Finite Group Databasebeta

← #7683620

Subgroups — #7683620

Order 512.

4668 conjugacy classes of subgroups.

The subgroup lattice has 1311 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59587C212yesmaximal, complemented
2#59527C214yesmaximal, complemented
3#59465C212yesmaximal, complemented
4#59453C214yesmaximal, complemented
5#59319C214yesmaximal, complemented
6#59230C212yesmaximal, complemented
7#59230C214yesmaximal, complemented
8#59155C212yesmaximal, complemented
9#45435C211yesmaximal, characteristic, complemented
10#45362C211yesmaximal, characteristic, complemented
11#45360C212yesmaximal, complemented
12#45164C211yesmaximal, characteristic, complemented
13#44948C211yesmaximal, characteristic, complemented
14#44945C212yesmaximal, complemented
15#43571C214yesmaximal, complemented
16#43567C214yesmaximal, complemented
17#43562C214yesmaximal, complemented
18#43561C214yesmaximal, complemented
19#35602C212yesmaximal, complemented
20#35581C212yesmaximal, complemented
21#35577C212yesmaximal, complemented
22#34941C212yesmaximal, complemented
23#34882C211yesmaximal, characteristic, complemented
24#34333C212yesmaximal, complemented
25#34287C212yesmaximal
26#34280C211yesmaximal, characteristic
27#34217C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#540C2211yescharacteristic
30C22×#125C2211yescharacteristic
31#2805C2214yes—
32#2792C2214yes—
33#2791C2214yes—
34#2790C2214yes—
35#2788C2214yes—
36#2784C2214yes—
37#2784C2214yes—
38#2784C2214yes—
39#2784C2214yes—
40#2784C2214yes—
41#2784C2214yes—
42#2780C2214yes—
43#2780C2214yes—
44#2774C2214yes—
45#2768C2214yes—
46#2755C2214yes—
47#2748C2214yes—
48#2734C2214yes—
49#2729C2214yes—
50#2720C2214yes—
51#2704C2214yes—
52#2692C2214yes—
53#2692C2214yes—
54#2683C2214yes—
55#2608C2214yes—
56#2607C2214yes—
57#2590C2214yes—
58#2590C2214yes—
59#2589C2214yes—
60#2589C2214yes—
61#2588C2214yes—
62#2587C2214yes—
63#2587C2214yes—
64#2586C2212yes—
65#2586C2214yes—
66#2586C2214yes—
67#2585C2214yes—
68#2585C2212yes—
69#2584C2212yes—
70#2580C2212yes—
71#2579C2214yes—
72#2574C2214yes—
73#2574C2214yes—
74#2574C2214yes—
75#2574C2214yes—
76#2574C2214yes—
77#2574C2212yes—
78#2574C2214yes—
79#2574C2214yes—
80#2571C2212yes—
81#2570C2212yes—
82#2569C2214yes—
83#2567C2212yes—
84#2566C2212yes—
85#2564C2214yes—
86#2564C2214yes—
87#2563C2212yes—
88#2563C2214yes—
89#2563C2214yes—
90#2563C2212yes—
91#2563C2214yes—
92#2556C2214yes—
93#2556C2212yes—
94#2552C2212yes—
95#2551C2214yes—
96#2551C2212yes—
97#2551C2212yes—
98#2550C2212yes—
99#2550C2212yes—
100#2549C2214yes—
101#2549C2214yes—
102#2546C2212yes—
103#2538C2212yes—
104#2538C2214yes—
105#2538C2212yes—
106#2522C2214yes—
107#2522C2212yes—
108#2520C2212yes—
109#2520C2214yes—
110#2520C2214yes—
111#2509C2212yes—
112#2508C2212yes—
113#2508C2214yes—
114#2508C2214yes—
115#2508C2212yes—
116#2508C2212yes—
117#2508C2212yes—
118#2507C2212yes—
119#2505C2214yes—
120#2497C2214yes—
121#2492C2214yes—
122#2492C2214yes—
123#2492C2214yes—
124#2473C2214yes—
125#2465C2214yes—
126#2465C2214yes—
127#2465C2214yes—
128#2465C2212yes—
129#2462C2214yes—
130#2462C2212yes—
131#2454C2212yes—
132#2454C2212yes—
133#2454C2214yes—
134#2454C2212yes—
135#2452C2212yes—
136#2452C2214yes—
137#2452C2212yes—
138#2452C2212yes—
139#2450C2214yes—
140#2450C2214yes—
141#2449C2214yes—
142#2449C2214yes—
143#2449C2214yes—
144#2449C2214yes—
145#2446C2214yes—
146#2442C2212yes—
147#2440C2212yes—
148#2439C2214yes—
149#2439C2214yes—
150#2439C2212yes—
151#2439C2212yes—
152#2438C2214yes—
153#2438C2214yes—
154#2429C2214yes—
155#2423C2214yes—
156#2417C2214yes—
157#2417C2214yes—
158#2417C2214yes—
159#2399C2211yescharacteristic
160#2399C2211yescharacteristic
161#2396C2214yes—
162#2396C2214yes—
163#2396C2211yescharacteristic
164#2396C2211yescharacteristic
165#2374C2214yes—
166#2374C2214yes—
167#2370C2212yes—
168#2370C2212yes—
169#2370C2214yes—
170#2370C2214yes—
171#2370C2212yes—
172#2370C2212yes—
173#2368C2214yes—
