2214yescomplemented
159#2506C2214yescomplemented
160#2505C2214yes—
161#2503C2212yes—
162#2503C2212yes—
163#2502C2212yes—
164#2499C2212yes—
165#2499C2212yes—
166#2496C2214yes—
167#2495C2214yes—
168#2495C2214yes—
169#2492C2214yes—
170#2492C2214yes—
171#2489C2214yes—
172#2489C2214yes—
173#2489C2214yes—
174#2484C2212yes—
175#2482C2212yes—
176#2480C2214yes—
177#2480C2214yes—
178#2480C2214yes—
179#2480C2214yes—
180#2478C2214yes—
181#2478C2214yes—
182#2475C2214yes—
183#2475C2214yes—
184#2473C2214yes—
185#2465C2214yes—
186#2462C2214yescomplemented
187#2446C2214yescomplemented
188#2442C2214yes—
189#2440C2214yes—
190#2440C2214yes—
191#2434C2212yes—
192#2434C2211yescharacteristic
193#2434C2211yescharacteristic
194#2421C2214yes—
195#2381C2212yescomplemented
196#2381C2212yescomplemented
197#2369C2212yescomplemented
198#2369C2212yescomplemented
199#2368C2214yes—
200#2345C2214yes—
201#2336C2214yescomplemented
202#2334C2214yes—
203#2334C2214yes—
204#2334C2214yes—
205#2334C2214yes—
206#2334C2214yes—
207#2332C2212yes—
208#2332C2212yes—
209#2315C2212yes—
210#2313C2211yescharacteristic
211#2310C2212yes—
212C4×#125C2214yescomplemented
213C4×#126C2214yes—
214#2298C2212yes—
215C2×#385C2212yes—
216#2280C2212yes—
217#2274C2211yescharacteristic
218#2273C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C24×C4C2311yescharacteristic
221#544—44no—
222#544—44no—
223#543—44no—
224#541—48no—
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#125C2314yes—
238C2×#125C2312yes—
239C2×#125C2314yes—
240C2×#125C2312yes—
241C2×#125C2312yes—
242C2×#125C2314yes—
243C2×#125C2314yes—
244C2×#125C2314yes—
245C2×C22⋊Q8—44no—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2314yes—
267C22×C22⋊C4C2311yescharacteristic
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2312yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
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#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#399C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#397C2312yes—
340#397C2312yes—
341#397C2314yes—
342#397C2312yes—
343#397C2312yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#393C2312yes—
379#393C2312yes—
380#393C2312yes—
381#393C2314yes—
382#393C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#391C2312yes—
389#391C2314yes—
390#391C2312yes—
391#391C2312yes—
392#391C2314yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
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#389C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
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#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
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#387C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2312yes—
527#385C2312yes—
528#385C2312yes—
529#385C2312yes—
530#385C2312yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2312yes—
540#385C2312yes—
541#385C2314yes—
542#385C2312yes—
543#385C2314yes—
544#384C2312yes—
545#384C2312yes—
546#384C2312yes—
547#384C2312yes—
548#383C2314yes—
549#383C2314yes—
550#383C2314yes—
551#383C2314yes—
552#383C2314yes—
553#383C2314yes—
554#382C2314yes—
555#382C2312yes—
556#382C2312yes—
557#382C2312yes—
558#382C2312yes—
559#382C2314yes—
560#382C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#381C2314yes—
568#381C2314yes—
569#381C2312yes—
570#381C2312yes—
571#381C2312yes—
572#381C2314yes—
573#380C2312yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583#379C2314yes—
584#379C2312yes—
585#379C2312yes—
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⋊C4C2312yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2311yescharacteristic
