Finite Group Databasebeta

← #7687607

Subgroups — #7687607

Order 512.

4679 conjugacy classes of subgroups.

The subgroup lattice has 1257 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59717C213yesmaximal, complemented
2#59713C213yesmaximal, complemented
3#59709C213yesmaximal, complemented
4#59427C213yesmaximal, complemented
5#59245C213yesmaximal, complemented
6#45370C213yesmaximal, complemented
7#45001C213yesmaximal, complemented
8#44983C213yesmaximal, complemented
9#44911C213yesmaximal, complemented
10#39801C213yesmaximal, complemented
11#39295C213yesmaximal, complemented
12#38236C213yesmaximal, complemented
13#37960C213yesmaximal, complemented
14Q8×#126C211yesmaximal, characteristic, complemented
15#36512C213yesmaximal, complemented
16#36467C211yesmaximal, characteristic
17#36458C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic, complemented
19#36431C211yesmaximal, characteristic, complemented
20#36371C213yesmaximal, complemented
21#35948C211yesmaximal, characteristic
22#35937C211yesmaximal, characteristic, complemented
23#35898C211yesmaximal, characteristic, complemented
24#35786C211yesmaximal, characteristic, complemented
25#34867C213yesmaximal, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34336C211yesmaximal, characteristic, complemented
28#34293C211yesmaximal, characteristic
29#34262C211yesmaximal, characteristic, complemented
30C4×Q82C211yesmaximal, characteristic, complemented
31#34129C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2863C2213yes—
39#2863C2213yes—
40#2861C2213yes—
41#2860C2213yes—
42#2851C2213yes—
43#2800C2216yes—
44#2798C2216yes—
45#2789C2216yes—
46#2788C2216yes—
47#2788C2216yes—
48#2787C2216yes—
49#2783C2216yes—
50#2783C2216yes—
51#2777C2216yes—
52#2775C2216yes—
53#2759C2216yes—
54#2727C2216yes—
55#2716C2216yes—
56#2715C2216yes—
57#2660C2213yes—
58#2644C2213yes—
59#2640C2213yes—
60#2629C2213yes—
61#2605C2213yes—
62#2604C2213yes—
63#2604C2216yes—
64#2601C2213yes—
65#2599C2213yes—
66#2599C2216yes—
67#2594C2213yes—
68#2594C2216yes—
69#2592C2213yes—
70#2592C2216yes—
71#2592C2213yes—
72#2588C2213yes—
73#2588C2216yes—
74#2584C2213yes—
75#2582C2213yes—
76#2580C2213yes—
77#2577C2213yes—
78#2568C2216yes—
79#2566C2213yes—
80#2565C2213yes—
81#2562C2213yes—
82#2560C2213yes—
83#2551C2213yes—
84#2551C2213yes—
85#2550C2213yes—
86#2550C2213yes—
87#2547C2213yes—
88#2546C2213yes—
89#2545C2216yes—
90#2533C2216yes—
91#2532C2216yes—
92#2532C2213yes—
93#2528C2213yes—
94#2525C2216yes—
95#2524C2213yes—
96#2523C2216yes—
97#2521C2213yes—
98#2514C2213yes—
99#2514C2213yes—
100#2513C2213yes—
101#2513C2213yes—
102#2512C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2512C2213yes—
106#2511C2213yes—
107#2511C2213yes—
108#2511C2213yes—
109#2511C2213yes—
110#2509C2216yes—
111#2497C2213yes—
112#2497C2213yes—
113#2497C2213yes—
114#2497C2213yes—
115#2497C2213yes—
116#2496C2213yes—
117#2496C2213yes—
118#2496C2213yes—
119#2495C2213yes—
120#2495C2213yes—
121#2494C2213yes—
122#2494C2213yes—
123#2492C2213yes—
124#2492C2213yes—
125#2492C2213yes—
126#2491C2213yes—
127#2491C2213yes—
128#2491C2213yes—
129#2490C2213yes—
130#2489C2213yes—
131#2478C2216yes—
132#2478C2213yes—
133#2478C2216yes—
134#2474C2213yes—
135#2474C2216yes—
136#2469C2216yes—
137#2469C2216yes—
138#2469C2211yescharacteristic
139#2465C2213yes—
140#2454C2213yes—
141#2453C2213yes—
142#2452C2213yes—
143#2451C2213yes—
144#2441C2213yes—
145#2441C2213yes—
146#2439C2213yes—
147#2439C2213yes—
148#2439C2216yes—
149#2401C2213yes—
150#2399C2213yes—
151#2398C2213yes—
152#2396C2213yes—
153#2373C2216yes—
154#2370C2213yes—
155#2370C2213yes—
156#2370C2213yes—
157#2370C2213yes—
158#2369C2213yes—
159#2369C2213yes—
160#2369C2213yes—
161#2369C2213yes—
162#2367C2213yes—
163#2365C2213yes—
164#2363C2213yes—
165#2362C2216yes—
166#2362C2213yes—
167#2356C2216yes—
168#2356C2213yes—
169#2355C2213yes—
170#2355C2213yes—
171#2354C2213yes—
172#2354C2213yes—
173#2354C2213yes—
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2213yes—
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2213yes—
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188#2347C2213yes—
189#2346C2213yes—
190#2346C2213yes—
191#2346C2213yes—
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202#2331C2213yes—
