Finite Group Databasebeta

← #7657185

Subgroups — #7657185

Order 512.

4838 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42939C213yesmaximal, complemented
2#42935C213yesmaximal, complemented
3#42925C213yesmaximal, complemented
4#42922C213yesmaximal, complemented
5#42622C213yesmaximal, complemented
6#42577C213yesmaximal, complemented
7#42556C213yesmaximal, complemented
8#42551C213yesmaximal, complemented
9#40077C213yesmaximal, complemented
10#40069C213yesmaximal, complemented
11#39533C213yesmaximal, complemented
12#39524C213yesmaximal, complemented
13#37524C213yesmaximal, complemented
14#37502C213yesmaximal, complemented
15Q8×#126C211yesmaximal, characteristic, complemented
16Q8×#125C211yesmaximal, characteristic, complemented
17#36445C211yesmaximal, characteristic, complemented
18#36432C211yesmaximal, characteristic, complemented
19#36005C211yesmaximal, characteristic, complemented
20#35996C211yesmaximal, characteristic, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35868C211yesmaximal, characteristic, complemented
23#35831C211yesmaximal, characteristic
24#35816C211yesmaximal, characteristic, complemented
25#35801C211yesmaximal, characteristic, complemented
26#35786C211yesmaximal, characteristic, complemented
27#35017C213yesmaximal, complemented
28#34592C213yesmaximal, complemented
29#34293C211yesmaximal, characteristic, complemented
30#34250C211yesmaximal, characteristic, complemented
31C4×#550C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41#2863C2213yes—
42#2859C2213yes—
43#2857C2213yes—
44#2855C2213yes—
45#2837C2216yes—
46#2836C2216yes—
47#2827C2216yes—
48#2827C2216yes—
49#2796C2216yes—
50#2796C2216yes—
51#2787C2216yes—
52#2786C2216yes—
53#2747C2216yes—
54#2740C2216yes—
55#2739C2216yes—
56#2728C2216yes—
57#2711C2216yes—
58#2707C2216yes—
59#2707C2216yes—
60#2705C2216yes—
61#2695C2216yes—
62#2694C2216yes—
63#2687C2216yes—
64#2681C2216yes—
65#2667C2213yes—
66#2667C2216yes—
67#2666C2213yes—
68#2664C2211yescharacteristic
69#2664C2216yes—
70#2663C2213yes—
71#2655C2213yes—
72#2654C2213yes—
73#2654C2216yes—
74#2653C2213yes—
75#2652C2213yes—
76#2652C2213yes—
77#2652C2213yes—
78#2649C2213yes—
79#2649C2213yes—
80#2647C2213yes—
81#2644C2213yes—
82#2638C2213yes—
83#2636C2213yes—
84#2633C2213yes—
85#2630C2213yes—
86#2629C2213yes—
87#2629C2213yes—
88#2625C2213yes—
89#2624C2213yes—
90#2624C2213yes—
91#2623C2216yes—
92#2620C2213yes—
93#2618C2216yes—
94#2585C2216yes—
95#2582C2213yes—
96#2570C2213yes—
97#2566C2213yes—
98#2565C2213yes—
99#2556C2216yes—
100#2552C2213yes—
101#2552C2213yes—
102#2552C2213yes—
103#2544C2213yes—
104#2542C2213yes—
105#2538C2213yes—
106#2538C2213yes—
107#2537C2213yes—
108#2513C2213yes—
109#2512C2213yes—
110#2512C2213yes—
111#2511C2213yes—
112#2511C2213yes—
113#2511C2213yes—
114#2509C2213yes—
115#2507C2213yes—
116#2507C2213yes—
117#2507C2213yes—
118#2507C2213yes—
119#2507C2213yes—
120#2506C2213yes—
121#2506C2213yes—
122#2502C2213yes—
123#2501C2213yes—
124#2500C2213yes—
125#2499C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2497C2213yes—
129#2497C2213yes—
130#2496C2213yes—
131#2494C2213yes—
132#2487C2213yes—
133#2486C2213yes—
134#2485C2213yes—
135#2485C2213yes—
136#2473C2216yes—
137#2466C2216yes—
138#2460C2216yes—
139#2454C2213yes—
140#2454C2213yes—
141#2454C2213yes—
142#2453C2213yes—
143#2452C2213yes—
144#2451C2213yes—
145#2449C2216yes—
146#2448C2213yes—
147#2448C2213yes—
148#2447C2213yes—
149#2447C2213yes—
150#2447C2213yes—
151#2447C2213yes—
152#2445C2213yes—
153#2445C2213yes—
154#2442C2213yes—
155#2441C2213yes—
156#2441C2213yes—
157#2441C2213yes—
158#2440C2213yes—
159#2439C2213yes—
160#2428C2213yes—
161#2427C2213yes—
162#2425C2216yes—
163#2423C2213yes—
164#2422C2213yes—
165#2422C2213yes—
166#2422C2213yes—
167#2422C2213yes—
168#2422C2213yes—
169#2421C2213yes—
170#2420C2213yes—
171#2419C2216yes—
172#2417C2213yes—
173#2416C2213yes—
174#2402C2213yes—
175#2401C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2395C2213yes—
179#2395C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2367C2213yes—
183#2366C2213yes—
184#2363C2213yes—
185#2363C2213yes—
186#2363C2213yes—
