Finite Group Databasebeta

← #7692852

Subgroups — #7692852

Order 512.

4710 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59751C213yesmaximal, complemented
2#59749C213yesmaximal, complemented
3#59501C213yesmaximal, complemented
4#59292C213yesmaximal, complemented
5#59259C213yesmaximal, complemented
6#45317C213yesmaximal, complemented
7#44990C213yesmaximal, complemented
8#44967C213yesmaximal, complemented
9#44905C213yesmaximal, complemented
10#38260C213yesmaximal, complemented
11#38225C213yesmaximal, complemented
12#37983C213yesmaximal, complemented
13#37936C213yesmaximal, complemented
14Q8×#125C211yesmaximal, characteristic, complemented
15#36483C211yesmaximal, characteristic
16#36475C211yesmaximal, characteristic, complemented
17#36458C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#36384C213yesmaximal, complemented
20#36367C213yesmaximal, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35868C211yesmaximal, characteristic, complemented
23#35801C211yesmaximal, characteristic
24#35786C211yesmaximal, characteristic, complemented
25#34873C213yesmaximal, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34293C211yesmaximal, characteristic
28#34262C211yesmaximal, characteristic, complemented
29#34249C211yesmaximal, characteristic, complemented
30#34129C211yesmaximal, characteristic, complemented
31Q8×#117C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2864C2213yes—
39#2860C2213yes—
40#2859C2213yes—
41#2854C2213yes—
42#2851C2213yes—
43#2793C2216yes—
44#2773C2216yes—
45#2773C2216yes—
46#2772C2216yes—
47#2770C2216yes—
48#2769C2216yes—
49#2768C2216yes—
50#2768C2216yes—
51#2754C2216yes—
52#2744C2216yes—
53#2721C2216yes—
54#2707C2216yes—
55#2695C2216yes—
56#2694C2216yes—
57#2647C2213yes—
58#2644C2213yes—
59#2629C2213yes—
60#2624C2213yes—
61#2612C2213yes—
62#2611C2216yes—
63#2611C2213yes—
64#2611C2213yes—
65#2609C2213yes—
66#2604C2216yes—
67#2601C2216yes—
68#2585C2216yes—
69#2585C2213yes—
70#2582C2213yes—
71#2580C2213yes—
72#2573C2213yes—
73#2570C2213yes—
74#2570C2213yes—
75#2570C2213yes—
76#2566C2213yes—
77#2565C2213yes—
78#2565C2216yes—
79#2556C2213yes—
80#2553C2213yes—
81#2552C2213yes—
82#2552C2213yes—
83#2552C2213yes—
84#2533C2213yes—
85#2532C2216yes—
86#2530C2213yes—
87#2529C2216yes—
88#2528C2216yes—
89#2528C2213yes—
90#2527C2213yes—
91#2525C2216yes—
92#2519C2216yes—
93#2519C2216yes—
94#2517C2216yes—
95#2513C2213yes—
96#2513C2213yes—
97#2512C2213yes—
98#2512C2213yes—
99#2512C2213yes—
100#2512C2213yes—
101#2509C2213yes—
102#2509C2213yes—
103#2508C2216yes—
104#2508C2213yes—
105#2507C2213yes—
106#2507C2213yes—
107#2507C2213yes—
108#2507C2213yes—
109#2507C2213yes—
110#2507C2213yes—
111#2506C2213yes—
112#2506C2213yes—
113#2506C2213yes—
114#2501C2213yes—
115#2500C2213yes—
116#2497C2213yes—
117#2497C2213yes—
118#2496C2213yes—
119#2496C2213yes—
120#2495C2213yes—
121#2494C2213yes—
122#2486C2213yes—
123#2485C2213yes—
124#2478C2216yes—
125#2478C2216yes—
126#2478C2213yes—
127#2477C2213yes—
128#2475C2211yescharacteristic
129#2470C2216yes—
130#2470C2213yes—
131#2458C2216yes—
132#2454C2213yes—
133#2453C2213yes—
134#2452C2213yes—
135#2451C2213yes—
136#2448C2213yes—
137#2448C2213yes—
138#2448C2213yes—
139#2448C2213yes—
140#2441C2213yes—
141#2441C2216yes—
142#2441C2213yes—
143#2439C2213yes—
144#2439C2213yes—
145#2423C2213yes—
146#2423C2213yes—
147#2423C2213yes—
148#2421C2213yes—
149#2402C2213yes—
150#2401C2213yes—
151#2396C2213yes—
152#2395C2213yes—
153#2373C2216yes—
154#2371C2216yes—
155#2370C2213yes—
156#2370C2213yes—
157#2367C2213yes—
158#2365C2213yes—
159#2363C2213yes—
160#2362C2213yes—
161#2362C2216yes—
162#2356C2213yes—
163#2355C2213yes—
164#2355C2213yes—
165#2355C2213yes—
166#2354C2213yes—
167#2354C2213yes—
168#2354C2213yes—
169#2351C2213yes—
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2213yes—
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2213yes—
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2213yes—
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2213yes—
190#2347C2213yes—
191#2346C2213yes—
192#2346C2213yes—
193#2346C2213yes—
194#2345C2213yes—
195#2345C2213yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2330C2213yes—
205#2330C2213yes—
206#2326C2213yes—
207#2324C2213yes—
208#2320C2213yes—
209#2317C2213yes—
210#2317C2213yes—
