Finite Group Databasebeta

← #8096323

Subgroups — #8096323

Order 512.

4288 conjugacy classes of subgroups.

The subgroup lattice has 1253 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53124C213yesmaximal, complemented
2#53091C213yesmaximal, complemented
3#53033C213yesmaximal, complemented
4#53012C213yesmaximal, complemented
5#53009C213yesmaximal
6#53002C213yesmaximal, complemented
7#52298C213yesmaximal
8#46344C213yesmaximal, complemented
9#46174C213yesmaximal
10#46045C213yesmaximal, complemented
11#46011C213yesmaximal, complemented
12#46006C213yesmaximal, complemented
13#46001C213yesmaximal, complemented
14#45627C213yesmaximal
15#45618C213yesmaximal, complemented
16#45611C213yesmaximal, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18Q8×#124C211yesmaximal, characteristic
19Q8×#123C211yesmaximal, characteristic
20Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
21#36475C211yesmaximal, characteristic, complemented
22#36448C211yesmaximal, characteristic, complemented
23#36448C211yesmaximal, characteristic, complemented
24#36447C211yesmaximal, characteristic, complemented
25#36435C211yesmaximal, characteristic, complemented
26#35937C211yesmaximal, characteristic, complemented
27#35920C211yesmaximal, characteristic, complemented
28#35883C211yesmaximal, characteristic, complemented
29#35845C211yesmaximal, characteristic, complemented
30#35723C211yesmaximal, characteristic
31#35711C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2868C2213yes—
39#2864C2213yes—
40#2863C2213yes—
41#2863C2213yes—
42#2862C2213yes—
43#2859C2213yes—
44#2857C2213yes—
45#2855C2213yes—
46#2851C2213yes—
47#2844C2216yes—
48#2843C2216yes—
49#2839C2216yes—
50#2838C2216yes—
51#2838C2216yes—
52#2835C2216yes—
53#2833C2216yes—
54#2833C2216yes—
55#2833C2216yes—
56#2821C2216yes—
57#2821C2216yes—
58#2805C2216yes—
59#2794C2216yes—
60#2793C2213yes—
61#2791C2216yes—
62#2789C2216yes—
63#2787C2213yes—
64#2776C2216yes—
65#2774C2213yes—
66#2774C2216yes—
67#2773C2213yes—
68#2769C2216yes—
69#2766C2213yes—
70#2762C2216yes—
71#2762C2213yes—
72#2762C2216yes—
73#2759C2213yes—
74#2758C2216yes—
75#2745C2216yes—
76#2738C2213yes—
77#2734C2216yes—
78#2729C2216yes—
79#2725C2213yes—
80#2723C2213yes—
81#2723C2216yes—
82#2721C2216yes—
83#2720C2213yes—
84#2716C2216yes—
85#2715C2213yes—
86#2713C2213yes—
87#2713C2216yes—
88#2713C2216yes—
89#2713C2216yes—
90#2707C2213yes—
91#2698C2213yes—
92#2690C2216yes—
93#2677C2216yes—
94#2674C2211yescharacteristic
95#2660C2213yes—
96#2645C2213yes—
97#2645C2213yes—
98#2628C2213yes—
99#2628C2213yes—
100#2625C2213yes—
101#2584C2213yes—
102#2582C2213yes—
103#2581C2213yes—
104#2581C2213yes—
105#2581C2213yes—
106#2571C2213yes—
107#2570C2213yes—
108#2570C2213yes—
109#2568C2213yes—
110#2568C2213yes—
111#2567C2213yes—
112#2567C2213yes—
113#2567C2213yes—
114#2567C2213yes—
115#2565C2213yes—
116#2563C2213yes—
117#2552C2213yes—
118#2551C2213yes—
119#2551C2213yes—
120#2551C2213yes—
121#2551C2213yes—
122#2551C2213yes—
123#2551C2213yes—
124#2550C2213yes—
125#2550C2213yes—
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#2508C2213yes—
141#2508C2213yes—
142#2508C2213yes—
143#2507C2213yes—
144#2506C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2502C2213yes—
148#2499C2213yes—
149#2497C2213yes—
150#2496C2213yes—
151#2496C2213yes—
152#2496C2213yes—
153#2496C2213yes—
154#2496C2213yes—
155#2495C2213yes—
156#2495C2213yes—
157#2495C2213yes—
158#2494C2213yes—
159#2494C2213yes—
160#2494C2213yes—
161#2492C2213yes—
162#2492C2213yes—
163#2492C2213yes—
164#2492C2213yes—
165#2487C2213yes—
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#2423C2213yes—
189#2423C2213yes—
190#2421C2213yes—
191#2401C2213yes—
192#2401C2213yes—
193#2399C2213yes—
194#2396C2213yes—
195#2396C2213yes—
196#2395C2213yes—
197#2383C2216yes—
198#2382C2216yes—
199#2381C2216yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
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—
241Q82—44no—
242#557—44no—
243D4×Q8—44no—
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2316yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2316yes—
255C2×C4⋊Q8C2316yes—
256C2×#126C2313yes—
257C2×#126C2313yes—
258C2×#126C2316yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#125C2313yes—
263C2×#125C2316yes—
264C2×#124C2311yescharacteristic
265C2×#123C2311yescharacteristic
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2316yes—
271#519—44no—
272C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×D4C2313yes—
294C2×#117C2313yes—
295C2×#117C2313yes—
296C22×C4⋊C4C2313yes—
297C22×C42C2313yes—
298#401C2316yes—
299#401C2313yes—
300#401C2313yes—
301#401C2316yes—
