Finite Group Databasebeta

← #7688438

Subgroups — #7688438

Order 512.

5261 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59831C213yesmaximal, complemented
2#59663C213yesmaximal, complemented
3#59460C213yesmaximal, complemented
4#59455C213yesmaximal, complemented
5#59326C213yesmaximal, complemented
6#45434C213yesmaximal, complemented
7#45409C213yesmaximal, complemented
8#45275C213yesmaximal, complemented
9#45213C213yesmaximal, complemented
10#39691C213yesmaximal, complemented
11#39674C213yesmaximal, complemented
12#38099C213yesmaximal, complemented
13#37875C213yesmaximal, complemented
14#36577C211yesmaximal, characteristic, complemented
15#36561C213yesmaximal, complemented
16Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
17Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
18#36456C211yesmaximal, characteristic, complemented
19#36447C211yesmaximal, characteristic, complemented
20#36261C213yesmaximal, complemented
21#35937C211yesmaximal, characteristic, complemented
22#35868C211yesmaximal, characteristic, complemented
23#35816C211yesmaximal, characteristic, complemented
24#35748C211yesmaximal, characteristic, complemented
25#34840C213yesmaximal, complemented
26#34335C211yesmaximal, characteristic, complemented
27#34294C211yesmaximal, characteristic
28#34294C211yesmaximal, characteristic
29#34250C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic
31C2×#2351C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#554C2216yes—
36C2×#548C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43#2859C2213yes—
44#2857C2213yes—
45#2857C2213yes—
46#2857C2213yes—
47#2857C2213yes—
48#2806C2216yes—
49#2802C2216yes—
50#2788C2216yes—
51#2788C2216yes—
52#2774C2216yes—
53#2768C2216yes—
54#2768C2216yes—
55#2768C2216yes—
56#2763C2216yes—
57#2763C2216yes—
58#2755C2216yes—
59#2729C2216yes—
60#2704C2216yes—
61#2704C2216yes—
62#2660C2213yes—
63#2647C2213yes—
64#2629C2213yes—
65#2628C2213yes—
66#2590C2213yes—
67#2589C2213yes—
68#2588C2213yes—
69#2587C2213yes—
70#2587C2216yes—
71#2586C2213yes—
72#2585C2213yes—
73#2584C2216yes—
74#2584C2213yes—
75#2583C2213yes—
76#2583C2216yes—
77#2582C2213yes—
78#2582C2213yes—
79#2582C2213yes—
80#2580C2213yes—
81#2579C2213yes—
82#2574C2213yes—
83#2574C2216yes—
84#2571C2213yes—
85#2570C2213yes—
86#2568C2213yes—
87#2567C2213yes—
88#2567C2213yes—
89#2566C2213yes—
90#2564C2213yes—
91#2564C2216yes—
92#2563C2213yes—
93#2556C2216yes—
94#2556C2213yes—
95#2556C2216yes—
96#2552C2213yes—
97#2552C2213yes—
98#2551C2213yes—
99#2551C2213yes—
100#2550C2213yes—
101#2550C2213yes—
102#2550C2216yes—
103#2549C2216yes—
104#2549C2211yescharacteristic
105#2549C2216yes—
106#2549C2216yes—
107#2546C2213yes—
108#2542C2213yes—
109#2538C2213yes—
110#2538C2213yes—
111#2509C2213yes—
112#2508C2213yes—
113#2508C2213yes—
114#2507C2213yes—
115#2506C2213yes—
116#2506C2213yes—
117#2506C2213yes—
118#2506C2213yes—
119#2505C2216yes—
120#2505C2213yes—
121#2492C2216yes—
122#2473C2216yes—
123#2473C2213yes—
124#2465C2216yes—
125#2454C2213yes—
126#2453C2213yes—
127#2453C2213yes—
128#2452C2213yes—
129#2452C2213yes—
130#2452C2213yes—
131#2452C2213yes—
132#2452C2213yes—
133#2451C2213yes—
134#2451C2213yes—
135#2451C2213yes—
136#2451C2213yes—
137#2450C2213yes—
138#2450C2216yes—
139#2450C2216yes—
140#2449C2213yes—
141#2442C2213yes—
142#2442C2213yes—
143#2442C2213yes—
144#2440C2213yes—
145#2440C2213yes—
146#2440C2213yes—
147#2440C2213yes—
148#2440C2213yes—
149#2440C2213yes—
150#2440C2213yes—
151#2439C2213yes—
152#2439C2213yes—
153#2417C2216yes—
