Finite Group Databasebeta

← #7687712

Subgroups — #7687712

Order 512.

4743 conjugacy classes of subgroups.

The subgroup lattice has 1263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59719C213yesmaximal, complemented
2#59716C213yesmaximal, complemented
3#59580C213yesmaximal, complemented
4#59433C213yesmaximal, complemented
5#59243C213yesmaximal, complemented
6#45256C213yesmaximal, complemented
7#45067C213yesmaximal, complemented
8#45058C213yesmaximal, complemented
9#44965C213yesmaximal, complemented
10#39803C213yesmaximal, complemented
11#39298C213yesmaximal, complemented
12#38238C213yesmaximal, complemented
13#37960C213yesmaximal, complemented
14#36585C211yesmaximal, characteristic, complemented
15#36585C211yesmaximal, characteristic, complemented
16#36583C211yesmaximal, characteristic
17#36503C213yesmaximal, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36431C211yesmaximal, characteristic, complemented
20#36300C213yesmaximal, complemented
21#36049C211yesmaximal, characteristic
22#35957C211yesmaximal, characteristic, complemented
23#35898C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic, complemented
25#34867C213yesmaximal, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34336C211yesmaximal, characteristic, complemented
28#34295C211yesmaximal, characteristic
29#34263C211yesmaximal, characteristic, complemented
30C4×#557C211yesmaximal, characteristic, complemented
31#34129C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2860C2213yes—
39#2860C2213yes—
40#2860C2213yes—
41#2858C2213yes—
42#2851C2213yes—
43#2808C2216yes—
44#2800C2216yes—
45#2793C2216yes—
46#2789C2216yes—
47#2787C2216yes—
48#2786C2216yes—
49#2786C2216yes—
50#2786C2216yes—
51#2783C2216yes—
52#2759C2216yes—
53#2740C2216yes—
54#2715C2216yes—
55#2715C2216yes—
56#2700C2216yes—
57#2660C2213yes—
58#2644C2213yes—
59#2641C2213yes—
60#2629C2213yes—
61#2605C2213yes—
62#2604C2213yes—
63#2601C2213yes—
64#2601C2216yes—
65#2601C2216yes—
66#2599C2213yes—
67#2596C2216yes—
68#2594C2216yes—
69#2594C2213yes—
70#2594C2216yes—
71#2588C2213yes—
72#2584C2213yes—
73#2580C2213yes—
74#2577C2213yes—
75#2567C2213yes—
76#2566C2213yes—
77#2566C2213yes—
78#2562C2213yes—
79#2560C2213yes—
80#2560C2216yes—
81#2552C2213yes—
82#2552C2213yes—
83#2550C2213yes—
84#2550C2213yes—
85#2548C2213yes—
86#2548C2213yes—
87#2547C2213yes—
88#2538C2213yes—
89#2532C2213yes—
90#2528C2213yes—
91#2527C2216yes—
92#2524C2211yescharacteristic
93#2521C2216yes—
94#2521C2213yes—
95#2513C2213yes—
96#2513C2213yes—
97#2513C2213yes—
98#2513C2213yes—
99#2513C2213yes—
100#2513C2213yes—
101#2513C2213yes—
102#2513C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2512C2213yes—
106#2512C2213yes—
107#2512C2216yes—
108#2499C2216yes—
109#2497C2213yes—
110#2497C2213yes—
111#2496C2213yes—
112#2496C2213yes—
113#2495C2213yes—
114#2494C2213yes—
115#2494C2213yes—
116#2494C2216yes—
117#2494C2213yes—
118#2494C2213yes—
119#2494C2213yes—
120#2494C2213yes—
121#2494C2213yes—
122#2491C2213yes—
123#2491C2213yes—
124#2490C2213yes—
125#2490C2213yes—
126#2490C2213yes—
127#2490C2213yes—
128#2490C2213yes—
129#2490C2213yes—
130#2478C2213yes—
131#2478C2216yes—
132#2474C2216yes—
133#2474C2213yes—
134#2474C2216yes—
135#2474C2216yes—
136#2469C2213yes—
137#2466C2216yes—
138#2465C2213yes—
139#2454C2213yes—
140#2454C2213yes—
141#2452C2213yes—
142#2452C2213yes—
143#2448C2216yes—
144#2442C2213yes—
145#2441C2213yes—
146#2440C2213yes—
147#2439C2213yes—
148#2415C2216yes—
149#2401C2213yes—
150#2399C2213yes—
151#2398C2213yes—
152#2396C2213yes—
153#2373C2216yes—
154#2370C2213yes—
155#2370C2213yes—
156#2370C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2370C2213yes—
160#2369C2213yes—
161#2369C2213yes—
162#2367C2216yes—
163#2366C2213yes—
164#2365C2213yes—
165#2363C2213yes—
166#2361C2213yes—
167#2357C2213yes—
168#2355C2213yes—
169#2355C2213yes—
170#2355C2213yes—
171#2354C2213yes—
172#2354C2213yes—
173#2354C2213yes—
174#2354C2216yes—
175#2352C2213yes—
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188#2346C2213yes—
189#2346C2213yes—
190#2345C2213yes—
191#2344C2213yes—
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2331C2213yes—
203#2331C2213yes—
204#2330C2213yes—
205#2330C2213yes—
206#2328C2213yes—
207#2324C2213yes—