302#401C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2316yes—
313#400C2313yes—
314#400C2313yes—
315#400C2316yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2316yes—
325#400C2313yes—
326#400C2313yes—
327#400C2316yes—
328#400C2313yes—
329#400C2313yes—
330#400C2313yes—
331#400C2313yes—
332#399C2316yes—
333#399C2313yes—
334#399C2316yes—
335#399C2313yes—
336#399C2311yescharacteristic
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2316yes—
344#398C2313yes—
345#398C2313yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2313yes—
351#398C2316yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2316yes—
362#397C2313yes—
363#397C2313yes—
364#397C2316yes—
365#397C2316yes—
366#397C2313yes—
367#397C2313yes—
368#397C2311yescharacteristic
369#397C2313yes—
370#396C2313yes—
371#396C2313yes—
372#396C2313yes—
373#396C2313yes—
374#396C2311yescharacteristic
375#396C2313yes—
376#395C2316yes—
377#395C2316yes—
378#395C2316yes—
379#395C2316yes—
380#395C2313yes—
381#395C2316yes—
382#395C2316yes—
383#395C2316yes—
384#395C2316yes—
385#395C2316yes—
386#395C2316yes—
387#395C2316yes—
388#395C2313yes—
389#395C2313yes—
390#395C2313yes—
391#395C2313yes—
392#395C2311yescharacteristic
393#394C2311yescharacteristic
394#394C2313yes—
395#393C2316yes—
396#393C2316yes—
397#393C2313yes—
398#393C2316yes—
399#393C2311yescharacteristic
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2316yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2316yes—
417#391C2316yes—
418#391C2316yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2313yes—
425#391C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2316yes—
429#391C2316yes—
430#391C2313yes—
431#390C2313yes—
432#389C2311yescharacteristic
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2316yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2316yes—
451#389C2316yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2316yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2316yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#388C2311yescharacteristic
481#388C2311yescharacteristic
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
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#387C2313yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
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#386C2313yes—
538#385C2313yes—
539#385C2316yes—
540#385C2316yes—
541#385C2313yes—
542#385C2313yes—
543#385C2311yescharacteristic
544#385C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2316yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#383C2313yes—
557#383C2313yes—
558#383C2316yes—
559#383C2316yes—
560#383C2316yes—
561#382C2313yes—
562#382C2313yes—
563#382C2316yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2316yes—
572#382C2313yes—
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×Q8C2411yescharacteristic
634C22×Q8C2413yes—
635C22×Q8C2416yes—
636C22×Q8C2416yes—
637C22×Q8C2411yescharacteristic
638C22×D4C2411yescharacteristic
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2411yescharacteristic
642C23×C4C2413yes—
643C4⋊Q8—24no—
644C4⋊Q8—412no—
645C4⋊Q8—46no—
646C4⋊Q8—46no—
647C4⋊Q8—46no—
648C4⋊Q8—46no—
649C4⋊Q8—46no—
650C4⋊Q8—46no—
651C4⋊Q8—46no—
652C4⋊Q8—46no—
653C4⋊Q8—86no—
654C4⋊Q8—86no—
655#126—212no—
656#126—46no—
657#126—86no—
658#125—212no—
659#125—46no—
660#125—46no—
661#125—46no—
662#125—86no—
663#124—24no—
664#123—24no—
665C22⋊Q8—24no—
666C22⋊Q8—46no—
667C22⋊Q8—46no—
668C22⋊Q8—46no—
669C22⋊Q8—86no—
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—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—46no—
684C4×Q8—46no—
685C4×Q8—46no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×D4—46no—
691#117—46no—
692#117—46no—
693C2×C4⋊C4—46no—
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⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C22⋊C4C2411yescharacteristic
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2411yescharacteristic
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2411yescharacteristic
787C2×C42—46no—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2411yescharacteristic
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2411yescharacteristic
806C2×C42C2416yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2416yes—
812C2×C42C2413yes—
813#95C2411yescharacteristic
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#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2411yescharacteristic
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2416yes—
845#95C2416yes—
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#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
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—
