Finite Group Databasebeta

← #7632382

Subgroups — #7632382

Order 512.

5084 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36589C213yesmaximal, complemented
2#36578C211yesmaximal, characteristic, complemented
3#36483C211yesmaximal, characteristic, complemented
4#36461C213yesmaximal, complemented
5#36458C211yesmaximal, characteristic, complemented
6#36458C211yesmaximal, characteristic, complemented
7#36414C213yesmaximal, complemented
8#36413C213yesmaximal, complemented
9#36050C213yesmaximal, complemented
10#36049C211yesmaximal, characteristic, complemented
11#36026C213yesmaximal, complemented
12#36018C211yesmaximal, characteristic
13#35968C213yesmaximal, complemented
14#35868C211yesmaximal, characteristic, complemented
15#35813C213yesmaximal, complemented
16#35786C211yesmaximal, characteristic, complemented
17#35591C213yesmaximal, complemented
18#35590C213yesmaximal, complemented
19#35587C213yesmaximal, complemented
20#35586C213yesmaximal, complemented
21#35287C213yesmaximal, complemented
22#35186C213yesmaximal, complemented
23#34898C213yesmaximal, complemented
24#34879C213yesmaximal, complemented
25#34336C211yesmaximal, characteristic, complemented
26#34293C211yesmaximal, characteristic, complemented
27#34293C211yesmaximal, characteristic, complemented
28#34197C211yesmaximal, characteristic, complemented
29#34193C211yesmaximal, characteristic, complemented
30C4×#550C211yesmaximal, characteristic, complemented
31C4×#519C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2861C2216yes—
42#2860C2213yes—
43#2860C2216yes—
44#2860C2213yes—
45#2854C2213yes—
46#2854C2213yes—
47#2651C2216yes—
48#2651C2216yes—
49#2647C2213yes—
50#2641C2213yes—
51#2629C2213yes—
52#2619C2213yes—
53#2597C2216yes—
54#2596C2216yes—
55#2593C2216yes—
56#2593C2216yes—
57#2582C2213yes—
58#2577C2216yes—
59#2575C2216yes—
60#2574C2213yes—
61#2574C2213yes—
62#2573C2213yes—
63#2573C2213yes—
64#2572C2213yes—
65#2572C2213yes—
66#2570C2213yes—
67#2565C2213yes—
68#2562C2213yes—
69#2558C2216yes—
70#2557C2216yes—
71#2554C2216yes—
72#2554C2216yes—
73#2553C2213yes—
74#2553C2213yes—
75#2552C2213yes—
76#2548C2213yes—
77#2548C2213yes—
78#2536C2213yes—
79#2532C2216yes—
80#2532C2216yes—
81#2531C2216yes—
82#2529C2216yes—
83#2526C2216yes—
84#2526C2216yes—
85#2525C2216yes—
86#2524C2213yes—
87#2524C2213yes—
88#2521C2216yes—
89#2519C2216yes—
90#2516C2216yes—
91#2515C2211yescharacteristic
92#2515C2213yes—
93#2513C2213yes—
94#2513C2213yes—
95#2512C2213yes—
96#2512C2213yes—
97#2512C2213yes—
98#2512C2213yes—
99#2509C2213yes—
100#2507C2213yes—
101#2506C2213yes—
102#2506C2213yes—
103#2504C2213yes—
104#2501C2213yes—
105#2497C2213yes—
106#2497C2213yes—
107#2496C2213yes—
108#2496C2213yes—
109#2495C2213yes—
110#2495C2213yes—
111#2491C2213yes—
112#2491C2213yes—
113#2490C2213yes—
114#2490C2213yes—
115#2487C2213yes—
116#2486C2213yes—
117#2479C2216yes—
118#2471C2216yes—
119#2468C2216yes—
120#2468C2213yes—
121#2468C2213yes—
122#2468C2216yes—
123#2457C2216yes—
124#2457C2213yes—
125#2457C2213yes—
126#2454C2216yes—
127#2453C2213yes—
128#2451C2213yes—
129#2448C2213yes—
130#2448C2213yes—
131#2448C2213yes—
132#2448C2213yes—
133#2447C2216yes—
134#2441C2213yes—
135#2439C2213yes—
136#2426C2213yes—
137#2426C2213yes—
138#2423C2213yes—
139#2423C2213yes—
140#2421C2213yes—
141#2421C2213yes—
142#2414C2213yes—
143#2414C2213yes—
144#2402C2213yes—
145#2402C2216yes—
146#2398C2213yes—
147#2396C2213yes—
148#2395C2216yes—
149#2392C2213yes—
150#2370C2213yes—
151#2370C2213yes—
152#2369C2213yes—
153#2367C2213yes—
154#2367C2213yes—
155#2366C2213yes—
156#2363C2213yes—
157#2363C2213yes—
158#2363C2213yes—
159#2363C2213yes—
160#2362C2213yes—
161#2362C2213yes—
162#2357C2213yes—
163#2357C2213yes—
164#2355C2213yes—
165#2354C2213yes—
166#2354C2213yes—
167#2354C2213yes—
168#2354C2213yes—
