Finite Group Databasebeta

← #8096093

Subgroups — #8096093

Order 512.

4226 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53143C213yesmaximal, complemented
2#53139C213yesmaximal, complemented
3#53092C213yesmaximal, complemented
4#53038C213yesmaximal, complemented
5#53026C213yesmaximal, complemented
6#52968C213yesmaximal
7#52298C213yesmaximal
8#46346C213yesmaximal, complemented
9#46180C213yesmaximal
10#46117C213yesmaximal, complemented
11#46069C213yesmaximal, complemented
12#46045C213yesmaximal, complemented
13#46006C213yesmaximal, complemented
14#45719C213yesmaximal, complemented
15#45605C213yesmaximal
16#45517C213yesmaximal, complemented
17#36584C211yesmaximal, characteristic, complemented
18Q8×#126C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36482C211yesmaximal, characteristic
21#36475C211yesmaximal, characteristic, complemented
22#36466C211yesmaximal, characteristic, complemented
23#36448C211yesmaximal, characteristic, complemented
24#36446C211yesmaximal, characteristic
25#36435C211yesmaximal, characteristic, complemented
26#35937C211yesmaximal, characteristic, complemented
27#35883C211yesmaximal, characteristic, complemented
28#35883C211yesmaximal, characteristic, complemented
29#35845C211yesmaximal, characteristic, complemented
30#35723C211yesmaximal, characteristic
31#35711C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2864C2213yes—
39#2863C2213yes—
40#2863C2213yes—
41#2862C2213yes—
42#2859C2213yes—
43#2859C2213yes—
44#2857C2213yes—
45#2855C2213yes—
46#2851C2213yes—
47#2844C2216yes—
48#2839C2216yes—
49#2839C2216yes—
50#2838C2216yes—
51#2838C2216yes—
52#2836C2216yes—
53#2833C2216yes—
54#2833C2216yes—
55#2833C2216yes—
56#2831C2216yes—
57#2817C2216yes—
58#2805C2216yes—
59#2794C2216yes—
60#2793C2213yes—
61#2789C2216yes—
62#2787C2213yes—
63#2777C2216yes—
64#2776C2216yes—
65#2775C2216yes—
66#2774C2216yes—
67#2774C2213yes—
68#2774C2216yes—
69#2774C2216yes—
70#2773C2213yes—
71#2771C2216yes—
72#2770C2216yes—
73#2769C2216yes—
74#2766C2213yes—
75#2766C2216yes—
76#2766C2216yes—
77#2765C2216yes—
78#2762C2213yes—
79#2759C2213yes—
80#2758C2216yes—
81#2758C2216yes—
82#2738C2213yes—
83#2734C2216yes—
84#2725C2213yes—
85#2723C2211yescharacteristic
86#2720C2213yes—
87#2715C2213yes—
88#2713C2213yes—
89#2713C2216yes—
90#2707C2213yes—
91#2698C2213yes—
92#2689C2216yes—
93#2674C2216yes—
94#2674C2213yes—
95#2660C2213yes—
96#2645C2213yes—
97#2645C2213yes—
98#2628C2213yes—
99#2628C2213yes—
100#2625C2213yes—
101#2584C2213yes—
102#2584C2213yes—
103#2584C2213yes—
104#2582C2213yes—
105#2581C2213yes—
106#2581C2213yes—
107#2581C2213yes—
108#2571C2213yes—
109#2571C2213yes—
110#2570C2213yes—
111#2570C2213yes—
112#2568C2213yes—
113#2568C2213yes—
114#2567C2213yes—
115#2567C2213yes—
116#2565C2213yes—
117#2552C2213yes—
118#2551C2213yes—
119#2551C2213yes—
120#2551C2213yes—
121#2550C2213yes—
122#2550C2213yes—
123#2550C2213yes—
124#2550C2213yes—
125#2547C2213yes—
126#2546C2213yes—
127#2514C2213yes—
128#2514C2213yes—
129#2514C2213yes—
130#2514C2213yes—
131#2514C2213yes—
132#2514C2213yes—
133#2511C2213yes—
134#2511C2213yes—
135#2511C2213yes—
136#2511C2213yes—
137#2511C2213yes—
138#2511C2213yes—
139#2509C2213yes—
140#2509C2213yes—
141#2509C2213yes—
142#2509C2213yes—
143#2509C2213yes—
144#2508C2213yes—
145#2507C2213yes—
146#2506C2213yes—
147#2503C2213yes—
148#2499C2213yes—
149#2497C2213yes—
150#2497C2213yes—
151#2497C2213yes—
152#2497C2213yes—
153#2497C2213yes—
154#2496C2213yes—
155#2495C2213yes—
156#2495C2213yes—
157#2495C2213yes—
158#2494C2213yes—
159#2494C2213yes—
160#2494C2213yes—
161#2489C2213yes—
162#2489C2213yes—
163#2489C2213yes—