203#2330C2213yes—
204#2330C2213yes—
205#2330C2213yes—
206#2326C2213yes—
207#2324C2213yes—
208#2320C2213yes—
209#2314C2213yes—
210C4×C4⋊Q8C2213yes—
211C4×C4⋊Q8C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×C4⋊Q8C2213yes—
214C4×#125C2213yes—
215C4×#126C2213yes—
216C4×#126C2213yes—
217C4×#126C2213yes—
218C4×#124C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221#2298C2213yes—
222#2295C2213yes—
223#2295C2213yes—
224#2295C2213yes—
225#2293C2213yes—
226#2293C2213yes—
227#2290C2213yes—
228#2285C2213yes—
229#2276C2211yescharacteristic
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232C42×Q8C2213yes—
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—28no—
241#557—28no—
242#557—28no—
243#548—28no—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2316yes—
250C2×#126C2311yescharacteristic
251C2×#126C2313yes—
252C2×#126C2313yes—
253C2×#126C2316yes—
254C2×#126C2316yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×#121C2313yes—
265#519—28no—
266C4×#41—28no—
267C2×C4×Q8C2313yes—
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2316yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2316yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×#117C2313yes—
293C2×#117C2313yes—
294C2×#117C2313yes—
295C2×#117C2313yes—
296C2×#117C2313yes—
297C2×#117C2316yes—
298C22×C42C2313yes—
299#401C2313yes—
300#401C2316yes—
301#400C2316yes—
302#400C2313yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2316yes—
310#400C2311yescharacteristic
311#400C2313yes—
312#400C2316yes—
313#400C2316yes—
314#399C2316yes—
315#399C2313yes—
316#398C2313yes—
317#398C2313yes—
318#398C2316yes—
319#398C2313yes—
320#398C2313yes—
321#398C2316yes—
322#398C2313yes—
323#398C2313yes—
324#398C2316yes—
325#397C2313yes—
326#397C2313yes—
327#397C2313yes—
328#397C2316yes—
329#397C2316yes—
330#397C2316yes—
331#397C2316yes—
332#397C2313yes—
333#397C2316yes—
334#397C2313yes—
335#397C2316yes—
336#397C2316yes—
337#396C2316yes—
338#396C2316yes—
339#396C2313yes—
340#396C2311yescharacteristic
341#396C2313yes—
342#396C2316yes—
343#396C2316yes—
344#396C2316yes—
345#396C2316yes—
346#395C2313yes—
347#395C2316yes—
348#395C2313yes—
349#395C2311yescharacteristic
350#395C2316yes—
351#395C2313yes—
352#395C2313yes—
353#394C2313yes—
354#394C2316yes—
355#394C2313yes—
356#393C2313yes—
357#393C2316yes—
358#393C2313yes—
359#393C2316yes—
360#393C2316yes—
361#393C2311yescharacteristic
362#393C2316yes—
363#391C2313yes—
364#391C2313yes—
365#391C2316yes—
366#391C2316yes—
367#391C2316yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2316yes—
373#391C2316yes—
374#391C2316yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2316yes—
384#391C2313yes—
385#391C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2316yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#390C2313yes—
397#390C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2316yes—
404#389C2316yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2316yes—
410#389C2316yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2316yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2316yes—
421#389C2316yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2313yes—
426#389C2313yes—
427#389C2316yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2311yescharacteristic
437#388C2311yescharacteristic
438#388C2313yes—
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2313yes—
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2316yes—
449#388C2313yes—
450#388C2316yes—
451#388C2313yes—
452#388C2316yes—
453#388C2316yes—
454#388C2316yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2311yescharacteristic
460#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2313yes—
468#388C2316yes—
469#388C2313yes—
470#388C2316yes—
471#388C2311yescharacteristic
472#388C2311yescharacteristic
473#387C2311yescharacteristic
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2313yes—
489#387C2311yescharacteristic
490#387C2313yes—
491#387C2313yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2311yescharacteristic
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2316yes—
512#387C2316yes—
513#387C2313yes—
514#386C2313yes—
515#386C2313yes—
516#385C2313yes—
517#385C2316yes—
518#385C2313yes—
519#385C2316yes—