169#2354C2213yes—
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174Q8×C4⋊C4C2211yescharacteristic
175Q8×C4⋊C4C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180#2347C2213yes—
181#2347C2213yes—
182#2346C2213yes—
183#2346C2213yes—
184#2341C2211yescharacteristic
185#2341C2211yescharacteristic
186#2341C2211yescharacteristic
187#2341C2211yescharacteristic
188#2341C2211yescharacteristic
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2211yescharacteristic
192Q8×C22⋊C4C2211yescharacteristic
193Q8×C22⋊C4C2211yescharacteristic
194#2331C2213yes—
195#2330C2213yes—
196#2326C2213yes—
197#2326C2213yes—
198#2324C2213yes—
199#2324C2213yes—
200#2319C2213yes—
201#2319C2213yes—
202#2319C2213yes—
203#2319C2213yes—
204C4×#127C2213yes—
205C4×#125C2213yes—
206C4×#126C2213yes—
207C4×#126C2213yes—
208C4×#126C2216yes—
209C4×C22⋊Q8C2213yes—
210C4×C22⋊Q8C2213yes—
211C4×#123C2213yes—
212C4×#123C2213yes—
213C4×#121C2213yes—
214C4×#121C2213yes—
215#2298C2216yes—
216#2295C2213yes—
217#2290C2213yes—
218#2290C2213yes—
219#2285C2213yes—
220#2283C2213yes—
221#2283C2213yes—
222#2283C2213yes—
223#2276C2213yes—
224#2276C2211yescharacteristic
225#2276C2211yescharacteristic
226#2276C2211yescharacteristic
227#2276C2213yes—
228#2276C2211yescharacteristic
229#2274C2213yes—
230#2274C2213yes—
231C42×Q8C2211yescharacteristic
232C42×Q8C2213yes—
233C42×Q8C2213yes—
234C42×Q8C2211yescharacteristic
235C42×D4C2213yes—
236C4×#117C2213yes—
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—28no—
242#550—28no—
243#548—28no—
244#548—28no—
245C2×C4⋊Q8C2313yes—
246C2×#127C2313yes—
247C2×#126C2316yes—
248C2×#126C2313yes—
249C2×#126C2313yes—
250C2×#126C2316yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2316yes—
254C2×#124C2313yes—
255C2×#124C2313yes—
256C2×#124C2316yes—
257C2×#123C2313yes—
258C2×#123C2313yes—
259C2×#123C2316yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×#121C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266#519—28no—
267#519—28no—
268C4×#41—28no—
269C4×#41—28no—
270C2×C4×Q8—28no—
271C2×C4×Q8C2313yes—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2313yes—
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×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2316yes—
300C2×#117C2313yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2316yes—
307C22×C4⋊C4C2313yes—
308C22×C42C2313yes—
309C22×C42C2313yes—
310C22×C42C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2313yes—
320#400C2316yes—
321#400C2311yescharacteristic
322#399C2316yes—
323#399C2316yes—
324#399C2316yes—
325#399C2313yes—
326#398C2313yes—
327#398C2316yes—
328#398C2316yes—
329#398C2313yes—
330#398C2313yes—
331#398C2316yes—
332#398C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2311yescharacteristic
338#397C2313yes—
339#397C2313yes—
340#397C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2311yescharacteristic
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#396C2313yes—
349#396C2313yes—
350#396C2313yes—
351#396C2316yes—
352#396C2316yes—
353#396C2316yes—
354#396C2311yescharacteristic
355#395C2313yes—
356#394C2316yes—
357#394C2313yes—
358#394C2313yes—
359#394C2313yes—
360#394C2316yes—
361#394C2316yes—
362#394C2316yes—
363#394C2316yes—
364#394C2313yes—
365#394C2313yes—
366#393C2313yes—
367#393C2313yes—
368#393C2313yes—
369#392C2313yes—
370#392C2316yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2316yes—
378#391C2316yes—
379#390C2316yes—
380#390C2316yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2316yes—
394#390C2316yes—
395#390C2313yes—
396#390C2313yes—
397#390C2313yes—
398#390C2313yes—
399#390C2316yes—
400#390C2316yes—
401#390C2316yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2316yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2316yes—
425#389C2313yes—
426#389C2313yes—
427#388C2316yes—