606C4×C22⋊C4C2311yescharacteristic
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616#376C2312yes—
617C2×#95C2314yes—
618C43C2312yes—
619C25C2411yescharacteristic
620C22×Q8—42no—
621C22×Q8—44no—
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2411yescharacteristic
629C22×Q8C2411yescharacteristic
630C22×Q8C2412yes—
631C23×C4—44no—
632C23×C4—42no—
633C23×C4C2411yescharacteristic
634C23×C4C2411yescharacteristic
635C23×C4C2411yescharacteristic
636C23×C4C2411yescharacteristic
637C23×C4C2414yes—
638C23×C4C2411yescharacteristic
639C23×C4C2414yes—
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2411yescharacteristic
643C4⋊Q8—44no—
644C4⋊Q8—44no—
645C4⋊Q8—44no—
646C4⋊Q8—44no—
647C4⋊Q8—44no—
648C4⋊Q8—44no—
649C4⋊Q8—44no—
650C4⋊Q8—48no—
651#126—216no—
652#126—216no—
653#126—48no—
654#126—48no—
655#125—44no—
656#125—44no—
657#125—44no—
658#125—48no—
659#125—48no—
660#125—48no—
661#125—48no—
662#125—48no—
663C22⋊Q8—28no—
664C22⋊Q8—28no—
665C22⋊Q8—44no—
666C22⋊Q8—42no—
667C22⋊Q8—42no—
668C22⋊Q8—44no—
669C22⋊Q8—44no—
670C22⋊Q8—48no—
671C22⋊Q8—48no—
672C22⋊Q8—48no—
673C22⋊Q8—48no—
674C22⋊Q8—48no—
675C4×Q8—44no—
676C4×Q8—44no—
677#117—28no—
678#117—44no—
679#117—44no—
680C2×C4⋊C4—24no—
681C2×C4⋊C4—24no—
682C2×C4⋊C4—48no—
683C2×C4⋊C4—42no—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C22⋊C4—24no—
746C2×C22⋊C4—28no—
747C2×C22⋊C4—44no—
748C2×C22⋊C4—42no—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2412yes—
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2412yes—
802#95C2414yes—
803#95C2412yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2412yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2412yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
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—
863C24—22no—
864C24—24no—
865C24—42no—
866C24—42no—
867C24C2511yescharacteristic
868C24C2512yes—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—24no—
873C2×Q8—42no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—42no—
882C2×Q8—41no—
883C2×Q8—42no—
884C2×Q8—41no—
885C2×Q8—42no—
886C2×Q8—44no—
887C2×Q8—42no—
888C2×Q8—42no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—88no—
893C22×C4—22no—
894C22×C4—24no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—28no—
900C22×C4—28no—
901C22×C4—42no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—42no—
906C22×C4—44no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—88no—
915C22×C4H(5,𝔽2)14yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2514yes—
920C22×C4C2514yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2514yes—
924C22×C4C2514yes—
925C22×C4C2514yes—
926C22×C4C2512yes—
927C22×C4C2512yes—
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2512yes—
935C22×C4C2514yes—
936C22×C4C2512yes—
937C4⋊C4—28no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—28no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—42no—
975C4⋊C4—41no—
976C4⋊C4—42no—
977C4⋊C4—41no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C22⋊C4—28no—
999C22⋊C4—24no—
1000C22⋊C4—24no—
1001C22⋊C4—28no—
1002C22⋊C4—24no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—28no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—44no—
1013C22⋊C4—42no—
1014C22⋊C4—44no—
1015C22⋊C4—42no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C42−1+418yes—
1020C42—24no—
1021C42—24no—
1022C42—28no—
1023C42—28no—
1024C42—42no—
1025C42—44no—
1026C42—42no—
1027C42—42no—
1028C42—42no—
1029C42—44no—
1030C42—44no—
1031C42—42no—
1032C42—42no—
1033C42—44no—
1034C42—44no—
1035C42—44no—
1036C42—44no—