520#385C2313yes—
521#385C2313yes—
522#385C2316yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#383C2313yes—
532#383C2313yes—
533#383C2313yes—
534#383C2316yes—
535#383C2316yes—
536#382C2313yes—
537#382C2313yes—
538#382C2316yes—
539#382C2316yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#380C2313yes—
544#380C2313yes—
545#380C2313yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
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⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2316yes—
566C4×C4⋊C4C2316yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2316yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2316yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2316yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊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⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2316yes—
620C43C2313yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2411yescharacteristic
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2413yes—
634C22×Q8C2416yes—
635C22×Q8C2411yescharacteristic
636C22×D4C2413yes—
637C22×D4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C4⋊Q8—212no—
643C4⋊Q8—212no—
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646C4⋊Q8—212no—
647C4⋊Q8—86no—
648#126—24no—
649#126—46no—
650#126—46no—
651#126—412no—
652#126—86no—
653#125—212no—
654#125—212no—
655#125—212no—
656#125—212no—
657#124—212no—
658#124—46no—
659#124—86no—
660C22⋊Q8—212no—
661C22⋊Q8—212no—
662#121—212no—
663C4×Q8—24no—
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—24no—
674C4×Q8—212no—
675C4×Q8—24no—
676C4×Q8—212no—
677C4×Q8—212no—
678C4×Q8—212no—
679C4×Q8—212no—
680C4×Q8—412no—
681C4×Q8—46no—
682C4×Q8—86no—
683C4×Q8#4118yes—
684C4×Q8#4118yes—
685C4×D4—212no—
686C4×D4—212no—
687C4×D4—212no—
688#117—212no—
689#117—212no—
690#117—212no—
691#117—46no—
692#117—46no—
693#117—86no—
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2416yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2411yescharacteristic
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2416yes—
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2411yescharacteristic
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2411yescharacteristic
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2416yes—
769C2×C22⋊C4C2416yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
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×C42—212no—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2416yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2411yescharacteristic
800C2×C42C2413yes—
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2416yes—
813C2×C42C2416yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2416yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2413yes—
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#95C2416yes—
842#95C2416yes—
843#95C2413yes—
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2411yescharacteristic
860#95C2416yes—
861#95C2416yes—
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2413yes—
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2413yes—
869#95C2413yes—
870#95C2411yescharacteristic
871#95C2416yes—
872#95C2413yes—
873#95C2413yes—
874#95C2416yes—
875#95C2416yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2416yes—
880#95C2416yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889C24C2511yescharacteristic
890C24C2513yes—
891#41—416no—
892C2×Q8—22no—
893C2×Q8—26no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—212no—
898C2×Q8—22no—
899C2×Q8—26no—
900C2×Q8—26no—
901C2×Q8—22no—
902C2×Q8—43no—
903C2×Q8—46no—
904C2×Q8—43no—
905C2×Q8—46no—
906C2×Q8—43no—
907C2×Q8—416no—
908C2×Q8C2×#4114yes—
909C2×Q8C2×#4114yes—
910C2×Q82−1+414yes—
911C2×D4—26no—
912C2×D4—26no—
913C2×D4—26no—
914C2×D4—26no—
915C2×D4—43no—
916C2×D4—43no—
917C22×C4—26no—
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—43no—
927C22×C4—43no—
928C22×C4—43no—
929C22×C4C2511yescharacteristic
930C22×C4C2513yes—
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—212no—
979C4⋊C4—212no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—22no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—46no—
997C4⋊C4—46no—