164#2489C2213yes—
165#2486C2213yes—
166#2485C2213yes—
167#2453C2213yes—
168#2453C2213yes—
169#2453C2213yes—
170#2451C2213yes—
171#2451C2213yes—
172#2451C2213yes—
173#2451C2213yes—
174#2451C2213yes—
175#2446C2213yes—
176#2446C2213yes—
177#2446C2213yes—
178#2446C2213yes—
179#2442C2213yes—
180#2441C2213yes—
181#2441C2213yes—
182#2440C2213yes—
183#2440C2213yes—
184#2440C2213yes—
185#2439C2213yes—
186#2439C2213yes—
187#2423C2213yes—
188#2421C2213yes—
189#2421C2213yes—
190#2421C2213yes—
191#2401C2213yes—
192#2401C2213yes—
193#2399C2213yes—
194#2396C2213yes—
195#2396C2213yes—
196#2395C2213yes—
197#2382C2216yes—
198#2381C2216yes—
199#2378C2216yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208#2351C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226C4×C4⋊Q8C2213yes—
227C4×#125C2213yes—
228C4×#125C2213yes—
229C4×#126C2213yes—
230C4×#126C2213yes—
231C4×#124C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×C22⋊Q8C2213yes—
234C4×#123C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—44no—
241#557—44no—
242#557—44no—
243D4×Q8—44no—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2316yes—
251C2×C4⋊Q8C2313yes—
252C2×#126C2311yescharacteristic
253C2×#126C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2313yes—
261C2×#123C2313yes—
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2316yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267#519—44no—
268C2×C4×Q8—44no—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×D4C2313yes—
290C2×#117C2313yes—
291C2×#117C2313yes—
292C22×C4⋊C4C2313yes—
293C22×C42C2313yes—
294#401C2316yes—
295#401C2316yes—
296#401C2313yes—
297#401C2316yes—
298#401C2313yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2313yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2316yes—
313#400C2316yes—
314#400C2313yes—
315#400C2316yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2313yes—
321#400C2316yes—
322#400C2316yes—
323#400C2313yes—
324#400C2313yes—
325#400C2316yes—
326#400C2313yes—
327#400C2316yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#399C2316yes—
332#399C2313yes—
333#399C2313yes—
334#399C2311yescharacteristic
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2313yes—
341#398C2316yes—
342#398C2316yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#397C2313yes—
356#397C2313yes—
357#397C2316yes—
358#397C2316yes—
359#397C2313yes—
360#397C2316yes—
361#397C2316yes—
362#397C2313yes—
363#397C2316yes—
364#397C2313yes—
365#397C2313yes—
366#397C2311yescharacteristic
367#397C2311yescharacteristic
368#397C2313yes—
369#396C2313yes—
370#396C2316yes—
371#396C2313yes—
372#396C2313yes—
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#395C2316yes—
377#395C2316yes—
378#395C2316yes—
379#395C2316yes—
380#395C2313yes—
381#395C2316yes—
382#395C2316yes—
383#395C2316yes—
384#395C2313yes—
385#395C2313yes—
386#395C2313yes—
387#395C2316yes—
388#395C2316yes—
389#395C2311yescharacteristic
390#395C2313yes—
391#394C2311yescharacteristic
392#394C2313yes—
393#393C2316yes—
394#393C2313yes—
395#393C2311yescharacteristic
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2316yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2316yes—
412#391C2316yes—
413#391C2316yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2316yes—
425#391C2313yes—
426#390C2311yescharacteristic
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2311yescharacteristic
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2316yes—
437#389C2316yes—
438#389C2316yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2316yes—
457#389C2316yes—
458#389C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2316yes—
