Finite Group Databasebeta

← #8096398

Subgroups — #8096398

Order 512.

4352 conjugacy classes of subgroups.

The subgroup lattice has 1259 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53119C213yesmaximal, complemented
2#53118C213yesmaximal, complemented
3#53092C213yesmaximal, complemented
4#53035C213yesmaximal, complemented
5#53001C213yesmaximal, complemented
6#52994C213yesmaximal, complemented
7#52302C213yesmaximal, complemented
8#46341C213yesmaximal, complemented
9#46117C213yesmaximal, complemented
10#46068C213yesmaximal, complemented
11#45674C213yesmaximal, complemented
12#45654C213yesmaximal, complemented
13#45640C213yesmaximal, complemented
14#45627C213yesmaximal, complemented
15#45517C213yesmaximal, complemented
16#45502C213yesmaximal, complemented
17#36578C211yesmaximal, characteristic
18Q8×#126C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36466C211yesmaximal, characteristic, complemented
21#36458C211yesmaximal, characteristic, complemented
22#36456C211yesmaximal, characteristic, complemented
23#36445C211yesmaximal, characteristic, complemented
24#36435C211yesmaximal, characteristic, complemented
25#36432C211yesmaximal, characteristic
26#35971C211yesmaximal, characteristic, complemented
27#35937C211yesmaximal, characteristic, complemented
28#35898C211yesmaximal, characteristic, complemented
29#35883C211yesmaximal, characteristic, complemented
30#35868C211yesmaximal, characteristic, complemented
31#35854C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2863C2213yes—
39#2860C2213yes—
40#2859C2213yes—
41#2857C2213yes—
42#2857C2213yes—
43#2857C2213yes—
44#2855C2213yes—
45#2854C2213yes—
46#2851C2213yes—
47#2841C2216yes—
48#2839C2216yes—
49#2838C2216yes—
50#2838C2216yes—
51#2838C2216yes—
52#2836C2216yes—
53#2836C2216yes—
54#2831C2216yes—
55#2827C2216yes—
56#2821C2216yes—
57#2817C2216yes—
58#2799C2213yes—
59#2794C2213yes—
60#2793C2216yes—
61#2789C2216yes—
62#2787C2216yes—
63#2777C2216yes—
64#2776C2213yes—
65#2776C2213yes—
66#2775C2216yes—
67#2774C2216yes—
68#2774C2216yes—
69#2770C2213yes—
70#2770C2216yes—
71#2770C2213yes—
72#2758C2216yes—
73#2745C2213yes—
74#2745C2213yes—
75#2729C2216yes—
76#2729C2213yes—
77#2729C2213yes—
78#2728C2213yes—
79#2725C2216yes—
80#2723C2216yes—
81#2722C2216yes—
82#2716C2216yes—
83#2707C2216yes—
84#2702C2216yes—
85#2698C2216yes—
86#2695C2213yes—
87#2695C2213yes—
88#2690C2216yes—
89#2689C2213yes—
90#2689C2211yescharacteristic
91#2689C2216yes—
92#2683C2216yes—
93#2680C2213yes—
94#2677C2216yes—
95#2660C2213yes—
96#2647C2213yes—
97#2647C2213yes—
98#2645C2213yes—
99#2644C2213yes—
100#2640C2213yes—
101#2592C2213yes—
102#2584C2213yes—
103#2584C2213yes—
104#2584C2213yes—
105#2582C2213yes—
106#2581C2213yes—
107#2571C2213yes—
108#2570C2213yes—
109#2570C2213yes—
110#2567C2213yes—
111#2565C2213yes—
112#2563C2213yes—
113#2563C2213yes—
114#2552C2213yes—
115#2552C2213yes—
116#2551C2213yes—
117#2551C2213yes—
118#2551C2213yes—
119#2550C2213yes—
120#2550C2213yes—
121#2550C2213yes—
122#2550C2213yes—
123#2546C2213yes—
124#2542C2213yes—
125#2538C2213yes—
126#2538C2213yes—
127#2514C2213yes—
128#2514C2213yes—
129#2513C2213yes—
130#2513C2213yes—
131#2512C2213yes—
132#2512C2213yes—
133#2512C2213yes—
134#2512C2213yes—
135#2511C2213yes—
136#2511C2213yes—
137#2511C2213yes—
138#2511C2213yes—
139#2509C2213yes—
140#2509C2213yes—
141#2508C2213yes—
142#2508C2213yes—
143#2507C2213yes—
144#2507C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2504C2213yes—
148#2499C2213yes—
149#2497C2213yes—
150#2497C2213yes—
151#2497C2213yes—
152#2497C2213yes—
153#2497C2213yes—
154#2497C2213yes—
155#2496C2213yes—
156#2496C2213yes—
157#2495C2213yes—
158#2495C2213yes—
159#2494C2213yes—
160#2494C2213yes—
161#2490C2213yes—
162#2490C2213yes—
163#2489C2213yes—
164#2489C2213yes—
165#2487C2213yes—
166#2485C2213yes—
167#2454C2213yes—
168#2454C2213yes—
169#2453C2213yes—
170#2452C2213yes—
171#2452C2213yes—
172#2451C2213yes—
173#2451C2213yes—
174#2451C2213yes—
175#2448C2213yes—
176#2448C2213yes—
177#2447C2213yes—
178#2447C2213yes—