428#388C2313yes—
429#388C2313yes—
430#388C2313yes—
431#388C2313yes—
432#388C2313yes—
433#388C2313yes—
434#388C2316yes—
435#388C2316yes—
436#388C2316yes—
437#388C2311yescharacteristic
438#388C2313yes—
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2316yes—
444#388C2316yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2316yes—
449#388C2316yes—
450#388C2316yes—
451#388C2316yes—
452#388C2316yes—
453#388C2316yes—
454#388C2316yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2313yes—
467#388C2316yes—
468#388C2311yescharacteristic
469#387C2311yescharacteristic
470#387C2311yescharacteristic
471#387C2313yes—
472#387C2316yes—
473#387C2316yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
490#387C2316yes—
491#387C2313yes—
492#387C2313yes—
493#387C2311yescharacteristic
494#386C2313yes—
495#386C2313yes—
496#386C2313yes—
497#386C2313yes—
498#386C2313yes—
499#386C2316yes—
500#386C2316yes—
501#386C2313yes—
502#386C2316yes—
503#385C2313yes—
504#385C2313yes—
505#385C2313yes—
506#385C2313yes—
507#385C2316yes—
508#385C2316yes—
509#385C2313yes—
510#385C2311yescharacteristic
511#384C2313yes—
512#384C2313yes—
513#384C2313yes—
514#384C2313yes—
515#384C2313yes—
516#384C2313yes—
517#383C2313yes—
518#383C2313yes—
519#383C2313yes—
520#383C2313yes—
521#383C2311yescharacteristic
522#383C2313yes—
523#382C2313yes—
524#382C2313yes—
525#382C2313yes—
526#382C2311yescharacteristic
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#381C2311yescharacteristic
532#381C2313yes—
533#381C2313yes—
534#381C2313yes—
535#381C2313yes—
536#381C2313yes—
537#381C2316yes—
538#380C2313yes—
539#380C2313yes—
540#380C2313yes—
541#380C2313yes—
542#380C2313yes—
543#380C2313yes—
544#380C2316yes—
545#380C2313yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553C4×C4⋊C4C2316yes—
554C4×C4⋊C4C2316yes—
555C4×C4⋊C4C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2316yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2316yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2316yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
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⋊C4C2316yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2311yescharacteristic
595C4×C4⋊C4C2316yes—
596C4×C22⋊C4C2313yes—
597C4×C22⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2316yes—
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2311yescharacteristic
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2316yes—
618#376C2313yes—
619#376C2313yes—
620#376C2313yes—
621#376C2316yes—
622#376C2313yes—
623#376C2316yes—
624C43C2313yes—
625C43C2316yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8#4118yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2411yescharacteristic
639C22×D4C2413yes—
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2416yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2411yescharacteristic
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2413yes—
654C4⋊Q8—212no—
655#127—212no—
656#126—46no—
657#126—412no—
658#126—46no—
659#126—86no—
660#125—212no—
661#125—212no—
662#125—86no—
663#124—212no—
664#124—212no—
665#124—86no—
666#123—46no—
667#123—46no—
668#123—86no—
669C22⋊Q8—212no—
670C22⋊Q8—212no—
671#121—212no—
672#121—212no—
673#121—212no—
674#121—212no—
675C4×Q8—212no—
676C4×Q8—212no—
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—24no—
686C4×Q8—24no—
687C4×Q8—212no—
688C4×Q8—212no—
689C4×Q8—212no—
690C4×Q8—212no—
691C4×Q8—212no—
692C4×Q8#4118yes—
693C4×Q8#4118yes—
694C4×D4—212no—
695C4×D4—212no—
696C4×D4—212no—
697C4×D4—212no—
698C4×D4—212no—
699C4×D4—212no—
700C4×D4—212no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—86no—
704#117—212no—
705#117—212no—
706#117—212no—
707#117—212no—
708#117—212no—
709#117—212no—
710#117—412no—
711C2×C4⋊C4—212no—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2416yes—
