Finite Group Databasebeta

← #7685717

Subgroups — #7685717

Order 512.

4684 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59716C213yesmaximal, complemented
2#59712C213yesmaximal, complemented
3#59574C213yesmaximal, complemented
4#59437C213yesmaximal, complemented
5#59234C213yesmaximal, complemented
6#45370C213yesmaximal, complemented
7#45124C213yesmaximal, complemented
8#45039C213yesmaximal, complemented
9#44984C213yesmaximal, complemented
10#39800C213yesmaximal, complemented
11#39294C213yesmaximal, complemented
12#38241C213yesmaximal, complemented
13#37960C213yesmaximal, complemented
14#36585C211yesmaximal, characteristic, complemented
15#36503C213yesmaximal, complemented
16#36467C211yesmaximal, characteristic
17#36458C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic, complemented
19#36435C211yesmaximal, characteristic, complemented
20#36395C213yesmaximal, complemented
21#35948C211yesmaximal, characteristic
22#35937C211yesmaximal, characteristic, complemented
23#35883C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic, complemented
25#34867C213yesmaximal, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34336C211yesmaximal, characteristic, complemented
28#34294C211yesmaximal, characteristic
29#34263C211yesmaximal, characteristic, complemented
30C4×Q82C211yesmaximal, characteristic, complemented
31Q8×#117C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2863C2213yes—
39#2861C2213yes—
40#2860C2213yes—
41#2860C2213yes—
42#2851C2213yes—
43#2805C2216yes—
44#2789C2216yes—
45#2788C2216yes—
46#2787C2216yes—
47#2787C2216yes—
48#2783C2216yes—
49#2776C2216yes—
50#2775C2216yes—
51#2775C2216yes—
52#2759C2216yes—
53#2745C2216yes—
54#2716C2216yes—
55#2715C2216yes—
56#2689C2216yes—
57#2660C2213yes—
58#2645C2213yes—
59#2640C2213yes—
60#2629C2213yes—
61#2605C2213yes—
62#2604C2213yes—
63#2601C2213yes—
64#2599C2216yes—
65#2599C2211yescharacteristic
66#2596C2216yes—
67#2594C2216yes—
68#2594C2216yes—
69#2594C2213yes—
70#2594C2216yes—
71#2592C2213yes—
72#2592C2213yes—
73#2588C2213yes—
74#2588C2216yes—
75#2584C2213yes—
76#2581C2213yes—
77#2577C2216yes—
78#2577C2213yes—
79#2566C2213yes—
80#2565C2213yes—
81#2562C2213yes—
82#2560C2213yes—
83#2551C2213yes—
84#2551C2213yes—
85#2550C2213yes—
86#2550C2213yes—
87#2547C2213yes—
88#2547C2216yes—
89#2546C2213yes—
90#2538C2213yes—
91#2532C2213yes—
92#2528C2213yes—
93#2527C2216yes—
94#2524C2213yes—
95#2521C2213yes—
96#2514C2213yes—
97#2514C2213yes—
98#2514C2216yes—
99#2514C2213yes—
100#2514C2213yes—
101#2513C2213yes—
102#2513C2213yes—
103#2513C2213yes—
104#2513C2213yes—
105#2512C2213yes—
106#2512C2213yes—
107#2511C2213yes—
108#2511C2213yes—
109#2497C2213yes—
110#2497C2213yes—
111#2496C2213yes—
112#2496C2213yes—
113#2495C2213yes—
114#2495C2213yes—
115#2495C2213yes—
116#2494C2213yes—
117#2494C2213yes—
118#2494C2213yes—
119#2494C2213yes—
120#2494C2213yes—
121#2492C2213yes—
122#2492C2216yes—
123#2492C2213yes—
124#2492C2213yes—
125#2491C2213yes—
126#2491C2213yes—
127#2491C2213yes—
128#2490C2213yes—
129#2489C2213yes—
130#2478C2213yes—
131#2478C2216yes—
132#2474C2213yes—
133#2474C2216yes—
134#2469C2213yes—
135#2469C2216yes—
136#2466C2216yes—
137#2465C2213yes—
138#2465C2216yes—
139#2454C2213yes—
140#2453C2213yes—
141#2452C2213yes—
142#2451C2213yes—
143#2446C2216yes—
144#2442C2213yes—
145#2442C2213yes—
146#2440C2213yes—
147#2440C2213yes—
148#2415C2216yes—
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#2369C2213yes—
163#2367C2213yes—
164#2367C2216yes—
165#2361C2213yes—
166#2360C2213yes—
167#2357C2213yes—
168#2355C2213yes—
169#2355C2213yes—
170#2355C2213yes—
171#2355C2213yes—
172#2354C2213yes—
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2213yes—
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186D4×C4⋊C4C2213yes—
187#2347C2216yes—
188#2345C2213yes—
189#2345C2213yes—
190#2345C2213yes—
191#2344C2213yes—
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#2331C2213yes—
204#2330C2213yes—
205#2330C2213yes—
206#2326C2213yes—
207#2323C2213yes—