179#2442C2213yes—
180#2441C2213yes—
181#2441C2213yes—
182#2440C2213yes—
183#2440C2213yes—
184#2440C2213yes—
185#2439C2213yes—
186#2439C2213yes—
187#2422C2213yes—
188#2421C2213yes—
189#2421C2213yes—
190#2420C2213yes—
191#2402C2213yes—
192#2402C2213yes—
193#2401C2213yes—
194#2401C2213yes—
195#2399C2213yes—
196#2398C2213yes—
197#2382C2216yes—
198#2378C2216yes—
199#2376C2216yes—
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
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226C4×C4⋊Q8C2213yes—
227C4×#126C2213yes—
228C4×#126C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×C22⋊Q8C2213yes—
231C4×C22⋊Q8C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×#123C2213yes—
234C4×#123C2213yes—
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—44no—
241#557—44no—
242#557—44no—
243#548—44no—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2316yes—
251C2×#126C2311yescharacteristic
252C2×#126C2313yes—
253C2×#126C2316yes—
254C2×#126C2316yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2316yes—
260C2×#124C2313yes—
261C2×#123C2313yes—
262C2×#123C2313yes—
263C2×C22⋊Q8C2311yescharacteristic
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2316yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2316yes—
270C2×C22⋊Q8C2316yes—
271C2×#121C2313yes—
272C4×#41—44no—
273C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×#117C2313yes—
296C22×C4⋊C4C2313yes—
297C22×C42C2313yes—
298C22×C42C2313yes—
299#401C2316yes—
300#401C2313yes—
301#401C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2316yes—
305#400C2316yes—
306#400C2313yes—
307#400C2316yes—
308#400C2313yes—
309#400C2313yes—
310#400C2316yes—
311#400C2313yes—
312#400C2316yes—
313#400C2313yes—
314#400C2316yes—
315#400C2316yes—
316#400C2313yes—
317#400C2316yes—
318#400C2313yes—
319#400C2313yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2313yes—
324#400C2311yescharacteristic
325#400C2313yes—
326#400C2313yes—
327#400C2311yescharacteristic
328#400C2313yes—
329#399C2316yes—
330#399C2316yes—
331#399C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2313yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2311yescharacteristic
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2313yes—
360#397C2316yes—
361#397C2313yes—
362#397C2316yes—
363#397C2316yes—
364#397C2313yes—
365#397C2313yes—
366#397C2316yes—
367#397C2316yes—
368#397C2316yes—
369#397C2311yescharacteristic
370#397C2311yescharacteristic
371#397C2313yes—
372#397C2313yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2316yes—
377#396C2316yes—
378#396C2313yes—
379#396C2316yes—
380#396C2316yes—
381#396C2313yes—
382#395C2316yes—
383#395C2316yes—
384#395C2316yes—
385#395C2316yes—
386#395C2316yes—
387#395C2316yes—
388#395C2316yes—
389#395C2313yes—
390#395C2313yes—
391#395C2313yes—
392#395C2311yescharacteristic
393#394C2313yes—
394#394C2316yes—
395#394C2313yes—
396#393C2313yes—
397#393C2316yes—
398#393C2316yes—
399#393C2316yes—
400#393C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2316yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2316yes—
417#391C2316yes—
418#391C2313yes—
419#391C2311yescharacteristic
420#390C2313yes—
421#390C2313yes—
422#390C2316yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#389C2311yescharacteristic
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2316yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2316yes—
450#389C2316yes—
451#389C2316yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2316yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2316yes—
478#389C2313yes—
479#389C2311yescharacteristic
480#388C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2313yes—
490#388C2316yes—
491#388C2316yes—
492#388C2316yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2311yescharacteristic
497#388C2313yes—
498#388C2313yes—
499#387C2311yescharacteristic
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2316yes—
514#387C2316yes—
515#387C2313yes—
516#387C2316yes—
517#387C2313yes—
518#387C2316yes—
519#387C2316yes—
520#387C2313yes—
521#387C2313yes—
522#387C2316yes—