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⋊C4C2413yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C22⋊C4C2411yescharacteristic
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2416yes—
767C2×C22⋊C4C2416yes—
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2416yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2416yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C42—212no—
805C2×C42—212no—
806C2×C42—212no—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2416yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2416yes—
813C2×C42C2411yescharacteristic
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2416yes—
828C2×C42C2416yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2416yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2411yescharacteristic
836C2×C42C2416yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839#95C2411yescharacteristic
840#95C2413yes—
841#95C2413yes—
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2413yes—
851#95C2413yes—
852#95C2416yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2416yes—
860#95C2416yes—
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2413yes—
869#95C2413yes—
870#95C2411yescharacteristic
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2413yes—
889#95C2413yes—
890#95C2411yescharacteristic
891#95C2416yes—
892#95C2416yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2416yes—
901#95C2413yes—
902#95C2413yes—
903C24C2513yes—
904C24C2513yes—
905C24C2511yescharacteristic
906#41—416no—
907#41—416no—
908C2×Q8—232no—
909C2×Q8—26no—
910C2×Q8—26no—
911C2×Q8—26no—
912C2×Q8—43no—
913C2×Q8—43no—
914C2×Q8C2×#41112yes—
915C2×Q8C2×#4114yes—
916C2×Q8C2×#4114yes—
917C2×Q8C2×#4114yes—
918C2×D4—26no—
919C2×D4—26no—
920C2×D4—26no—
921C2×D4—26no—
922C2×D4—26no—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—212no—
928C2×D4—43no—
929C2×D4—43no—
930C2×D4—46no—
931C2×D4—43no—
932C2×D4—43no—
933C2×D4—43no—
934C2×D4—46no—
935C2×D4—43no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—22no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—22no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—41no—
953C22×C4—43no—
954C22×C4—43no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4C2×#41112yes—
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C22×C4C2513yes—
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2513yes—
972C22×C4C2513yes—
973C22×C4C2511yescharacteristic
974C22×C4C2513yes—
975C22×C4C2513yes—
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2511yescharacteristic
987C22×C4C2513yes—
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2513yes—
991C4⋊C4—212no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—22no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—22no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—212no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—22no—
1016C4⋊C4—26no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—43no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—43no—
1024C4⋊C4—46no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—46no—
1036C4⋊C4—46no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4C2×#41112yes—
1040C4⋊C4C2×#41112yes—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—26no—
1044C22⋊C4—22no—
1045C22⋊C4—26no—
1046C22⋊C4—22no—
1047C22⋊C4—212no—
1048C22⋊C4—212no—
1049C22⋊C4—26no—
1050C22⋊C4—26no—
1051C22⋊C4—26no—
1052C22⋊C4—26no—
1053C22⋊C4—212no—
1054C22⋊C4—212no—
1055C22⋊C4—26no—
1056C22⋊C4—26no—
1057C22⋊C4—26no—
1058C22⋊C4—22no—
1059C22⋊C4—43no—
1060C22⋊C4—43no—
1061C22⋊C4—43no—
1062C22⋊C4—41no—
1063C22⋊C4—46no—
1064C22⋊C4—46no—
1065C22⋊C4—43no—
1066C22⋊C4—46no—
1067C22⋊C4—46no—
1068C22⋊C4—43no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—46no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—46no—