208#2319C2213yes—
209#2314C2213yes—
210C4×C4⋊Q8C2213yes—
211C4×C4⋊Q8C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#125C2213yes—
214C4×#125C2213yes—
215C4×#126C2213yes—
216C4×#126C2213yes—
217C4×#126C2213yes—
218C4×#124C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×#121C2213yes—
221#2298C2213yes—
222#2295C2213yes—
223#2295C2213yes—
224#2295C2213yes—
225#2295C2213yes—
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
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×#126C2313yes—
251C2×#126C2313yes—
252C2×#126C2313yes—
253C2×#126C2316yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#124C2313yes—
259C2×#124C2316yes—
260C2×#124C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2316yes—
264C2×#121C2313yes—
265#520—28no—
266C2×C4×Q8—28no—
267C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2316yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2316yes—
292C2×#117C2313yes—
293C2×#117C2311yescharacteristic
294C2×#117C2316yes—
295C2×#117C2313yes—
296C22×C4⋊C4C2313yes—
297C22×C4⋊C4C2313yes—
298C22×C42C2313yes—
299#401C2316yes—
300#401C2313yes—
301#401C2316yes—
302#401C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2316yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2316yes—
313#400C2316yes—
314#400C2316yes—
315#400C2316yes—
316#399C2313yes—
317#398C2313yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2313yes—
322#398C2313yes—
323#398C2316yes—
324#398C2313yes—
325#398C2313yes—
326#398C2311yescharacteristic
327#397C2313yes—
328#397C2316yes—
329#397C2316yes—
330#397C2313yes—
331#397C2313yes—
332#397C2316yes—
333#397C2316yes—
334#397C2313yes—
335#397C2311yescharacteristic
336#397C2316yes—
337#397C2316yes—
338#397C2316yes—
339#397C2316yes—
340#396C2313yes—
341#396C2316yes—
342#396C2316yes—
343#396C2313yes—
344#396C2313yes—
345#396C2316yes—
346#395C2316yes—
347#395C2313yes—
348#395C2313yes—
349#395C2316yes—
350#395C2311yescharacteristic
351#395C2313yes—
352#395C2313yes—
353#395C2316yes—
354#394C2313yes—
355#394C2316yes—
356#394C2313yes—
357#393C2313yes—
358#393C2313yes—
359#393C2316yes—
360#393C2311yescharacteristic
361#393C2316yes—
362#393C2316yes—
363#391C2313yes—
364#391C2316yes—
365#391C2316yes—
366#391C2316yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2316yes—
376#391C2316yes—
377#391C2313yes—
378#391C2316yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2316yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#390C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2316yes—
404#389C2313yes—
405#389C2313yes—
406#389C2316yes—
407#389C2316yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2316yes—
412#389C2313yes—
413#389C2316yes—
414#389C2316yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2316yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#388C2311yescharacteristic
435#388C2313yes—
436#388C2313yes—
437#388C2313yes—
438#388C2313yes—
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2313yes—
444#388C2313yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2313yes—
449#388C2311yescharacteristic
450#388C2313yes—
451#388C2316yes—
452#388C2316yes—
453#388C2316yes—
454#388C2313yes—
455#388C2313yes—
456#388C2316yes—
457#388C2316yes—
458#388C2313yes—
459#388C2316yes—
460#388C2313yes—
461#388C2316yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2313yes—
467#388C2316yes—
468#387C2311yescharacteristic
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2316yes—
484#387C2313yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2313yes—
489#387C2316yes—
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2311yescharacteristic
497#387C2313yes—
498#387C2316yes—
499#387C2316yes—
500#387C2311yescharacteristic
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2311yescharacteristic
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2313yes—
510#386C2313yes—
511#386C2313yes—
512#385C2316yes—
513#385C2316yes—
514#385C2316yes—
515#385C2313yes—
516#385C2316yes—
517#385C2313yes—
518#385C2316yes—
519#385C2311yescharacteristic