187#2362C2213yes—
188#2354C2213yes—
189#2354C2213yes—
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204#2349C2213yes—
205#2349C2213yes—
206D4×C4⋊C4C2213yes—
207D4×C4⋊C4C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2329C2216yes—
219#2326C2213yes—
220#2324C2213yes—
221#2318C2216yes—
222#2317C2213yes—
223#2316C2213yes—
224C4×#127C2213yes—
225C4×#125C2213yes—
226C4×#126C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×#123C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2296C2213yes—
233C2×#389C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—44no—
242#550—28no—
243#548—28no—
244#548—44no—
245C2×C4⋊Q8C2313yes—
246C2×#127C2313yes—
247C2×#126C2311yescharacteristic
248C2×#126C2316yes—
249C2×#125C2311yescharacteristic
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2316yes—
253C2×#125C2316yes—
254C2×#124C2313yes—
255C2×#124C2313yes—
256C2×#123C2313yes—
257C2×#123C2316yes—
258C2×#123C2316yes—
259C2×#123C2316yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2316yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2316yes—
270#520—28no—
271#520—44no—
272#519—44no—
273C4×#41—44no—
274C4×#41—44no—
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×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×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2316yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2316yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315#401C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2313yes—
322#400C2316yes—
323#400C2316yes—
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2311yescharacteristic
330#400C2313yes—
331#400C2313yes—
332#399C2316yes—
333#399C2316yes—
334#399C2313yes—
335#399C2316yes—
336#399C2316yes—
337#399C2313yes—
338#399C2313yes—
339#399C2313yes—
340#399C2311yescharacteristic
341#398C2313yes—
342#398C2316yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2316yes—
351#398C2316yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2311yescharacteristic
358#398C2311yescharacteristic
359#398C2313yes—
360#398C2313yes—
361#398C2311yescharacteristic
362#398C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2316yes—
366#397C2316yes—
367#397C2316yes—
368#397C2316yes—
369#397C2316yes—
370#397C2316yes—
371#397C2316yes—
372#397C2313yes—
373#397C2316yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2311yescharacteristic
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#396C2313yes—
385#396C2316yes—
386#396C2316yes—
387#396C2316yes—
388#396C2316yes—
389#396C2316yes—
390#396C2316yes—
391#396C2316yes—
392#396C2316yes—
393#396C2313yes—
394#396C2313yes—
395#396C2311yescharacteristic
396#396C2313yes—
397#396C2313yes—
398#396C2311yescharacteristic
399#395C2313yes—
400#395C2313yes—
401#394C2316yes—
402#394C2316yes—
403#394C2316yes—
404#394C2316yes—
405#394C2313yes—
406#394C2316yes—
407#394C2316yes—
408#394C2313yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#393C2313yes—
417#393C2313yes—
418#392C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2316yes—
423#391C2313yes—
424#391C2313yes—
425#391C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2316yes—
432#390C2316yes—
433#390C2313yes—
434#390C2313yes—
435#390C2316yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2316yes—
458#389C2316yes—
459#389C2316yes—
460#389C2316yes—
461#389C2316yes—
462#389C2313yes—
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#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2311yescharacteristic
484#389C2311yescharacteristic
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2316yes—
492#388C2313yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2311yescharacteristic
497#388C2313yes—
498#388C2311yescharacteristic
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2313yes—
514#387C2313yes—
515#387C2316yes—
516#387C2316yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#386C2316yes—
526#386C2316yes—
527#386C2316yes—
528#386C2313yes—
529#386C2313yes—
530#386C2316yes—
531#386C2316yes—
532#386C2313yes—
533#385C2316yes—
534#385C2316yes—
535#385C2316yes—
536#385C2313yes—
537#385C2313yes—
538#385C2316yes—
539#385C2316yes—