1076C22⋊C4—46no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—46no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C42—22no—
1084C42—22no—
1085C42—26no—
1086C42—26no—
1087C42—26no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—212no—
1094C42—212no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—22no—
1102C42—26no—
1103C42—43no—
1104C42—41no—
1105C42—46no—
1106C42—46no—
1107C42—46no—
1108C42—43no—
1109C42—43no—
1110C42—46no—
1111C42—43no—
1112C42—43no—
1113C42C2×#41112yes—
1114C42C2×#41112yes—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—23no—
1122C23—23no—
1123C23—23no—
1124C23—23no—
1125C23—23no—
1126C23—23no—
1127C23—23no—
1128C23—23no—
1129C23—23no—
1130C23—23no—
1131C23—23no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23C22×#4112yes—
1136C23C2611yescharacteristic
1137Q8—224no—
1138Q8—86no—
1139Q8#529116yes—
1140D4—412no—
1141D4—412no—
1142D4—412no—
1143D4—812no—
1144D4—86no—
1145D4—86no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—224no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—21no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—21no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—412no—
1222C2×C4—44no—
1223C2×C4—412no—
1224C2×C4—412no—
1225C2×C4—86no—
1226C2×C4—86no—
1227C2×C4—86no—
1228C2×C4—86no—
1229C2×C4C22×#4116yes—
1230C2×C4C22×#4112yes—
1231C2×C4C22×#4116yes—
1232C2×C4C22×#4116yes—
1233C2×C4C22×#4112yes—
1234C2×C4C22×#4116yes—
1235C2×C4C22×#4116yes—
1236C2×C4C22×#4116yes—
1237C2×C4#58512yes—
1238C2×C4#58512yes—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—43no—
1247C22—43no—
1248C22—43no—
1249C22—43no—
1250C22—43no—
1251C22—43no—
1252C22—43no—
1253C22—43no—
1254C22—43no—
1255C22—43no—
1256C22—43no—
1257C22—43no—
1258C22—43no—
1259C22—43no—
1260C22C23×#4111yescharacteristic
1261C22C23×#4111yescharacteristic
1262C22C23×#4111yescharacteristic
1263C22C2×#58511yescharacteristic
1264C22C2×#58511yescharacteristic
1265C22H(7,𝔽2)11yescharacteristic
1266C222−1+611yescharacteristic
1267C4—22no—
1268C4—26no—
1269C4—22no—
1270C4—22no—
1271C4—22no—
1272C4—26no—
1273C4—26no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—43no—
1279C4—43no—
1280C4—41no—
1281C4—43no—
1282C4—43no—
1283C4—43no—
1284C4—43no—
1285C4—43no—
1286C4—43no—
1287C4—41no—
1288C4—43no—
1289C4—41no—
1290C4—43no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4C2×#529112yes—
1295C2—42no—
1296C2—83no—
1297C2—83no—
1298C2C22×#52911yescharacteristic
1299C2#6279311yescharacteristic
1300C2#6285711yescharacteristic
1301C2#6299311yescharacteristic
1302C2#6300511yescharacteristic
1303C2#6300611yescharacteristic
1304C2#6300611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36018C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36589C2semidirect
2. #36578C2semidirect
3. #36483C2semidirect
4. #36461C2semidirect
5. #36458C2semidirect
6. #36458C2semidirect
7. #36414C2semidirect
8. #36413C2semidirect
9. #36050C2semidirect
10. #36049C2semidirect
11. #36026C2semidirect
13. #35968C2semidirect
14. #35868C2semidirect
15. #35813C2semidirect
16. #35786C2semidirect
17. #35591C2semidirect
18. #35590C2semidirect
19. #35587C2semidirect
20. #35586C2semidirect
21. #35287C2semidirect
22. #35186C2semidirect
23. #34898C2semidirect
24. #34879C2semidirect
25. #34336C2semidirect
26. #34293C2semidirect
27. #34293C2semidirect
28. #34197C2semidirect
29. #34193C2semidirect
30. C4×#550C2semidirect
31. C4×#519C2semidirect

Maximal subgroups

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

subgroupindex
#365892
#365782
#364832
#364612
#364582
#364142
#364132
#360502
#360492
#360262
#360182
#359682
#358682
#358132
#357862
#355912
#355902
#355872
#355862
#352872
#351862
#348982
#348792
#343362
#342932
#341972
#341932
C4×#5502
C4×#5192