208#2319C2213yes—
209#2314C2213yes—
210C4×C4⋊Q8C2213yes—
211C4×#125C2213yes—
212C4×#125C2213yes—
213C4×#125C2213yes—
214C4×#125C2213yes—
215C4×#126C2213yes—
216C4×#126C2213yes—
217C4×#126C2213yes—
218C4×#124C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×#121C2213yes—
221#2298C2213yes—
222#2295C2213yes—
223#2295C2213yes—
224#2293C2213yes—
225#2293C2213yes—
226#2293C2213yes—
227#2290C2213yes—
228#2285C2213yes—
229#2276C2211yescharacteristic
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2213yes—
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#557—28no—
241#557—28no—
242#557—28no—
243#550—28no—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#127C2313yes—
248C2×#126C2313yes—
249C2×#126C2313yes—
250C2×#126C2313yes—
251C2×#126C2316yes—
252C2×#126C2316yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2316yes—
261C2×#124C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2316yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266#520—28no—
267C4×#41—28no—
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2313yes—
287C2×C4×D4C2313yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2316yes—
292C2×#117C2313yes—
293C2×#117C2313yes—
294C2×#117C2313yes—
295C2×#117C2313yes—
296C2×#117C2316yes—
297C2×#117C2316yes—
298C22×C4⋊C4C2313yes—
299C22×C42C2313yes—
300#401C2313yes—
301#401C2316yes—
302#401C2316yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2316yes—
307#400C2311yescharacteristic
308#400C2311yescharacteristic
309#400C2313yes—
310#399C2316yes—
311#399C2313yes—
312#398C2313yes—
313#398C2316yes—
314#398C2313yes—
315#398C2313yes—
316#398C2316yes—
317#398C2316yes—
318#398C2313yes—
319#398C2311yescharacteristic
320#398C2311yescharacteristic
321#397C2313yes—
322#397C2316yes—
323#397C2313yes—
324#397C2313yes—
325#397C2316yes—
326#397C2313yes—
327#397C2316yes—
328#397C2316yes—
329#397C2313yes—
330#397C2316yes—
331#397C2316yes—
332#397C2316yes—
333#397C2316yes—
334#397C2316yes—
335#397C2316yes—
336#397C2316yes—
337#397C2316yes—
338#396C2313yes—
339#396C2316yes—
340#396C2316yes—
341#396C2316yes—
342#396C2313yes—
343#396C2316yes—
344#396C2313yes—
345#396C2316yes—
346#396C2316yes—
347#395C2313yes—
348#395C2316yes—
349#395C2313yes—
350#395C2313yes—
351#395C2313yes—
352#395C2313yes—
353#394C2313yes—
354#394C2316yes—
355#394C2316yes—
356#394C2316yes—
357#394C2313yes—
358#394C2316yes—
359#394C2316yes—
360#393C2316yes—
361#393C2313yes—
362#393C2313yes—
363#393C2313yes—
364#391C2313yes—
365#391C2313yes—
366#391C2316yes—
367#391C2316yes—
368#391C2313yes—
369#391C2316yes—
370#391C2316yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#390C2316yes—
375#390C2313yes—
376#390C2313yes—
377#390C2313yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2316yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#390C2313yes—
397#390C2316yes—
398#390C2316yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2316yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2316yes—
417#389C2316yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2316yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#388C2313yes—
434#388C2313yes—
435#388C2313yes—
436#388C2313yes—
437#388C2313yes—
438#388C2313yes—
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2316yes—
444#388C2316yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2313yes—
449#388C2316yes—
450#388C2313yes—
451#388C2313yes—
452#388C2316yes—
453#388C2313yes—
454#388C2313yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2313yes—
460#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2313yes—
470#388C2313yes—
471#387C2311yescharacteristic
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2311yescharacteristic
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2313yes—
491#387C2316yes—
492#387C2313yes—
493#387C2313yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2311yescharacteristic
498#387C2313yes—
499#387C2311yescharacteristic
500#387C2313yes—
501#387C2313yes—
502#387C2316yes—
503#387C2316yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2311yescharacteristic
508#387C2311yescharacteristic
509#386C2316yes—
510#386C2313yes—
511#386C2316yes—
512#386C2313yes—
513#386C2316yes—
514#385C2313yes—
515#385C2316yes—
516#385C2316yes—
517#385C2316yes—