154#2402C2213yes—
155#2399C2213yes—
156#2396C2213yes—
157#2396C2213yes—
158#2369C2213yes—
159#2367C2213yes—
160#2367C2213yes—
161#2367C2213yes—
162#2365C2213yes—
163#2365C2213yes—
164#2362C2213yes—
165#2361C2213yes—
166#2361C2213yes—
167#2361C2213yes—
168#2360C2216yes—
169#2360C2213yes—
170#2360C2213yes—
171#2355C2213yes—
172#2352C2213yes—
173#2351C2213yes—
174#2351C2213yes—
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2213yes—
182#2351C2213yes—
183#2351C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193#2349C2213yes—
194#2349C2216yes—
195#2349C2213yes—
196D4×C4⋊C4C2213yes—
197D4×C4⋊C4C2213yes—
198D4×C4⋊C4C2213yes—
199D4×C4⋊C4C2213yes—
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2331C2213yes—
207#2331C2213yes—
208#2326C2213yes—
209#2326C2213yes—
210#2323C2213yes—
211#2323C2213yes—
212#2317C2213yes—
213#2316C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×#125C2213yes—
216C4×#124C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×#121C2213yes—
223C4×#121C2213yes—
224C4×#121C2213yes—
225#2296C2213yes—
226#2295C2213yes—
227C2×#389C2213yes—
228C2×#389C2213yes—
229C2×#389C2213yes—
230#2290C2213yes—
231#2290C2213yes—
232C2×#382C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—28no—
241Q82—44no—
242#557—44no—
243#554—424no—
244#548Q8116yescomplemented
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2316yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2316yes—
256C2×#125C2313yes—
257C2×#125C2316yes—
258C2×#124C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2316yes—
264C2×C22⋊Q8C2316yes—
265C2×C22⋊Q8C2316yes—
266C2×C22⋊Q8C2316yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×#121C2313yes—
271#520—28no—
272#520—44no—
273C4×#41—44no—
274C2×C4×Q8—28no—
275C2×C4×Q8—44no—
276C2×C4×Q8—44no—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2316yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2316yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2316yes—
310C2×C4×D4C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C2×#117C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C4⋊C4C2313yes—
316C22×C4⋊C4C2313yes—
317C22×C4⋊C4C2313yes—
318C22×C4⋊C4C2316yes—
319C22×C4⋊C4C2313yes—
320C22×C4⋊C4C2313yes—
321C22×C4⋊C4C2313yes—
322C22×C42C2313yes—
323C22×C42C2313yes—
324C22×C42C2313yes—
325C22×C42C2313yes—
326#400C2316yes—
327#400C2313yes—
328#400C2316yes—
329#400C2316yes—
330#400C2313yes—
331#400C2316yes—
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2313yes—
336#400C2316yes—
337#399C2316yes—
338#399C2313yes—
339#399C2313yes—
340#398C2316yes—
341#398C2311yescharacteristic
342#398C2316yes—
343#398C2313yes—
344#398C2313yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2316yes—
350#398C2313yes—
351#398C2313yes—
352#398C2316yes—
353#398C2316yes—
354#398C2311yescharacteristic
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#398C2313yes—
361#398C2316yes—
362#398C2316yes—
363#398C2316yes—
364#396C2313yes—
365#396C2316yes—
366#396C2313yes—
367#396C2313yes—
368#396C2313yes—
369#396C2316yes—
370#396C2316yes—
371#396C2316yes—
372#395C2313yes—
373#395C2316yes—
374#395C2316yes—
375#395C2316yes—
376#395C2316yes—
377#395C2316yes—
378#395C2313yes—
379#395C2313yes—
380#395C2316yes—
381#395C2313yes—
382#395C2316yes—
383#395C2311yescharacteristic
384#395C2311yescharacteristic
385#393C2316yes—
386#393C2316yes—
387#393C2313yes—
388#393C2313yes—
389#393C2316yes—
390#391C2316yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2316yes—
398#391C2316yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2316yes—