211#2314C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#125C2213yes—
214C4×#125C2213yes—
215C4×#126C2213yes—
216C4×C22⋊Q8C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×#123C2213yes—
219#2298C2213yes—
220#2296C2213yes—
221#2296C2213yes—
222#2295C2213yes—
223#2295C2213yes—
224#2295C2213yes—
225#2295C2213yes—
226#2293C2213yes—
227#2293C2213yes—
228#2290C2213yes—
229#2285C2213yes—
230#2285C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C4×#117C2213yes—
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240#557—28no—
241#548—28no—
242C2×C4⋊Q8C2313yes—
243C2×#126C2313yes—
244C2×#126C2316yes—
245C2×#126C2316yes—
246C2×#125C2311yescharacteristic
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2316yes—
251C2×#125C2316yes—
252C2×#124C2313yes—
253C2×#123C2313yes—
254C2×#123C2316yes—
255C2×C22⋊Q8C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×#121C2313yes—
258#519—28no—
259#519—28no—
260C4×#41—28no—
261C2×C4×Q8—28no—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2313yes—
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
278C2×C4×Q8C2313yes—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2316yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×D4C2313yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×#117C2313yes—
287C2×#117C2313yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C2×#117C2313yes—
291C2×#117C2311yescharacteristic
292C2×#117C2313yes—
293C2×#117C2313yes—
294C2×#117C2313yes—
295C2×#117C2316yes—
296C22×C4⋊C4C2313yes—
297C22×C42C2313yes—
298C22×C42C2313yes—
299#401C2313yes—
300#400C2313yes—
301#400C2316yes—
302#400C2316yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2316yes—
307#400C2316yes—
308#400C2313yes—
309#400C2313yes—
310#400C2311yescharacteristic
311#400C2313yes—
312#400C2313yes—
313#399C2316yes—
314#399C2316yes—
315#399C2313yes—
316#399C2313yes—
317#399C2316yes—
318#399C2316yes—
319#398C2313yes—
320#398C2313yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2313yes—
328#398C2313yes—
329#398C2316yes—
330#398C2313yes—
331#398C2313yes—
332#398C2316yes—
333#398C2316yes—
334#398C2311yescharacteristic
335#398C2316yes—
336#398C2316yes—
337#397C2313yes—
338#397C2313yes—
339#397C2316yes—
340#397C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2311yescharacteristic
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#396C2316yes—
350#396C2316yes—
351#396C2313yes—
352#396C2316yes—
353#396C2313yes—
354#396C2316yes—
355#396C2311yescharacteristic
356#396C2316yes—
357#395C2313yes—
358#394C2316yes—
359#394C2313yes—
360#394C2313yes—
361#393C2316yes—
362#393C2313yes—
363#391C2313yes—
364#391C2313yes—
365#391C2316yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#390C2313yes—
374#390C2313yes—
375#390C2313yes—
376#390C2316yes—
377#390C2313yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2316yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2316yes—
398#389C2313yes—
399#389C2313yes—
400#389C2316yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2316yes—
407#389C2316yes—
408#389C2316yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2316yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2316yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2316yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2311yescharacteristic
435#389C2313yes—
436#388C2313yes—
437#388C2313yes—
438#388C2313yes—
439#388C2313yes—
440#388C2316yes—
441#388C2311yescharacteristic
442#388C2313yes—
443#388C2316yes—
444#388C2316yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2316yes—
449#388C2316yes—
450#388C2313yes—
451#388C2316yes—
452#388C2316yes—
453#388C2316yes—
454#388C2316yes—
455#388C2316yes—
456#388C2316yes—
457#388C2313yes—
458#388C2316yes—
459#388C2316yes—
460#388C2313yes—
461#388C2316yes—
462#388C2313yes—
463#388C2311yescharacteristic
464#387C2311yescharacteristic
465#387C2313yes—
466#387C2313yes—
467#387C2311yescharacteristic
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2311yescharacteristic
488#387C2313yes—
489#387C2316yes—
490#387C2316yes—
491#387C2313yes—
492#387C2316yes—
493#387C2313yes—
494#387C2313yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#386C2313yes—
508#386C2313yes—
509#386C2313yes—
510#385C2313yes—
511#385C2316yes—
512#385C2313yes—
513#385C2316yes—
514#385C2313yes—
515#385C2316yes—