518#385C2313yes—
519#385C2313yes—
520#385C2313yes—
521#385C2316yes—
522#384C2313yes—
523#384C2313yes—
524#384C2316yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#383C2311yescharacteristic
529#383C2311yescharacteristic
530#383C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2316yes—
538#382C2313yes—
539#382C2311yescharacteristic
540#381C2316yes—
541#380C2313yes—
542#380C2313yes—
543#380C2313yes—
544#380C2313yes—
545#380C2313yes—
546#380C2316yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2316yes—
554#380C2316yes—
555C4×C4⋊C4C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
574C4×C4⋊C4C2316yes—
575C4×C4⋊C4C2316yes—
576C4×C4⋊C4C2316yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2311yescharacteristic
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⋊C4C2316yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620C43C2313yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2411yescharacteristic
634C22×D4C2413yes—
635C22×D4C2413yes—
636C22×D4C2416yes—
637C22×D4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2416yes—
642C23×C4C2413yes—
643C4⋊Q8—212no—
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646#127—212no—
647#126—46no—
648#126—412no—
649#126—46no—
650#126—46no—
651#126—86no—
652#125—212no—
653#125—212no—
654#125—212no—
655#125—212no—
656#125—212no—
657#125—212no—
658#124—46no—
659#124—412no—
660#124—86no—
661C22⋊Q8—46no—
662C22⋊Q8—86no—
663#121—212no—
664#121—212no—
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—212no—
677C4×Q8—212no—
678C4×Q8—212no—
679C4×Q8—46no—
680C4×Q8—46no—
681C4×Q8#4118yes—
682C4×Q8#4118yes—
683C4×D4—212no—
684C4×D4—212no—
685C4×D4—212no—
686C4×D4—212no—
687C4×D4—212no—
688C4×D4—412no—
689#117—212no—
690#117—212no—
691#117—46no—
692#117—46no—
693#117—86no—
694#117—86no—
695C2×C4⋊C4—212no—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2416yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2416yes—
765C2×C22⋊C4C2416yes—
766C2×C22⋊C4C2416yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2416yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2416yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2416yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2416yes—
788C2×C42—212no—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2411yescharacteristic
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2416yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2416yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2416yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
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#95C2413yes—
843#95C2413yes—
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2416yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2416yes—
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2413yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2416yes—
878#95C2413yes—
879#95C2416yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2416yes—
884#95C2416yes—
885#95C2416yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2416yes—
890C24C2513yes—
891C24C2513yes—
892#41—416no—
893#41—416no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—26no—
898C2×Q8—43no—
899C2×Q8—43no—
900C2×Q8—43no—
901C2×Q8—43no—
902C2×Q8—43no—
903C2×Q8C2×#4114yes—
904C2×Q8C2×#4114yes—
905C2×Q82−1+414yes—
906C2×D4—26no—
907C2×D4—26no—
908C2×D4—26no—
909C2×D4—26no—
910C2×D4—26no—
911C2×D4—212no—
912C2×D4—26no—
913C2×D4—26no—
914C2×D4—46no—
915C2×D4—43no—
916C2×D4—46no—
917C2×D4—43no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—26no—
924C22×C4—26no—
925C22×C4—26no—
926C22×C4—26no—
927C22×C4—212no—
928C22×C4—43no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4—46no—
932C22×C4—46no—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2513yes—
937C22×C4C2511yescharacteristic
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2511yescharacteristic
943C22×C4C2513yes—
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2511yescharacteristic
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2513yes—
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2513yes—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—22no—
965C4⋊C4—26no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—212no—
983C4⋊C4—212no—