520#385C2311yescharacteristic
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#384C2313yes—
527#383C2311yescharacteristic
528#383C2313yes—
529#383C2313yes—
530#383C2316yes—
531#383C2316yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2316yes—
539#382C2313yes—
540#381C2316yes—
541#380C2313yes—
542#380C2313yes—
543#380C2313yes—
544#380C2313yes—
545#380C2313yes—
546#380C2316yes—
547#380C2316yes—
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⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
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⋊C4C2316yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
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×C4C2411yescharacteristic
641C23×C4C2413yes—
642C23×C4C2416yes—
643C4⋊Q8—212no—
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646C4⋊Q8—212no—
647C4⋊Q8—212no—
648C4⋊Q8—86no—
649#126—212no—
650#126—46no—
651#126—46no—
652#126—86no—
653#125—212no—
654#125—212no—
655#125—212no—
656#125—212no—
657#124—212no—
658#124—412no—
659#124—46no—
660C22⋊Q8—212no—
661C22⋊Q8—46no—
662C22⋊Q8—86no—
663#121—212no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—212no—
676C4×Q8—212no—
677C4×Q8—212no—
678C4×Q8—212no—
679C4×Q8—212no—
680C4×Q8—24no—
681C4×Q8—46no—
682C4×Q8—86no—
683C4×Q8#4118yes—
684C4×Q8#4118yes—
685C4×D4—212no—
686C4×D4—212no—
687C4×D4—212no—
688C4×D4—86no—
689#117—212no—
690#117—24no—
691#117—412no—
692#117—46no—
693C2×C4⋊C4—212no—
694C2×C4⋊C4—212no—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2411yescharacteristic
759C2×C22⋊C4C2411yescharacteristic
760C2×C22⋊C4C2411yescharacteristic
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2416yes—
763C2×C22⋊C4C2411yescharacteristic
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2416yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2416yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C42—212no—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2411yescharacteristic
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2411yescharacteristic
798C2×C42C2411yescharacteristic
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2416yes—
804C2×C42C2416yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2416yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
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#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2411yescharacteristic
842#95C2411yescharacteristic
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2416yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2416yes—
859#95C2416yes—
860#95C2416yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2413yes—
870#95C2413yes—
871#95C2411yescharacteristic
872#95C2416yes—
873#95C2413yes—
874#95C2413yes—
875#95C2416yes—
876#95C2416yes—
877#95C2416yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2416yes—
882#95C2416yes—
883#95C2416yes—
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889C24C2513yes—
890C24C2511yescharacteristic
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—22no—
901C2×Q8—46no—
902C2×Q8—43no—
903C2×Q8—43no—
904C2×Q8—46no—
905C2×Q8—43no—
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—26no—
916C2×D4—43no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
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—46no—
929C22×C4—43no—
930C22×C4—46no—
931C22×C4—43no—
932C22×C4C2513yes—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2511yescharacteristic
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2513yes—
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—212no—
965C4⋊C4—22no—
966C4⋊C4—26no—
967C4⋊C4—22no—
968C4⋊C4—22no—
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—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—212no—
983C4⋊C4—212no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—22no—
998C4⋊C4—46no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—46no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—46no—
1005C4⋊C4—46no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—46no—