404#391C2316yes—
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2316yes—
408#391C2316yes—
409#391C2316yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#389C2311yescharacteristic
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2316yes—
438#389C2316yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2316yes—
452#389C2316yes—
453#389C2316yes—
454#389C2316yes—
455#389C2313yes—
456#389C2316yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2316yes—
463#389C2311yescharacteristic
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2316yes—
472#389C2316yes—
473#389C2313yes—
474#388C2316yes—
475#388C2313yes—
476#388C2316yes—
477#388C2313yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2313yes—
482#388C2313yes—
483#388C2316yes—
484#388C2316yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
490#387C2316yes—
491#387C2313yes—
492#387C2316yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2313yes—
508#387C2313yes—
509#387C2316yes—
510#386C2313yes—
511#386C2316yes—
512#386C2313yes—
513#386C2313yes—
514#386C2313yes—
515#385C2316yes—
516#385C2316yes—
517#385C2313yes—
518#385C2313yes—
519#385C2316yes—
520#385C2316yes—
521#385C2316yes—
522#385C2313yes—
523#385C2313yes—
524#385C2313yes—
525#385C2313yes—
526#385C2313yes—
527#385C2316yes—
528#385C2316yes—
529#385C2316yes—
530#385C2316yes—
531#385C2316yes—
532#385C2313yes—
533#385C2313yes—
534#385C2313yes—
535#385C2313yes—
536#385C2313yes—
537#385C2316yes—
538#385C2313yes—
539#385C2313yes—
540#385C2311yescharacteristic
541#385C2311yescharacteristic
542#384C2313yes—
543#384C2313yes—
544#384C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2316yes—
559#382C2313yes—
560#382C2316yes—
561#382C2316yes—
562#380C2313yes—
563#380C2316yes—
564#380C2313yes—
565#380C2313yes—
566#380C2316yes—
567#380C2316yes—
568#380C2316yes—
569#380C2313yes—
570#380C2313yes—
571#380C2311yescharacteristic
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2316yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2316yes—
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×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2311yescharacteristic
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2316yes—
622#376C2313yes—
623#376C2313yes—
624C2×#95C2311yescharacteristic
625C2×#95C2313yes—
626C2×#95C2316yes—
627C2×#95C2316yes—
628C43C2313yes—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41C2×Q818yes—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8C2×Q818yes—
635C22×Q8C2411yescharacteristic
636C22×Q8C2411yescharacteristic
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2416yes—
640C22×Q8C2416yes—
641C22×Q8C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C23×C4C2413yes—
645C23×C4C2411yescharacteristic
646C23×C4C2411yescharacteristic
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2416yes—
652C23×C4C2413yes—
653C23×C4C2413yes—
654C23×C4C2416yes—
655C23×C4C2411yescharacteristic
656C4⋊Q8—212no—
657C4⋊Q8—212no—
658C4⋊Q8—212no—
659C4⋊Q8—46no—
660C4⋊Q8—46no—
661C4⋊Q8—46no—
662C4⋊Q8—46no—
663C4⋊Q8—412no—
664#125—412no—
665#125—46no—
666#125—46no—
667#125—46no—
668#125—412no—
669#124C2×Q8124yes—
670C22⋊Q8—212no—
671C22⋊Q8—24no—
672C22⋊Q8—24no—
673C22⋊Q8—412no—
674C22⋊Q8—412no—
675C22⋊Q8—412no—
676C22⋊Q8—412no—
677C22⋊Q8—46no—
678C22⋊Q8—412no—
679C22⋊Q8—412no—
680C22⋊Q8C2×Q8124yes—
681#121C2×Q8124yes—
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—24no—
692C4×Q8—24no—
693C4×Q8—212no—
694C4×Q8—212no—
695C4×Q8—212no—