523#387C2316yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2313yes—
528#387C2313yes—
529#387C2313yes—
530#386C2316yes—
531#386C2313yes—
532#386C2313yes—
533#385C2313yes—
534#385C2316yes—
535#385C2313yes—
536#385C2316yes—
537#385C2313yes—
538#385C2313yes—
539#385C2313yes—
540#385C2313yes—
541#385C2311yescharacteristic
542#385C2313yes—
543#385C2313yes—
544#385C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#383C2313yes—
556#383C2313yes—
557#383C2316yes—
558#382C2313yes—
559#382C2313yes—
560#382C2316yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2316yes—
567#381C2316yes—
568#381C2313yes—
569#381C2311yescharacteristic
570#380C2313yes—
571#380C2316yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2316yes—
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—
622#376C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2413yes—
631C22×Q8C2411yescharacteristic
632C22×Q8C2413yes—
633C22×Q8C2413yes—
634C22×Q8C2416yes—
635C22×Q8C2411yescharacteristic
636C22×D4C2413yes—
637C22×D4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2411yescharacteristic
641C23×C4C2413yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C4⋊Q8—46no—
645C4⋊Q8—46no—
646C4⋊Q8—46no—
647C4⋊Q8—46no—
648C4⋊Q8—46no—
649C4⋊Q8—46no—
650C4⋊Q8—86no—
651#126—24no—
652#126—46no—
653#126—86no—
654#126—86no—
655#125—46no—
656#125—46no—
657#125—46no—
658#125—46no—
659#125—412no—
660#124—46no—
661#123—212no—
662#123—46no—
663C22⋊Q8—24no—
664C22⋊Q8—46no—
665C22⋊Q8—46no—
666C22⋊Q8—412no—
667C22⋊Q8—46no—
668C22⋊Q8—46no—
669C22⋊Q8—86no—
670C22⋊Q8—86no—
671#121—46no—
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—24no—
684C4×Q8—24no—
685C4×Q8—46no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×D4—46no—
691C4×D4—46no—
692C4×D4—46no—
693#117—46no—
694C2×C4⋊C4—46no—
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⋊C4C2411yescharacteristic
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C22⋊C4C2411yescharacteristic
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2416yes—
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2416yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2416yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2416yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2416yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2411yescharacteristic
791C2×C42—46no—
792C2×C42—46no—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2411yescharacteristic
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2416yes—
811C2×C42C2413yes—
812C2×C42C2416yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2411yescharacteristic
851#95C2416yes—
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#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2416yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2416yes—
884#95C2416yes—
885#95C2416yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889C24C2513yes—
890C24C2511yescharacteristic
891#41—416no—
892C2×Q8—26no—
893C2×Q8—22no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—22no—
897C2×Q8—26no—
898C2×Q8—41no—
899C2×Q8—43no—
900C2×Q8—43no—
901C2×Q8—43no—
902C2×Q8—43no—
903C2×Q8—43no—
904C2×Q8—46no—
905C2×Q8—46no—
906C2×Q8—46no—
907C2×Q8—416no—
908C2×Q8H(5,𝔽2)14yes—
909C2×Q82−1+414yes—
910C2×Q82−1+414yes—
911C2×D4—26no—
912C2×D4—26no—
913C2×D4—26no—
914C2×D4—26no—
915C2×D4—43no—
916C2×D4—43no—
917C22×C4—22no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—26no—
924C22×C4—22no—
925C22×C4—26no—
926C22×C4—26no—
927C22×C4—41no—
928C22×C4—43no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4—43no—
932C22×C4—43no—
933C22×C4—43no—
934C22×C4—43no—
935C22×C4C2511yescharacteristic
936C22×C4C2513yes—
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2513yes—
942C22×C4C2511yescharacteristic
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2511yescharacteristic
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C22×C4C2513yes—
956C22×C4C2513yes—
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2513yes—