470#389C2316yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#388C2311yescharacteristic
480#388C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2316yes—
488#388C2313yes—
489#388C2316yes—
490#388C2316yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2311yescharacteristic
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2313yes—
530#387C2316yes—
531#387C2316yes—
532#387C2316yes—
533#387C2316yes—
534#387C2313yes—
535#387C2313yes—
536#387C2313yes—
537#386C2311yescharacteristic
538#385C2313yes—
539#385C2316yes—
540#385C2313yes—
541#385C2313yes—
542#385C2313yes—
543#385C2311yescharacteristic
544#384C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#383C2313yes—
553#383C2313yes—
554#383C2316yes—
555#383C2316yes—
556#383C2316yes—
557#382C2311yescharacteristic
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2316yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2316yes—
571#382C2316yes—
572#381C2316yes—
573#381C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621#376C2313yes—
622C43C2313yes—
623C43C2313yes—
624C22×Q8—24no—
625C22×Q8—24no—
626C22×Q8—24no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2411yescharacteristic
633C22×Q8C2413yes—
634C22×Q8C2413yes—
635C22×Q8C2416yes—
636C22×Q8C2411yescharacteristic
637C22×D4C2411yescharacteristic
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2411yescharacteristic
642C4⋊Q8—46no—
643C4⋊Q8—46no—
644C4⋊Q8—46no—
645C4⋊Q8—46no—
646C4⋊Q8—46no—
647C4⋊Q8—46no—
648C4⋊Q8—46no—
649C4⋊Q8—412no—
650#126—24no—
651#126—46no—
652#125—212no—
653#125—46no—
654#125—46no—
655#125—46no—
656#125—46no—
657#125—46no—
658#124—46no—
659#123—46no—
660C22⋊Q8—24no—
661C22⋊Q8—46no—
662C22⋊Q8—412no—
663C22⋊Q8—46no—
664C22⋊Q8—46no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—46no—
679C4×Q8—46no—
680C4×Q8—46no—
681C4×Q8—46no—
682C4×Q8—46no—
683C4×Q8—46no—
684C4×Q8—46no—
685C4×D4—46no—
686#117—46no—
687#117—46no—
688C2×C4⋊C4—46no—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2416yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C22⋊C4C2411yescharacteristic
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2411yescharacteristic
762C2×C22⋊C4C2411yescharacteristic
763C2×C22⋊C4C2411yescharacteristic
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2411yescharacteristic
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C42—46no—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2411yescharacteristic
796C2×C42C2413yes—
797C2×C42C2411yescharacteristic
798C2×C42C2416yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2416yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807#95C2411yescharacteristic
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2416yes—
841#95C2416yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871#95C2416yes—
872#95C2416yes—
873#95C2416yes—
874#95C2416yes—
875#95C2416yes—
876#95C2416yes—
877#95C2416yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2416yes—
884C24C2511yescharacteristic
885C24C2511yescharacteristic
886C2×Q8—26no—
887C2×Q8—26no—
888C2×Q8—22no—
889C2×Q8—26no—
890C2×Q8—26no—
891C2×Q8—26no—
892C2×Q8—26no—
893C2×Q8—26no—
894C2×Q8—41no—
895C2×Q8—41no—
896C2×Q8—43no—
897C2×Q8—43no—
898C2×Q8—43no—
899C2×Q8—43no—
900C2×Q8—43no—
901C2×Q8—46no—
902C2×Q8—46no—
903C2×Q8—46no—
904C2×Q8—416no—
905C2×Q8—416no—
906C2×Q8H(5,𝔽2)14yes—
907C2×Q82−1+414yes—
908C2×Q82−1+414yes—
909C2×D4—22no—
910C2×D4—22no—
911C2×D4—41no—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—22no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—43no—
923C22×C4—43no—
924C22×C4C2513yes—
925C22×C4C2513yes—