696C4×Q8—46no—
697C4×Q8—46no—
698C4×Q8—412no—
699C4×Q8—46no—
700C4×Q8—46no—
701C4×Q8—46no—
702C4×Q8—46no—
703C4×Q8C2×Q818yes—
704C4×Q8#4118yes—
705C4×D4—212no—
706C4×D4—212no—
707C4×D4—212no—
708C4×D4—212no—
709C4×D4—46no—
710C4×D4—46no—
711C4×D4—46no—
712C4×D4—46no—
713C4×D4—412no—
714C4×D4—412no—
715C4×D4C2×Q8124yes—
716#117—212no—
717#117—46no—
718#117—46no—
719C2×C4⋊C4—212no—
720C2×C4⋊C4—212no—
721C2×C4⋊C4—212no—
722C2×C4⋊C4—46no—
723C2×C4⋊C4—46no—
724C2×C4⋊C4—46no—
725C2×C4⋊C4—46no—
726C2×C4⋊C4—412no—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2413yes—
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×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2416yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2413yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C42—212no—
823C2×C42—46no—
824C2×C42—46no—
825C2×C42—46no—
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×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2416yes—
843C2×C42C2416yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2411yescharacteristic
850C2×C42C2411yescharacteristic
851C2×C42C2413yes—
852C2×C42C2413yes—
853#95C2416yes—
854#95C2413yes—
855#95C2413yes—
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2416yes—
889#95C2416yes—
890#95C2416yes—
891#95C2416yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2416yes—
899#95C2413yes—
900#95C2416yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916C24C2513yes—
917C24C2511yescharacteristic
918#41—232no—
919C2×Q8—232no—
920C2×Q8—26no—
921C2×Q8—22no—
922C2×Q8—212no—
923C2×Q8—26no—
924C2×Q8—26no—
925C2×Q8—22no—
926C2×Q8—22no—
927C2×Q8—22no—
928C2×Q8—41no—
929C2×Q8—41no—
930C2×Q8—46no—
931C2×Q8—43no—
932C2×Q8—46no—
933C2×Q8—43no—
934C2×Q8—46no—
935C2×Q8—46no—
936C2×Q8—46no—
937C2×Q8C22×Q8112yes—
938C2×Q8C22×Q814yes—
939C2×Q8C2×#4114yes—
940C2×Q8H(5,𝔽2)14yes—
941C2×D4—26no—
942C2×D4—26no—
943C2×D4—26no—
944C2×D4—26no—
945C2×D4C22×Q8112yes—
946C2×D4C22×Q8112yes—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—22no—
957C22×C4—26no—
958C22×C4—22no—
959C22×C4—212no—
960C22×C4—26no—
961C22×C4—26no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—43no—
965C22×C4—41no—
966C22×C4—41no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—43no—
970C22×C4—43no—
971C22×C4—46no—
972C22×C4—43no—
973C22×C4—46no—
974C22×C4—43no—
975C22×C4—43no—
976C22×C4—43no—
977C22×C4—46no—
978C22×C4—46no—
979C22×C4—46no—
980C22×C4C22×Q8112yes—
981C22×C4C22×Q8112yes—
982C22×C4H(5,𝔽2)14yes—
983C22×C4C2511yescharacteristic
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2513yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2513yes—
990C22×C4C2513yes—
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C22×C4C2513yes—
994C22×C4C2513yes—
995C22×C4C2513yes—
996C22×C4C2513yes—
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2513yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2513yes—
1002C22×C4C2513yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2513yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2511yescharacteristic
1010C22×C4C2511yescharacteristic
1011C22×C4C2513yes—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—212no—
1015C4⋊C4—26no—
1016C4⋊C4—22no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—22no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—46no—
1053C4⋊C4—46no—
1054C4⋊C4—46no—
1055C4⋊C4—41no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—41no—
1060C4⋊C4—43no—
1061C4⋊C4—41no—
1062C4⋊C4—46no—
1063C4⋊C4—46no—
1064C4⋊C4—41no—