174#2368C2214yes—
175#2366C2212yes—
176#2366C2212yes—
177#2365C2212yes—
178#2364C2214yes—
179#2364C2214yes—
180#2363C2214yes—
181#2363C2212yes—
182#2363C2214yes—
183#2363C2212yes—
184#2361C2212yes—
185#2361C2212yes—
186#2360C2214yes—
187#2359C2214yes—
188#2359C2214yes—
189#2355C2212yes—
190#2355C2214yes—
191#2349C2212yes—
192#2349C2212yes—
193#2349C2214yes—
194D4×C4⋊C4C2214yes—
195D4×C4⋊C4C2212yes—
196#2345C2214yes—
197#2345C2214yes—
198#2345C2214yes—
199#2345C2214yes—
200#2335C2214yes—
201#2333C2214yes—
202#2331C2212yes—
203#2331C2212yes—
204#2330C2211yescharacteristic
205#2330C2211yescharacteristic
206#2330C2211yescharacteristic
207#2330C2211yescharacteristic
208#2330C2211yescharacteristic
209#2329C2214yes—
210#2329C2214yes—
211#2328C2211yescharacteristic
212#2324C2212yes—
213#2319C2212yes—
214#2316C2212yes—
215#2314C2211yescharacteristic
216C4×C4⋊Q8C2212yes—
217C4×#127C2211yescharacteristic
218C4×#125C2212yes—
219C4×#125C2212yes—
220C4×#125C2212yes—
221C4×#125C2212yes—
222C4×#125C2211yescharacteristic
223C4×C22⋊Q8C2212yes—
224C4×C22⋊Q8C2214yes—
225C4×C22⋊Q8C2214yes—
226C4×#123C2214yes—
227C4×#121C2212yes—
228C4×#121C2214yes—
229#2298C2212yes—
230#2295C2211yescharacteristic
231#2295C2212yes—
232#2293C2212yes—
233#2293C2212yes—
234C2×#387C2214yes—
235#2285C2211yescharacteristic
236#2285C2214yes—
237#2275C2212yes—
238#2275C2212yes—
239#2274C2212yes—
240C42×Q8C2211yescharacteristic
241C42×D4C2212yes—
242C4×#117C2211yescharacteristic
243#554—216no—
244#540Q8116yescomplemented
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2312yes—
247C2×C4⋊Q8C2312yes—
248C2×C4⋊Q8C2314yes—
249C2×C4⋊Q8C2314yes—
250C2×C4⋊Q8C2314yes—
251C2×#127C2311yescharacteristic
252C2×#125—28no—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2314yes—
257C2×#125C2312yes—
258C2×#125C2311yescharacteristic
259C2×#125C2311yescharacteristic
260C2×#123C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2312yes—
292C2×#117C2311yescharacteristic
293C2×#117C2312yes—
294C2×#117C2314yes—
295C2×#117C2314yes—
296C2×#117C2311yescharacteristic
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2314yes—
301C22×C42C2311yescharacteristic
302C22×C42C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2311yescharacteristic
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2311yescharacteristic
314#400C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2311yescharacteristic
320#399C2311yescharacteristic
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2312yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2312yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2312yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2312yes—
358#396C2314yes—
359#395C2314yes—
360#395C2314yes—
361#395C2314yes—
362#395C2314yes—
363#395C2314yes—
364#395C2312yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2311yescharacteristic
369#395C2312yes—
370#395C2314yes—
371#395C2312yes—
372#395C2314yes—
373#395C2311yescharacteristic
374#395C2312yes—
375#393C2311yescharacteristic
376#393C2314yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2314yes—
381#393C2314yes—
382#393C2314yes—
383#393C2314yes—
384#393C2314yes—
385#393C2314yes—
386#393C2311yescharacteristic
387#391C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2312yes—
393#391C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#390C2312yes—
405#390C2314yes—
406#390C2314yes—
407#390C2312yes—
408#390C2314yes—
409#390C2314yes—
410#390C2314yes—
411#390C2312yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#390C2314yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2312yes—
436#389C2312yes—
437#389C2314yes—
438#389C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#388C2314yes—
463#388C2312yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2312yes—
473#388C2314yes—
474#388C2314yes—
475#388C2312yes—
476#388C2312yes—
477#388C2314yes—
478#388C2314yes—
479#387C2312yes—
480#387C2312yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2312yes—