884#95C2416yes—
885#95C2416yes—
886#95C2416yes—
887#95C2416yes—
888C24C2511yescharacteristic
889C24C2511yescharacteristic
890C2×Q8—26no—
891C2×Q8—26no—
892C2×Q8—22no—
893C2×Q8—22no—
894C2×Q8—22no—
895C2×Q8—22no—
896C2×Q8—26no—
897C2×Q8—26no—
898C2×Q8—26no—
899C2×Q8—26no—
900C2×Q8—41no—
901C2×Q8—41no—
902C2×Q8—43no—
903C2×Q8—43no—
904C2×Q8—43no—
905C2×Q8—46no—
906C2×Q8—46no—
907C2×Q8—46no—
908C2×Q8—46no—
909C2×Q8—46no—
910C2×Q8—46no—
911C2×Q8—416no—
912C2×Q8—416no—
913C2×Q8H(5,𝔽2)14yes—
914C2×Q82−1+414yes—
915C2×Q82−1+414yes—
916C2×D4—22no—
917C2×D4—22no—
918C2×D4—41no—
919C22×C4—22no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—22no—
923C22×C4—26no—
924C22×C4—26no—
925C22×C4—26no—
926C22×C4—26no—
927C22×C4—41no—
928C22×C4—43no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4C2513yes—
932C22×C4C2513yes—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2513yes—
936C22×C4C2513yes—
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2513yes—
946C22×C4C2513yes—
947C22×C4C2511yescharacteristic
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2511yescharacteristic
959C22×C4C2513yes—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—22no—
991C4⋊C4—26no—
992C4⋊C4—46no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—41no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—46no—
1007C4⋊C4—46no—
1008C4⋊C4—46no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—46no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—46no—
1017C4⋊C4—46no—
1018C4⋊C4—46no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—46no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C42−1+414yes—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—26no—
1032C22⋊C4—26no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—22no—
1040C22⋊C4—41no—
1041C22⋊C4—43no—
1042C22⋊C4—43no—
1043C22⋊C4—43no—
1044C22⋊C4—43no—
1045C22⋊C4—43no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C42−1+414yes—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—22no—
1067C42—26no—
1068C42—26no—
1069C42—22no—
1070C42—26no—
1071C42—43no—
1072C42—43no—
1073C42—46no—
1074C42—43no—
1075C42—43no—
1076C42—46no—
1077C42—43no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23C2×2−1+412yes—
1092C23C2611yescharacteristic
1093Q8—44no—
1094Q8—44no—
1095Q8—412no—
1096Q8—412no—
1097Q8—86no—
1098Q8—166no—
1099Q8—166no—
1100Q8#563116yes—
1101D4—44no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—23no—
1144C2×C4—21no—
1145C2×C4—23no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—21no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—44no—
1181C2×C4—412no—
1182C2×C4—412no—
1183C2×C4—86no—
1184C2×C4C2×H(5,𝔽2)16yes—
1185C2×C4C2×2−1+412yes—
1186C2×C4C2×2−1+412yes—
1187C2×C4C2×2−1+412yes—
1188C2×C4C2×2−1+412yes—
1189C2×C4C2×2−1+412yes—
1190C2×C4C2×2−1+416yes—
1191C2×C4C2×2−1+416yes—
1192C2×C4#58512yes—
1193C22—22no—
1194C22—22no—
1195C22—22no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22C22×H(5,𝔽2)11yescharacteristic
1208C22C22×2−1+411yescharacteristic
1209C22C22×2−1+411yescharacteristic
1210C22C22×2−1+411yescharacteristic
1211C22C22×2−1+411yescharacteristic
1212C22C2×#58511yescharacteristic
1213C22H(7,𝔽2)11yescharacteristic
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—43no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—41no—
1225C4—43no—
1226C4—41no—
1227C4—43no—
1228C4—43no—
1229C4—43no—
1230C4—41no—
1231C4—43no—
1232C4—43no—
1233C4—43no—
1234C4—43no—
1235C4—43no—
1236C4—43no—
1237C4—41no—
1238C4—43no—
1239C4—43no—
1240C4—43no—
1241C4—43no—
1242C4C2×#563112yes—
1243C2—42no—
1244C2—81no—
1245C2C22×#56311yescharacteristic
1246C2#6292311yescharacteristic
1247C2#6294311yescharacteristic
1248C2#6294311yescharacteristic
1249C2#6301611yescharacteristic
1250C2#6303211yescharacteristic
1251C2#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. #53124C2semidirect
2. #53091C2semidirect
3. #53033C2semidirect
4. #53012C2semidirect
6. #53002C2semidirect
8. #46344C2semidirect
10. #46045C2semidirect
11. #46011C2semidirect
12. #46006C2semidirect
13. #46001C2semidirect
15. #45618C2semidirect
16. #45611C2semidirect
17. Q8×C4⋊Q8C2semidirect
20. Q8×C22⋊Q8C2semidirect
21. #36475C2semidirect
22. #36448C2semidirect
23. #36448C2semidirect
24. #36447C2semidirect
25. #36435C2semidirect
26. #35937C2semidirect
27. #35920C2semidirect
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
#531242
#530912
#530332
#530122
#530092
#530022
#522982
#463442
#461742
#460452
#460112
#460062
#460012
#456272
#456182
#456112
Q8×C4⋊Q82
Q8×#1242
Q8×#1232
Q8×C22⋊Q82
#364752
#364482
#364472
#364352
#359372
#359202
#358832
#358452
#357232
#357112