1037C42—44no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C23—28no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—24no—
1048C23—22no—
1049C23—24no—
1050C23—82no—
1051C23—82no—
1052C23—88no—
1053C23C2×H(5,𝔽2)12yes—
1054C23C2×2−1+414yes—
1055C23C2611yescharacteristic
1056Q8—84no—
1057Q8—84no—
1058Q8—84no—
1059Q8—84no—
1060Q8—162no—
1061Q8—162no—
1062Q8—161no—
1063Q8—161no—
1064Q8—162no—
1065C2×C4—28no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—44no—
1119C2×C4—88no—
1120C2×C4—88no—
1121C2×C4—82no—
1122C2×C4—82no—
1123C2×C4—82no—
1124C2×C4—82no—
1125C2×C4—162no—
1126C2×C4—162no—
1127C2×C4C2×H(5,𝔽2)14yes—
1128C2×C4C2×2−1+418yes—
1129C2×C4#58514yes—
1130C22—22no—
1131C22—22no—
1132C22—24no—
1133C22—22no—
1134C22—28no—
1135C22—42no—
1136C22—42no—
1137C22—44no—
1138C22—44no—
1139C22—88no—
1140C22C22×H(5,𝔽2)11yescharacteristic
1141C22C22×2−1+412yes—
1142C22C2×#58512yes—
1143C222−1+612yes—
1144C4—24no—
1145C4—24no—
1146C4—28no—
1147C4—42no—
1148C4—42no—
1149C4—41no—
1150C4—41no—
1151C4—44no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—44no—
1157C4—42no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C2—42no—
1166C2—44no—
1167C2#6282411yescharacteristic
1168C2#6283311yescharacteristic
1169C2#6287111yescharacteristic
1170C2#6295014yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58666C2semidirect
2. #54744C2semidirect
3. #54475C2semidirect
4. #51668C2semidirect
5. #51668C2semidirect
6. #50996C2semidirect
7. #50982C2semidirect
8. #47732C2semidirect
9. #47211C2semidirect
10. #46913C2semidirect
13. #46855C2semidirect
15. #40096C2semidirect
16. #39699C2semidirect
18. #37392C2semidirect
21. #35496C2semidirect
29. #2862C22semidirect
30. #2859C22semidirect
32. #2844C22semidirect
33. #2839C22semidirect
34. #2839C22semidirect
38. #2809C22semidirect
39. #2809C22semidirect
40. #2806C22semidirect
41. #2802C22semidirect
42. #2794C22semidirect
45. #2774C22semidirect
46. #2774C22semidirect
47. #2774C22semidirect
50. #2769C22semidirect
51. #2767C22semidirect
52. #2767C22semidirect
55. #2758C22semidirect
56. #2758C22semidirect
57. #2758C22semidirect
58. #2758C22semidirect
59. #2758C22semidirect
60. #2755C22semidirect
61. #2755C22semidirect
67. #2734C22semidirect
68. #2734C22semidirect
69. #2734C22semidirect
75. #2719C22semidirect
76. #2719C22semidirect
77. #2719C22semidirect
78. #2719C22semidirect
79. #2713C22semidirect
80. #2713C22semidirect
81. #2713C22semidirect
82. #2713C22semidirect
83. #2713C22semidirect
100. #2666C22semidirect
101. #2666C22semidirect
102. #2666C22semidirect
103. #2666C22semidirect
104. #2660C22semidirect
107. #2642C22semidirect
110. #2590C22semidirect
112. #2588C22semidirect
113. #2588C22semidirect
114. #2588C22semidirect
115. #2586C22semidirect
125. #2570C22semidirect
128. #2568C22semidirect
129. #2567C22semidirect
130. #2565C22semidirect
131. #2565C22semidirect
137. #2550C22semidirect
138. #2550C22semidirect
139. #2550C22semidirect
142. #2533C22semidirect
144. #2524C22semidirect
145. #2524C22semidirect
149. #2520C22semidirect
150. #2520C22semidirect
151. #2520C22semidirect
156. #2508C22semidirect
157. #2508C22semidirect
158. #2506C22semidirect
159. #2506C22semidirect
186. #2462C22semidirect
187. #2446C22semidirect
195. #2381C22semidirect
196. #2381C22semidirect
197. #2369C22semidirect
198. #2369C22semidirect
201. #2336C22semidirect
212. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#586662
#547442
#544752
#516682
#509962
#509822
#477322
#472112
#469132
#468822
#468552
#468152
#400962
#396992
#383892
#373922
#367082
#356442
#354962
#354882
#353912