516#385C2313yes—
517#385C2313yes—
518#385C2316yes—
519#385C2313yes—
520#385C2311yescharacteristic
521#385C2311yescharacteristic
522#385C2313yes—
523#384C2313yes—
524#384C2316yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#383C2313yes—
536#383C2316yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2316yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2316yes—
546#382C2316yes—
547#382C2316yes—
548#381C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2316yes—
558#380C2316yes—
559#380C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2316yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2316yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2316yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2316yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2316yes—
600C4×C4⋊C4C2311yescharacteristic
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2316yes—
619#376C2313yes—
620#376C2313yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8#4118yes—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2411yescharacteristic
633C22×D4C2413yes—
634C22×D4C2413yes—
635C23×C4C2411yescharacteristic
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C4⋊Q8—212no—
642#126—412no—
643#126—46no—
644#126—86no—
645#125—212no—
646#125—24no—
647#125—212no—
648#125—46no—
649#125—412no—
650#125—86no—
651#124—212no—
652#123—46no—
653#123—86no—
654C22⋊Q8—212no—
655C22⋊Q8—212no—
656#121—212no—
657C4×Q8—212no—
658C4×Q8—212no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—24no—
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—212no—
674C4×Q8—212no—
675C4×Q8—212no—
676C4×Q8—86no—
677C4×Q8#4118yes—
678C4×D4—212no—
679C4×D4—212no—
680C4×D4—212no—
681#117—212no—
682#117—212no—
683#117—212no—
684#117—212no—
685#117—24no—
686#117—212no—
687#117—46no—
688#117—46no—
689#117—46no—
690#117—86no—
691C2×C4⋊C4—212no—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2416yes—
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C22⋊C4C2411yescharacteristic
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2411yescharacteristic
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2416yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2411yescharacteristic
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2416yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2416yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2416yes—
787C2×C42—212no—
788C2×C42—212no—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2416yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2416yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2416yes—
819C2×C42C2416yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
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#95C2416yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2411yescharacteristic
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2411yescharacteristic
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2416yes—
869#95C2416yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2416yes—
877#95C2416yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2416yes—
888#95C2416yes—
889C24C2513yes—
890C24C2511yescharacteristic
891#41—416no—
892C2×Q8—232no—
893C2×Q8—26no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—43no—
898C2×Q8C2×#41112yes—
899C2×Q8C2×#4114yes—
900C2×Q8C2×#4114yes—
901C2×Q82−1+414yes—
902C2×D4—26no—
903C2×D4—26no—
904C2×D4—26no—
905C2×D4—26no—
906C2×D4—43no—
907C2×D4—43no—
908C22×C4—22no—
909C22×C4—26no—
910C22×C4—22no—
911C22×C4—26no—
912C22×C4—22no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—43no—
921C22×C4—43no—
922C22×C4—43no—
923C22×C4—43no—
924C22×C4—43no—
925C22×C4C2×#41112yes—
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2513yes—
932C22×C4C2513yes—
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2511yescharacteristic
936C22×C4C2513yes—
937C22×C4C2513yes—
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2511yescharacteristic
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C4⋊C4—212no—
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—26no—
967C4⋊C4—22no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—212no—
974C4⋊C4—22no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—26no—
988C4⋊C4—22no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—22no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—46no—