984C4⋊C4—212no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—26no—
991C4⋊C4—22no—
992C4⋊C4—26no—
993C4⋊C4—22no—
994C4⋊C4—26no—
995C4⋊C4—22no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—46no—
999C4⋊C4—43no—
1000C4⋊C4—46no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—46no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—46no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4C2×#41112yes—
1018C4⋊C4C2×#41112yes—
1019C22⋊C4—26no—
1020C22⋊C4—212no—
1021C22⋊C4—26no—
1022C22⋊C4—26no—
1023C22⋊C4—26no—
1024C22⋊C4—26no—
1025C22⋊C4—26no—
1026C22⋊C4—26no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—43no—
1030C22⋊C4—43no—
1031C22⋊C4—43no—
1032C22⋊C4—46no—
1033C22⋊C4—46no—
1034C22⋊C4—46no—
1035C22⋊C4—46no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—46no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—46no—
1043C22⋊C4—46no—
1044C22⋊C4—46no—
1045C22⋊C4—43no—
1046C22⋊C4—46no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C22⋊C4—46no—
1051C22⋊C4—43no—
1052C22⋊C4—43no—
1053C22⋊C4—43no—
1054C42—22no—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—22no—
1070C42—22no—
1071C42—22no—
1072C42—22no—
1073C42—43no—
1074C42—43no—
1075C42—43no—
1076C42—43no—
1077C42—43no—
1078C42—46no—
1079C42—46no—
1080C42—43no—
1081C42—43no—
1082C42—43no—
1083C42—43no—
1084C42—46no—
1085C42—43no—
1086C42C2×#41112yes—
1087C42C2×#41112yes—
1088C23—23no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23—23no—
1096C23—23no—
1097C23—23no—
1098C23—23no—
1099C23—23no—
1100C23—23no—
1101C23—23no—
1102C23C2611yescharacteristic
1103Q8—412no—
1104Q8—86no—
1105Q8—86no—
1106Q8#556116yes—
1107D4—412no—
1108D4—412no—
1109D4—86no—
1110D4—812no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
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—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—412no—
1189C2×C4—412no—
1190C2×C4—412no—
1191C2×C4—412no—
1192C2×C4—812no—
1193C2×C4C22×#4112yes—
1194C2×C4C22×#4116yes—
1195C2×C4C22×#4112yes—
1196C2×C4C22×#4116yes—
1197C2×C4C22×#4116yes—
1198C2×C4C22×#4116yes—
1199C2×C4C2×2−1+416yes—
1200C2×C4#58512yes—
1201C2×C4#58512yes—
1202C2×C4#58512yes—
1203C22—43no—
1204C22—43no—
1205C22—43no—
1206C22—43no—
1207C22—43no—
1208C22—43no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22—43no—
1213C22—43no—
1214C22—43no—
1215C22—43no—
1216C22—43no—
1217C22C23×#4111yescharacteristic
1218C22C23×#4111yescharacteristic
1219C22C22×2−1+411yescharacteristic
1220C22C2×#58511yescharacteristic
1221C22C2×#58511yescharacteristic
1222C22C2×#58511yescharacteristic
1223C22H(7,𝔽2)11yescharacteristic
1224C4—22no—
1225C4—22no—
1226C4—26no—
1227C4—22no—
1228C4—22no—
1229C4—26no—
1230C4—22no—
1231C4—41no—
1232C4—43no—
1233C4—43no—
1234C4—43no—
1235C4—43no—
1236C4—43no—
1237C4—41no—
1238C4—41no—
1239C4—43no—
1240C4—41no—
1241C4—41no—
1242C4—43no—
1243C4—43no—
1244C4—41no—
1245C4—41no—
1246C4—43no—
1247C4—41no—
1248C4—43no—
1249C4—43no—
1250C4—41no—
1251C4—41no—
1252C4C2×#556112yes—
1253C2—83no—
1254C2—83no—
1255C2C22×#55611yescharacteristic
1256C2#6279311yescharacteristic
1257C2#6281011yescharacteristic
1258C2#6295211yescharacteristic
1259C2#6300611yescharacteristic
1260C2#6300811yescharacteristic
1261C2#6303311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59719C2semidirect
2. #59716C2semidirect
3. #59580C2semidirect
4. #59433C2semidirect
5. #59243C2semidirect
6. #45256C2semidirect
7. #45067C2semidirect
8. #45058C2semidirect
9. #44965C2semidirect
10. #39803C2semidirect
11. #39298C2semidirect
12. #38238C2semidirect
13. #37960C2semidirect
14. #36585C2semidirect
15. #36585C2semidirect
17. #36503C2semidirect
18. #36458C2semidirect
19. #36431C2semidirect
20. #36300C2semidirect
22. #35957C2semidirect
23. #35898C2semidirect
24. #35816C2semidirect
25. #34867C2semidirect
26. #34336C2semidirect
27. #34336C2semidirect
29. #34263C2semidirect
30. C4×#557C2semidirect
31. #34129C2semidirect

Maximal subgroups

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

subgroupindex
#597192
#597162
#595802
#594332
#592432
#452562
#450672
#450582
#449652
#398032
#392982
#382382
#379602
#365852
#365832
#365032
#364582
#364312
#363002
#360492
#359572
#358982
#358162
#348672
#343362
#342952
#342632
C4×#5572
#341292