540#385C2316yes—
541#385C2313yes—
542#385C2316yes—
543#385C2316yes—
544#385C2316yes—
545#385C2313yes—
546#385C2313yes—
547#385C2313yes—
548#385C2313yes—
549#385C2313yes—
550#385C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2313yes—
561#384C2313yes—
562#383C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#381C2316yes—
568#381C2316yes—
569#381C2313yes—
570#380C2316yes—
571#380C2316yes—
572#380C2316yes—
573#380C2313yes—
574#380C2316yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
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⋊C4C2316yes—
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⋊C4C2311yescharacteristic
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624#376C2313yes—
625C2×#95C2316yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41#4118yes—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2411yescharacteristic
639C22×D4C2413yes—
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2416yes—
644C22×D4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2416yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2416yes—
654C4⋊Q8—46no—
655#127—212no—
656#126—24no—
657#126—86no—
658#125—24no—
659#125—46no—
660#125—46no—
661#125—86no—
662#125—86no—
663#124—212no—
664#124—46no—
665#123—46no—
666#123—86no—
667#123—86no—
668#123—86no—
669C22⋊Q8—212no—
670C22⋊Q8—412no—
671C22⋊Q8—46no—
672C22⋊Q8—46no—
673C22⋊Q8—86no—
674#121—212no—
675#121—212no—
676#121—212no—
677#121—46no—
678#121—86no—
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—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×D4—212no—
695C4×D4—212no—
696C4×D4—212no—
697C4×D4—212no—
698C4×D4—212no—
699C4×D4—46no—
700C4×D4—46no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706C4×D4—46no—
707C4×D4—86no—
708#117—212no—
709#117—46no—
710#117—46no—
711#117—46no—
712#117—46no—
713#117—46no—
714C2×C4⋊C4—212no—
715C2×C4⋊C4—46no—
716C2×C4⋊C4—86no—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C42—46no—
824C2×C42—46no—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2416yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2416yes—
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846C2×C42C2411yescharacteristic
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2416yes—
851#95C2411yescharacteristic
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
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#95C2413yes—
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2416yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907C24C2511yescharacteristic
908C24C2513yes—
909C24C2513yes—
910#41—232no—
911#41—416no—
912C2×Q8—26no—
913C2×Q8—26no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—43no—
917C2×Q8—43no—
918C2×Q8—416no—
919C2×Q8C2×#4114yes—
920C2×Q8H(5,𝔽2)14yes—
921C2×Q82−1+414yes—
922C2×D4—26no—
923C2×D4—26no—
924C2×D4—212no—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—26no—
931C2×D4—43no—
932C2×D4—43no—
933C2×D4—46no—
934C2×D4—43no—
935C2×D4—43no—
936C2×D4—46no—
937C2×D4—43no—
938C2×D4—43no—
939C2×D4C2×#41112yes—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—212no—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—43no—
953C22×C4—43no—
954C22×C4—43no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—46no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4—46no—
963C22×C4—46no—
964C22×C4—46no—
965C22×C4—46no—
966C22×C4C2×#41112yes—
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2513yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2513yes—
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C22×C4C2513yes—
988C22×C4C2513yes—
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—22no—
999C4⋊C4—22no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—26no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—41no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—46no—
1034C4⋊C4—41no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—46no—
1038C4⋊C4—46no—
1039C4⋊C4—46no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—46no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—46no—
1048C4⋊C4—46no—
1049C4⋊C4—46no—
1050C4⋊C4—46no—