1009C4⋊C4—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—26no—
1021C22⋊C4—22no—
1022C22⋊C4—26no—
1023C22⋊C4—22no—
1024C22⋊C4—26no—
1025C22⋊C4—26no—
1026C22⋊C4—22no—
1027C22⋊C4—26no—
1028C22⋊C4—212no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—26no—
1032C22⋊C4—26no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—22no—
1036C22⋊C4—46no—
1037C22⋊C4—43no—
1038C22⋊C4—46no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—46no—
1042C22⋊C4—43no—
1043C22⋊C4—46no—
1044C22⋊C4—43no—
1045C22⋊C4—46no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C42—26no—
1050C42—26no—
1051C42—26no—
1052C42—26no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—26no—
1057C42—26no—
1058C42—26no—
1059C42—22no—
1060C42—26no—
1061C42—22no—
1062C42—22no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—43no—
1067C42—43no—
1068C42—46no—
1069C42—46no—
1070C42—43no—
1071C42—43no—
1072C42—43no—
1073C42—43no—
1074C42—43no—
1075C42—43no—
1076C42—46no—
1077C42—43no—
1078C42—43no—
1079C42—43no—
1080C42C2×#41112yes—
1081C42C2×#41112yes—
1082C422−1+414yes—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23—23no—
1096C23#58512yes—
1097C23C2611yescharacteristic
1098Q8—28no—
1099Q8—412no—
1100Q8—86no—
1101Q8—86no—
1102Q8—812no—
1103Q8#556116yes—
1104D4—412no—
1105D4—412no—
1106C2×C4—28no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
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—21no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—23no—
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—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—21no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
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—412no—
1184C2×C4—412no—
1185C2×C4—86no—
1186C2×C4—812no—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4116yes—
1189C2×C4C22×#4112yes—
1190C2×C4C22×#4116yes—
1191C2×C4C22×#4116yes—
1192C2×C4C22×#4116yes—
1193C2×C4C2×2−1+412yes—
1194C2×C4C2×2−1+412yes—
1195C2×C4C2×2−1+412yes—
1196C2×C4C2×2−1+416yes—
1197C2×C4#58512yes—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—43no—
1206C22—43no—
1207C22—43no—
1208C22—43no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22C23×#4111yescharacteristic
1213C22C23×#4111yescharacteristic
1214C22C22×2−1+411yescharacteristic
1215C22C22×2−1+411yescharacteristic
1216C22C2×#58511yescharacteristic
1217C22C2×#58511yescharacteristic
1218C22H(7,𝔽2)11yescharacteristic
1219C4—26no—
1220C4—26no—
1221C4—22no—
1222C4—22no—
1223C4—22no—
1224C4—22no—
1225C4—22no—
1226C4—22no—
1227C4—43no—
1228C4—43no—
1229C4—43no—
1230C4—41no—
1231C4—43no—
1232C4—43no—
1233C4—43no—
1234C4—41no—
1235C4—41no—
1236C4—43no—
1237C4—43no—
1238C4—41no—
1239C4—43no—
1240C4—41no—
1241C4—41no—
1242C4—43no—
1243C4—41no—
1244C4—43no—
1245C4—41no—
1246C4—43no—
1247C4C2×#556112yes—
1248C2—42no—
1249C2—83no—
1250C2C22×#55611yescharacteristic
1251C2#6278811yescharacteristic
1252C2#6278811yescharacteristic
1253C2#6294311yescharacteristic
1254C2#6299411yescharacteristic
1255C2#6300811yescharacteristic
1256C2#6303311yescharacteristic
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. #59716C2semidirect
2. #59712C2semidirect
3. #59574C2semidirect
4. #59437C2semidirect
5. #59234C2semidirect
6. #45370C2semidirect
7. #45124C2semidirect
8. #45039C2semidirect
9. #44984C2semidirect
10. #39800C2semidirect
11. #39294C2semidirect
12. #38241C2semidirect
13. #37960C2semidirect
14. #36585C2semidirect
15. #36503C2semidirect
17. #36458C2semidirect
18. #36448C2semidirect
19. #36435C2semidirect
20. #36395C2semidirect
22. #35937C2semidirect
23. #35883C2semidirect
24. #35816C2semidirect
25. #34867C2semidirect
26. #34336C2semidirect
27. #34336C2semidirect
29. #34263C2semidirect
30. C4×Q82C2semidirect
31. Q8×#117C2semidirect

Maximal subgroups

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

subgroupindex
#597162
#597122
#595742
#594372
#592342
#453702
#451242
#450392
#449842
#398002
#392942
#382412
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