997C4⋊C4—46no—
998C4⋊C4—43no—
999C4⋊C4—46no—
1000C4⋊C4—43no—
1001C4⋊C4—46no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—46no—
1005C4⋊C4—46no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—46no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—46no—
1014C4⋊C4—46no—
1015C4⋊C4—46no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4C2×#41112yes—
1020C4⋊C42−1+414yes—
1021C22⋊C4—26no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—26no—
1025C22⋊C4—22no—
1026C22⋊C4—212no—
1027C22⋊C4—26no—
1028C22⋊C4—212no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—26no—
1032C22⋊C4—26no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—22no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—43no—
1040C22⋊C4—46no—
1041C22⋊C4—46no—
1042C22⋊C4—43no—
1043C22⋊C4—43no—
1044C22⋊C4—46no—
1045C22⋊C4—46no—
1046C22⋊C4—46no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C42—22no—
1051C42—26no—
1052C42—26no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—26no—
1057C42—212no—
1058C42—212no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—22no—
1066C42—22no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—22no—
1071C42—26no—
1072C42—26no—
1073C42—26no—
1074C42—43no—
1075C42—43no—
1076C42—43no—
1077C42—43no—
1078C42—43no—
1079C42—46no—
1080C42—46no—
1081C42—43no—
1082C42C2×#41112yes—
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—
1096C23C22×#4112yes—
1097C23C2611yescharacteristic
1098Q8—224no—
1099Q8—412no—
1100Q8#552116yes—
1101D4—412no—
1102D4—86no—
1103C2×C4—28no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—23no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—23no—
1120C2×C4—224no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—21no—
1169C2×C4—21no—
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—21no—
1179C2×C4—23no—
1180C2×C4—21no—
1181C2×C4—412no—
1182C2×C4—412no—
1183C2×C4—412no—
1184C2×C4—86no—
1185C2×C4C22×#4116yes—
1186C2×C4C22×#4116yes—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4116yes—
1189C2×C4C22×#4116yes—
1190C2×C4C2×2−1+412yes—
1191C2×C4C2×2−1+412yes—
1192C2×C4C2×2−1+412yes—
1193C2×C4C2×2−1+416yes—
1194C2×C4#58512yes—
1195C2×C4#58512yes—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—43no—
1204C22—43no—
1205C22—43no—
1206C22—43no—
1207C22—43no—
1208C22—43no—
1209C22—43no—
1210C22C23×#4111yescharacteristic
1211C22C23×#4111yescharacteristic
1212C22C22×2−1+411yescharacteristic
1213C22C22×2−1+411yescharacteristic
1214C22C2×#58511yescharacteristic
1215C22C2×#58511yescharacteristic
1216C22H(7,𝔽2)11yescharacteristic
1217C4—22no—
1218C4—26no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—22no—
1223C4—22no—
1224C4—26no—
1225C4—41no—
1226C4—43no—
1227C4—43no—
1228C4—41no—
1229C4—43no—
1230C4—43no—
1231C4—43no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—43no—
1237C4—43no—
1238C4—41no—
1239C4—43no—
1240C4—43no—
1241C4—43no—
1242C4—43no—
1243C4—43no—
1244C4—41no—
1245C4C2×#552112yes—
1246C2—42no—
1247C2—83no—
1248C2C22×#55211yescharacteristic
1249C2#6278811yescharacteristic
1250C2#6279311yescharacteristic
1251C2#6295211yescharacteristic
1252C2#6300011yescharacteristic
1253C2#6300611yescharacteristic
1254C2#6303811yescharacteristic
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. #59751C2semidirect
2. #59749C2semidirect
3. #59501C2semidirect
4. #59292C2semidirect
5. #59259C2semidirect
6. #45317C2semidirect
7. #44990C2semidirect
8. #44967C2semidirect
9. #44905C2semidirect
10. #38260C2semidirect
11. #38225C2semidirect
12. #37983C2semidirect
13. #37936C2semidirect
14. Q8×#125C2semidirect
16. #36475C2semidirect
17. #36458C2semidirect
18. #36431C2semidirect
19. #36384C2semidirect
20. #36367C2semidirect
21. #35898C2semidirect
22. #35868C2semidirect
24. #35786C2semidirect
25. #34873C2semidirect
26. #34337C2semidirect
28. #34262C2semidirect
29. #34249C2semidirect
30. #34129C2semidirect
31. Q8×#117C2semidirect

Maximal subgroups

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

subgroupindex
#597512
#597492
#595012
#592922
#592592
#453172
#449902
#449672
#449052
#382602
#382252
#379832
#379362
Q8×#1252
#364832
#364752
#364582
#364312
#363842
#363672
#358982
#358682
#358012
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Q8×#1172