1051C4⋊C4—46no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C22⋊C4—26no—
1060C22⋊C4—26no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—212no—
1064C22⋊C4—22no—
1065C22⋊C4—26no—
1066C22⋊C4—26no—
1067C22⋊C4—26no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—26no—
1072C22⋊C4—22no—
1073C22⋊C4—41no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—46no—
1078C22⋊C4—46no—
1079C22⋊C4—43no—
1080C22⋊C4—41no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C22⋊C4—46no—
1084C22⋊C4—46no—
1085C22⋊C4—43no—
1086C22⋊C4—46no—
1087C22⋊C4—46no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—46no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—46no—
1100C22⋊C4—43no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—41no—
1114C42—41no—
1115C42—43no—
1116C42—43no—
1117C42—46no—
1118C42—43no—
1119C42—43no—
1120C42—43no—
1121C42—46no—
1122C422−1+414yes—
1123C23—23no—
1124C23—23no—
1125C23—23no—
1126C23—23no—
1127C23—23no—
1128C23—23no—
1129C23—21no—
1130C23—23no—
1131C23—21no—
1132C23—23no—
1133C23—21no—
1134C23—23no—
1135C23—21no—
1136C23—23no—
1137C23—21no—
1138C23—23no—
1139C23—23no—
1140C23—21no—
1141C23—23no—
1142C23—21no—
1143C23C22×#4116yes—
1144C23C2611yescharacteristic
1145Q8—412no—
1146Q8—86no—
1147Q8#539116yes—
1148D4—224no—
1149D4—412no—
1150D4—412no—
1151D4—86no—
1152D4—812no—
1153D4—86no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—224no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—21no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—21no—
1203C2×C4—23no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—412no—
1232C2×C4—412no—
1233C2×C4—86no—
1234C2×C4—86no—
1235C2×C4—86no—
1236C2×C4—812no—
1237C2×C4—86no—
1238C2×C4—166no—
1239C2×C4C22×#4112yes—
1240C2×C4C22×#4116yes—
1241C2×C4C2×H(5,𝔽2)16yes—
1242C2×C4C2×2−1+412yes—
1243C2×C4C2×2−1+412yes—
1244C2×C4C2×2−1+412yes—
1245C2×C4C2×2−1+416yes—
1246C2×C4#58512yes—
1247C22—26no—
1248C22—26no—
1249C22—26no—
1250C22—43no—
1251C22—43no—
1252C22—43no—
1253C22—43no—
1254C22—43no—
1255C22—41no—
1256C22—41no—
1257C22—43no—
1258C22—43no—
1259C22—41no—
1260C22—43no—
1261C22—41no—
1262C22—41no—
1263C22—43no—
1264C22—41no—
1265C22—43no—
1266C22—41no—
1267C22—43no—
1268C22C23×#4111yescharacteristic
1269C22C22×H(5,𝔽2)11yescharacteristic
1270C22C22×2−1+411yescharacteristic
1271C22C22×2−1+411yescharacteristic
1272C22C2×#58511yescharacteristic
1273C22H(7,𝔽2)11yescharacteristic
1274C22H(7,𝔽2)11yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—43no—
1284C4—43no—
1285C4—43no—
1286C4—43no—
1287C4—43no—
1288C4—41no—
1289C4—43no—
1290C4—43no—
1291C4—43no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—43no—
1296C4—43no—
1297C4—41no—
1298C4—43no—
1299C4—41no—
1300C4—43no—
1301C4—43no—
1302C4C2×#539112yes—
1303C2—46no—
1304C2—83no—
1305C2—81no—
1306C2C22×#53911yescharacteristic
1307C2#6280511yescharacteristic
1308C2#6285811yescharacteristic
1309C2#6289911yescharacteristic
1310C2#6291711yescharacteristic
1311C2#6294311yescharacteristic
1312C2#6295211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35831C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42939C2semidirect
2. #42935C2semidirect
3. #42925C2semidirect
4. #42922C2semidirect
5. #42622C2semidirect
6. #42577C2semidirect
7. #42556C2semidirect
8. #42551C2semidirect
9. #40077C2semidirect
10. #40069C2semidirect
11. #39533C2semidirect
12. #39524C2semidirect
13. #37524C2semidirect
14. #37502C2semidirect
15. Q8×#126C2semidirect
16. Q8×#125C2semidirect
17. #36445C2semidirect
18. #36432C2semidirect
19. #36005C2semidirect
20. #35996C2semidirect
21. #35898C2semidirect
22. #35868C2semidirect
24. #35816C2semidirect
25. #35801C2semidirect
26. #35786C2semidirect
27. #35017C2semidirect
28. #34592C2semidirect
29. #34293C2semidirect
30. #34250C2semidirect
31. C4×#550C2semidirect

Maximal subgroups

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

subgroupindex
#429392
#429352
#429252
#429222
#426222
#425772
#425562
#425512
#400772
#400692
#395332
#395242
#375242
#375022
Q8×#1262
Q8×#1252
#364452
#364322
#360052
#359962
#358982
#358682
#358312
#358162
#358012
#357862
#350172
#345922
#342932
#342502
C4×#5502