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2513yes—
929C22×C4C2513yes—
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2513yes—
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2511yescharacteristic
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2513yes—
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2513yes—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—22no—
979C4⋊C4—46no—
980C4⋊C4—43no—
981C4⋊C4—41no—
982C4⋊C4—46no—
983C4⋊C4—46no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—46no—
1001C4⋊C4—43no—
1002C4⋊C4—46no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—46no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—46no—
1018C4⋊C4—46no—
1019C4⋊C4—43no—
1020C4⋊C42−1+414yes—
1021C22⋊C4—22no—
1022C22⋊C4—26no—
1023C22⋊C4—26no—
1024C22⋊C4—26no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—43no—
1034C22⋊C4—43no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—43no—
1043C22⋊C4—43no—
1044C22⋊C4—43no—
1045C42—26no—
1046C42—26no—
1047C42—26no—
1048C42—26no—
1049C42—26no—
1050C42—26no—
1051C42—26no—
1052C42—26no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—22no—
1060C42—22no—
1061C42—43no—
1062C42—43no—
1063C42—43no—
1064C42—43no—
1065C42—46no—
1066C42—43no—
1067C42—43no—
1068C42—43no—
1069C42—46no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23#58512yes—
1084C23C2611yescharacteristic
1085Q8—44no—
1086Q8—412no—
1087Q8—412no—
1088Q8—86no—
1089Q8—86no—
1090Q8—166no—
1091Q8#563116yes—
1092D4—44no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—44no—
1174C2×C4—412no—
1175C2×C4—412no—
1176C2×C4—86no—
1177C2×C4C2×H(5,𝔽2)16yes—
1178C2×C4C2×2−1+412yes—
1179C2×C4C2×2−1+412yes—
1180C2×C4C2×2−1+412yes—
1181C2×C4C2×2−1+416yes—
1182C2×C4C2×2−1+416yes—
1183C2×C4#58512yes—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22C22×H(5,𝔽2)11yescharacteristic
1199C22C22×2−1+411yescharacteristic
1200C22C22×2−1+411yescharacteristic
1201C22C22×2−1+411yescharacteristic
1202C22C2×#58511yescharacteristic
1203C22C2×#58511yescharacteristic
1204C222−1+611yescharacteristic
1205C4—22no—
1206C4—22no—
1207C4—22no—
1208C4—22no—
1209C4—43no—
1210C4—43no—
1211C4—43no—
1212C4—41no—
1213C4—43no—
1214C4—43no—
1215C4—43no—
1216C4—41no—
1217C4—41no—
1218C4—43no—
1219C4—41no—
1220C4—43no—
1221C4—43no—
1222C4—41no—
1223C4—41no—
1224C4—41no—
1225C4—43no—
1226C4—43no—
1227C4—41no—
1228C4—43no—
1229C4—43no—
1230C4—41no—
1231C4—43no—
1232C4—43no—
1233C4C2×#563112yes—
1234C2—42no—
1235C2—81no—
1236C2C22×#56311yescharacteristic
1237C2#6291311yescharacteristic
1238C2#6294911yescharacteristic
1239C2#6295311yescharacteristic
1240C2#6302011yescharacteristic
1241C2#6303211yescharacteristic
1242C2#6303811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53143C2semidirect
2. #53139C2semidirect
3. #53092C2semidirect
4. #53038C2semidirect
5. #53026C2semidirect
8. #46346C2semidirect
10. #46117C2semidirect
11. #46069C2semidirect
12. #46045C2semidirect
13. #46006C2semidirect
14. #45719C2semidirect
16. #45517C2semidirect
17. #36584C2semidirect
18. Q8×#126C2semidirect
19. Q8×C22⋊Q8C2semidirect
21. #36475C2semidirect
22. #36466C2semidirect
23. #36448C2semidirect
25. #36435C2semidirect
26. #35937C2semidirect
27. #35883C2semidirect
28. #35883C2semidirect
29. #35845C2semidirect
31. #35711C2semidirect

Maximal subgroups

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

subgroupindex
#531432
#531392
#530922
#530382
#530262
#529682
#522982
#463462
#461802
#461172
#460692
#460452
#460062
#457192
#456052
#455172
#365842
Q8×#1262
Q8×C22⋊Q82
#364822
#364752
#364662
#364482
#364462
#364352
#359372
#358832
#358452
#357232
#357112