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—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—46no—
994C4⋊C4—43no—
995C4⋊C4—41no—
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—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—46no—
1013C4⋊C4—46no—
1014C4⋊C4—46no—
1015C4⋊C4—46no—
1016C4⋊C4—43no—
1017C4⋊C4—46no—
1018C4⋊C4—46no—
1019C4⋊C4—46no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—46no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C22⋊C4—22no—
1032C22⋊C4—26no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—26no—
1036C22⋊C4—22no—
1037C22⋊C4—26no—
1038C22⋊C4—46no—
1039C22⋊C4—41no—
1040C22⋊C4—43no—
1041C22⋊C4—46no—
1042C22⋊C4—43no—
1043C22⋊C4—46no—
1044C22⋊C4—43no—
1045C22⋊C4—43no—
1046C22⋊C4—46no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C22⋊C4—46no—
1051C22⋊C4—46no—
1052C22⋊C4—43no—
1053C22⋊C4—43no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—43no—
1057C22⋊C4—46no—
1058C22⋊C4—43no—
1059C22⋊C42−1+414yes—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42—22no—
1074C42—41no—
1075C42—43no—
1076C42—43no—
1077C42—43no—
1078C42—46no—
1079C42—43no—
1080C42—43no—
1081C42—46no—
1082C42—43no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23—23no—
1096C23C2×2−1+412yes—
1097C23C2611yescharacteristic
1098Q8—44no—
1099Q8—412no—
1100Q8—86no—
1101Q8—86no—
1102Q8—166no—
1103Q8#563116yes—
1104D4—412no—
1105D4—86no—
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—21no—
1126C2×C4—23no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
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—21no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
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—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—21no—
1186C2×C4—44no—
1187C2×C4—412no—
1188C2×C4—412no—
1189C2×C4—86no—
1190C2×C4—86no—
1191C2×C4—86no—
1192C2×C4C2×H(5,𝔽2)16yes—
1193C2×C4C2×2−1+412yes—
1194C2×C4C2×2−1+412yes—
1195C2×C4C2×2−1+416yes—
1196C2×C4C2×2−1+416yes—
1197C2×C4#58512yes—
1198C2×C4#58512yes—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—43no—
1207C22—43no—
1208C22—43no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22—43no—
1213C22C22×H(5,𝔽2)11yescharacteristic
1214C22C22×2−1+411yescharacteristic
1215C22C22×2−1+411yescharacteristic
1216C22C22×2−1+411yescharacteristic
1217C22C2×#58511yescharacteristic
1218C22C2×#58511yescharacteristic
1219C22H(7,𝔽2)11yescharacteristic
1220C4—22no—
1221C4—22no—
1222C4—22no—
1223C4—22no—
1224C4—41no—
1225C4—41no—
1226C4—43no—
1227C4—43no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—43no—
1233C4—43no—
1234C4—43no—
1235C4—43no—
1236C4—43no—
1237C4—43no—
1238C4—41no—
1239C4—43no—
1240C4—41no—
1241C4—41no—
1242C4—43no—
1243C4—41no—
1244C4—43no—
1245C4—43no—
1246C4—43no—
1247C4—43no—
1248C4C2×#563112yes—
1249C2—42no—
1250C2—83no—
1251C2C22×#56311yescharacteristic
1252C2#6289911yescharacteristic
1253C2#6294311yescharacteristic
1254C2#6295211yescharacteristic
1255C2#6301511yescharacteristic
1256C2#6303211yescharacteristic
1257C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53119C2semidirect
2. #53118C2semidirect
3. #53092C2semidirect
4. #53035C2semidirect
5. #53001C2semidirect
6. #52994C2semidirect
7. #52302C2semidirect
8. #46341C2semidirect
9. #46117C2semidirect
10. #46068C2semidirect
11. #45674C2semidirect
12. #45654C2semidirect
13. #45640C2semidirect
14. #45627C2semidirect
15. #45517C2semidirect
16. #45502C2semidirect
18. Q8×#126C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36466C2semidirect
21. #36458C2semidirect
22. #36456C2semidirect
23. #36445C2semidirect
24. #36435C2semidirect
26. #35971C2semidirect
27. #35937C2semidirect
28. #35898C2semidirect
29. #35883C2semidirect
30. #35868C2semidirect

Maximal subgroups

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

subgroupindex
#531192
#531182
#530922
#530352
#530012
#529942
#523022
#463412
#461172
#460682
#456742
#456542
#456402
#456272
#455172
#455022
#365782
Q8×#1262
Q8×C22⋊Q82
#364662
#364582
#364562
#364452
#364352
#364322
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