487#387C2314yes—
488#387C2312yes—
489#387C2314yes—
490#387C2312yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2312yes—
497#387C2312yes—
498#387C2312yes—
499#387C2312yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2312yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2312yes—
518#387C2312yes—
519#387C2314yes—
520#387C2312yes—
521#387C2314yes—
522#387C2312yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2312yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2312yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2312yes—
569#384C2311yescharacteristic
570#384C2312yes—
571#384C2314yes—
572#384C2311yescharacteristic
573#384C2311yescharacteristic
574#384C2314yes—
575#382C2312yes—
576#382C2312yes—
577#382C2312yes—
578#382C2311yescharacteristic
579#382C2314yes—
580#382C2312yes—
581#382C2314yes—
582#382C2314yes—
583#382C2314yes—
584#382C2314yes—
585#382C2312yes—
586#381C2314yes—
587#380C2312yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600#380C2314yes—
601#380C2314yes—
602#380C2314yes—
603#380C2312yes—
604#380C2314yes—
605#380C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2312yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2311yescharacteristic
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667#376C2312yes—
668#376C2311yescharacteristic
669#376C2311yescharacteristic
670C2×#95C2314yes—
671C2×#95C2314yes—
672C2×#95C2314yes—
673C2×#95C2314yes—
674C43C2311yescharacteristic
675C43C2311yescharacteristic
676C43C2312yes—
677C22×Q8C2411yescharacteristic
678C22×Q8C2412yes—
679C22×Q8C2414yes—
680C22×Q8C2414yes—
681C22×Q8C2411yescharacteristic
682C22×Q8C2414yes—
683C22×D4C2412yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C23×C4C2411yescharacteristic
687C23×C4C2414yes—
688C23×C4C2414yes—
689C23×C4C2412yes—
690C23×C4C2414yes—
691C23×C4C2414yes—
692C23×C4C2414yes—
693C23×C4C2414yes—
694C23×C4C2414yes—
695C23×C4C2414yes—
696C4⋊Q8—28no—
697C4⋊Q8—44no—
698C4⋊Q8—44no—
699C4⋊Q8—84no—
700C4⋊Q8—84no—
701C4⋊Q8—84no—
702#127C2×Q818yes—
703#125—216no—
704#125—28no—
705#125—28no—
706#125—24no—
707#125—44no—
708#125C2×Q818yes—
709#125#4118yes—
710#123C2×Q8132yes—
711C22⋊Q8—216no—
712C22⋊Q8—216no—
713C22⋊Q8—216no—
714C22⋊Q8—44no—
715C22⋊Q8—48no—
716C22⋊Q8—84no—
717C22⋊Q8—84no—
718C22⋊Q8—84no—
719C22⋊Q8—84no—
720C22⋊Q8—84no—
721#121C2×Q8132yes—
722#121C2×Q8116yes—
723C4×Q8—28no—
724C4×Q8—42no—
725C4×Q8—42no—
726C4×Q8—48no—
727C4×Q8—44no—
728C4×Q8—84no—
729C4×D4—28no—
730C4×D4—28no—
731C4×D4—28no—
732C4×D4—48no—
733C4×D4—44no—
734C4×D4—44no—
735C4×D4—44no—
736C4×D4—48no—
737C4×D4—84no—
738C4×D4—84no—
739C4×D4—84no—
740C4×D4—84no—
741C4×D4C2×Q8116yes—
742#117—42no—
743#117—44no—
744#117—84no—
745#117—84no—
746#117C2×Q818yes—
747C2×C4⋊C4—216no—
748C2×C4⋊C4—28no—
749C2×C4⋊C4—216no—
750C2×C4⋊C4—48no—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C42—24no—
848C2×C42—48no—
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2412yes—
857C2×C42C2411yescharacteristic
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2412yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880#95C2412yes—
881#95C2412yes—
882#95C2414yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2411yescharacteristic
917#95C2412yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2411yescharacteristic
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2411yescharacteristic
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949C24C2514yes—
950C24C2511yescharacteristic
951C2×Q8—24no—
952C2×Q8—28no—
953C2×Q8—24no—
954C2×Q8—41no—
955C2×Q8—44no—
956C2×Q8—41no—
957C2×Q8—44no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—42no—
964C2×Q8—44no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4C22×Q818yes—
974C2×D4C22×Q8116yes—
975C2×D4C22×Q8116yes—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—24no—
979C22×C4—28no—
980C22×C4—28no—
981C22×C4—28no—
982C22×C4—28no—