998C4⋊C4—46no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—46no—
1002C4⋊C4—46no—
1003C4⋊C4—43no—
1004C4⋊C4—46no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4C2×#41112yes—
1015C4⋊C4C2×#41112yes—
1016C4⋊C42−1+414yes—
1017C22⋊C4—26no—
1018C22⋊C4—22no—
1019C22⋊C4—212no—
1020C22⋊C4—22no—
1021C22⋊C4—26no—
1022C22⋊C4—212no—
1023C22⋊C4—26no—
1024C22⋊C4—26no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—26no—
1029C22⋊C4—26no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—43no—
1033C22⋊C4—43no—
1034C22⋊C4—46no—
1035C22⋊C4—46no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—43no—
1040C22⋊C4—46no—
1041C22⋊C4—43no—
1042C22⋊C4—43no—
1043C22⋊C4—43no—
1044C22⋊C4—43no—
1045C22⋊C4—46no—
1046C22⋊C4—46no—
1047C22⋊C4—43no—
1048C42—22no—
1049C42—26no—
1050C42—26no—
1051C42—26no—
1052C42—212no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—22no—
1060C42—22no—
1061C42—22no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—22no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—43no—
1071C42—43no—
1072C42—43no—
1073C42—43no—
1074C42—43no—
1075C42—43no—
1076C42—43no—
1077C42—46no—
1078C42—46no—
1079C42—46no—
1080C42—43no—
1081C42C2×#41112yes—
1082C42C2×#41112yes—
1083C23—21no—
1084C23—23no—
1085C23—23no—
1086C23—21no—
1087C23—21no—
1088C23—23no—
1089C23—21no—
1090C23—23no—
1091C23—21no—
1092C23—23no—
1093C23—23no—
1094C23—21no—
1095C23—23no—
1096C23—21no—
1097C23C2611yescharacteristic
1098Q8—28no—
1099Q8—412no—
1100Q8—412no—
1101Q8—86no—
1102Q8—812no—
1103Q8#556116yes—
1104D4—412no—
1105D4—86no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—23no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
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—23no—
1150C2×C4—23no—
1151C2×C4—21no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—23no—
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—21no—
1181C2×C4—412no—
1182C2×C4—412no—
1183C2×C4—412no—
1184C2×C4—412no—
1185C2×C4C22×#4116yes—
1186C2×C4C22×#4112yes—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4116yes—
1189C2×C4C22×#4116yes—
1190C2×C4C22×#4116yes—
1191C2×C4C2×2−1+412yes—
1192C2×C4C2×2−1+412yes—
1193C2×C4C2×2−1+412yes—
1194C2×C4C2×2−1+416yes—
1195C2×C4#58512yes—
1196C2×C4#58512yes—
1197C22—41no—
1198C22—43no—
1199C22—43no—
1200C22—41no—
1201C22—41no—
1202C22—43no—
1203C22—43no—
1204C22—41no—
1205C22—43no—
1206C22—41no—
1207C22—41no—
1208C22—43no—
1209C22—41no—
1210C22—43no—
1211C22C23×#4111yescharacteristic
1212C22C23×#4111yescharacteristic
1213C22C22×2−1+411yescharacteristic
1214C22C22×2−1+411yescharacteristic
1215C22C2×#58511yescharacteristic
1216C22C2×#58511yescharacteristic
1217C22H(7,𝔽2)11yescharacteristic
1218C4—26no—
1219C4—22no—
1220C4—26no—
1221C4—22no—
1222C4—22no—
1223C4—22no—
1224C4—22no—
1225C4—22no—
1226C4—22no—
1227C4—43no—
1228C4—43no—
1229C4—43no—
1230C4—41no—
1231C4—41no—
1232C4—43no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—43no—
1237C4—43no—
1238C4—41no—
1239C4—43no—
1240C4—43no—
1241C4—43no—
1242C4—43no—
1243C4—43no—
1244C4—41no—
1245C4—43no—
1246C4C2×#556112yes—
1247C2—81no—
1248C2—83no—
1249C2C22×#55611yescharacteristic
1250C2#6278811yescharacteristic
1251C2#6279311yescharacteristic
1252C2#6295211yescharacteristic
1253C2#6299411yescharacteristic
1254C2#6300011yescharacteristic
1255C2#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. #59717C2semidirect
2. #59713C2semidirect
3. #59709C2semidirect
4. #59427C2semidirect
5. #59245C2semidirect
6. #45370C2semidirect
7. #45001C2semidirect
8. #44983C2semidirect
9. #44911C2semidirect
10. #39801C2semidirect
11. #39295C2semidirect
12. #38236C2semidirect
13. #37960C2semidirect
14. Q8×#126C2semidirect
15. #36512C2semidirect
17. #36458C2semidirect
18. #36448C2semidirect
19. #36431C2semidirect
20. #36371C2semidirect
22. #35937C2semidirect
23. #35898C2semidirect
24. #35786C2semidirect
25. #34867C2semidirect
26. #34337C2semidirect
27. #34336C2semidirect
29. #34262C2semidirect
30. C4×Q82C2semidirect
31. #34129C2semidirect

Maximal subgroups

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

subgroupindex
#597172
#597132
#597092
#594272
#592452
#453702
#450012
#449832
#449112
#398012
#392952
#382362
#379602
Q8×#1262
#365122
#364672
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