983C22×C4—28no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4C22×Q814yes—
1005C22×C4C22×Q8116yes—
1006C22×C4C2514yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2514yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2511yescharacteristic
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—41no—
1067C4⋊C4—42no—
1068C4⋊C4—41no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—42no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4C22×Q818yes—
1094C4⋊C4C22×Q818yes—
1095C4⋊C4C22×Q8116yes—
1096C4⋊C4C2×#41116yes—
1097C4⋊C4C2×#4118yes—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—24no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—42no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—42no—
1121C22⋊C4—44no—
1122C22⋊C4—42no—
1123C22⋊C4—44no—
1124C22⋊C4C22×Q818yes—
1125C22⋊C4C22×Q8116yes—
1126C22⋊C4C22×Q8116yes—
1127C42—24no—
1128C42—22no—
1129C42—24no—
1130C42—24no—
1131C42—24no—
1132C42—28no—
1133C42—22no—
1134C42—22no—
1135C42—24no—
1136C42—24no—
1137C42—44no—
1138C42—44no—
1139C42—44no—
1140C42—42no—
1141C42—42no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C42—42no—
1146C42—44no—
1147C42—44no—
1148C42—44no—
1149C42—42no—
1150C42—42no—
1151C42—44no—
1152C42—44no—
1153C42—42no—
1154C42—42no—
1155C42C22×Q814yes—
1156C42C22×Q814yes—
1157C42C2×#4114yes—
1158C23—24no—
1159C23—21no—
1160C23—22no—
1161C23—24no—
1162C23—21no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—22no—
1167C23—24no—
1168C23C23×Q818yes—
1169C23C23×Q812yes—
1170C23C2611yescharacteristic
1171Q8—44no—
1172Q8—84no—
1173Q8—88no—
1174Q8—88no—
1175Q8—82no—
1176Q8—164no—
1177D4—216no—
1178D4—416no—
1179D4—416no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—22no—
1194C2×C4—28no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—416no—
1243C2×C4—84no—
1244C2×C4—88no—
1245C2×C4—88no—
1246C2×C4—88no—
1247C2×C4—88no—
1248C2×C4—88no—
1249C2×C4—164no—
1250C2×C4—164no—
1251C2×C4C23×Q814yes—
1252C2×C4C23×Q814yes—
1253C2×C4C23×Q812yes—
1254C2×C4C23×Q818yes—
1255C2×C4C23×Q812yes—
1256C2×C4C22×#4114yes—
1257C2×C4C22×#4118yes—
1258C2×C4C22×#4112yes—
1259C2×C4#58514yes—
1260C2×C4#58512yes—
1261C22—28no—
1262C22—28no—
1263C22—24no—
1264C22—22no—
1265C22—28no—
1266C22—42no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—41no—
1271C22—44no—
1272C22—41no—
1273C22C24×Q811yescharacteristic
1274C22C23×#4111yescharacteristic
1275C22C2×#58512yes—
1276C22C2×#58511yescharacteristic
1277C22H(7,𝔽2)12yes—
1278C4—24no—
1279C4—28no—
1280C4—24no—
1281C4—28no—
1282C4—24no—
1283C4—24no—
1284C4—22no—
1285C4—42no—
1286C4—44no—
1287C4—42no—
1288C4—42no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—41no—
1293C4—44no—
1294C4—42no—
1295C4—41no—
1296C4—41no—
1297C4—44no—
1298C4—41no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4Q8×#4114yes—
1303C2—48no—
1304C2—42no—
1305C2C2×Q8×#4111yescharacteristic
1306C2#6282911yescharacteristic
1307C2#6288311yescharacteristic
1308C2#6298912yes—
1309C2#6299412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#540C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59587C2semidirect
2. #59527C2semidirect
3. #59465C2semidirect
4. #59453C2semidirect
5. #59319C2semidirect
6. #59230C2semidirect
7. #59230C2semidirect
8. #59155C2semidirect
9. #45435C2semidirect
10. #45362C2semidirect
11. #45360C2semidirect
12. #45164C2semidirect
13. #44948C2semidirect
14. #44945C2semidirect
15. #43571C2semidirect
16. #43567C2semidirect
17. #43562C2semidirect
18. #43561C2semidirect
19. #35602C2semidirect
20. #35581C2semidirect
21. #35577C2semidirect
22. #34941C2semidirect
23. #34882C2semidirect
24. #34333C2semidirect
27. #34217C2semidirect
244. #540Q8semidirect

Maximal subgroups

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

subgroupindex
#595872
#595272
#594652
#594532
#593192
#592302
#591552
#454352
#453622
#453602
#451642
#449482
#449452
#435712
#435672
#435622
#435612
#356022
#355812
#355772
#349412
#348822
#343332
#342872
#342802
#342172