1065C4⋊C4—46no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—46no—
1074C4⋊C4—46no—
1075C4⋊C4—46no—
1076C4⋊C4—46no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—46no—
1081C4⋊C4C22×Q8112yes—
1082C4⋊C4C22×Q8112yes—
1083C4⋊C4C2×#41112yes—
1084C22⋊C4—26no—
1085C22⋊C4—26no—
1086C22⋊C4—26no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—26no—
1090C22⋊C4—26no—
1091C22⋊C4—26no—
1092C22⋊C4—26no—
1093C22⋊C4—26no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—46no—
1099C22⋊C4—46no—
1100C22⋊C4—46no—
1101C22⋊C4—46no—
1102C22⋊C4—43no—
1103C22⋊C4C22×Q814yes—
1104C22⋊C4C22×Q8112yes—
1105C22⋊C4C22×Q8124yes—
1106C22⋊C42−1+414yes—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—26no—
1115C42—26no—
1116C42—26no—
1117C42—26no—
1118C42—26no—
1119C42—26no—
1120C42—26no—
1121C42—26no—
1122C42—41no—
1123C42—43no—
1124C42—43no—
1125C42—43no—
1126C42—43no—
1127C42—43no—
1128C42—41no—
1129C42—46no—
1130C42—46no—
1131C42—43no—
1132C42C22×Q8112yes—
1133C42C2×#41112yes—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23—23no—
1143C23—23no—
1144C23C23×Q816yes—
1145C23C23×Q812yes—
1146C23C2×H(5,𝔽2)12yes—
1147C23C2×2−1+412yes—
1148C23C2611yescharacteristic
1149Q8—224no—
1150Q8—44no—
1151Q8—44no—
1152Q8—812no—
1153Q8—86no—
1154Q8—166no—
1155Q8#554116yescomplemented
1156D4—224no—
1157D4—224no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—23no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—224no—
1181C2×C4—224no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—21no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—23no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—44no—
1234C2×C4—44no—
1235C2×C4—44no—
1236C2×C4—412no—
1237C2×C4—86no—
1238C2×C4—812no—
1239C2×C4—86no—
1240C2×C4—86no—
1241C2×C4—86no—
1242C2×C4—166no—
1243C2×C4C23×Q812yes—
1244C2×C4C23×Q816yes—
1245C2×C4C23×Q816yes—
1246C2×C4C23×Q812yes—
1247C2×C4C23×Q816yes—
1248C2×C4C22×#4112yes—
1249C2×C4C22×#4116yes—
1250C2×C4C22×#4116yes—
1251C2×C4C2×H(5,𝔽2)12yes—
1252C2×C4C2×H(5,𝔽2)12yes—
1253C2×C4C2×H(5,𝔽2)16yes—
1254C2×C4C2×2−1+412yes—
1255C2×C4C2×2−1+412yes—
1256C2×C4#58512yes—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—26no—
1264C22—26no—
1265C22—26no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22#350314yes—
1271C22C24×Q811yescharacteristic
1272C22C23×#4111yescharacteristic
1273C22C22×H(5,𝔽2)11yescharacteristic
1274C22C22×H(5,𝔽2)11yescharacteristic
1275C22C22×2−1+411yescharacteristic
1276C22C2×#58511yescharacteristic
1277C222−1+611yescharacteristic
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—26no—
1284C4—26no—
1285C4—22no—
1286C4—22no—
1287C4—22no—
1288C4—26no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—43no—
1295C4—43no—
1296C4—41no—
1297C4—43no—
1298C4—43no—
1299C4—43no—
1300C4—43no—
1301C4—43no—
1302C4—43no—
1303C4—43no—
1304C4—43no—
1305C4—43no—
1306C4C2×#554112yes—
1307C2—24no—
1308C2—46no—
1309C2C22×#55411yescharacteristic
1310C2C2×#350311yescharacteristic
1311C2#6280011yescharacteristic
1312C2#6289511yescharacteristic
1313C2#6299811yescharacteristic
1314C2#6300411yescharacteristic
1315C2#6301511yescharacteristic
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. #59831C2semidirect
2. #59663C2semidirect
3. #59460C2semidirect
4. #59455C2semidirect
5. #59326C2semidirect
6. #45434C2semidirect
7. #45409C2semidirect
8. #45275C2semidirect
9. #45213C2semidirect
10. #39691C2semidirect
11. #39674C2semidirect
12. #38099C2semidirect
13. #37875C2semidirect
14. #36577C2semidirect
15. #36561C2semidirect
16. Q8×C22⋊Q8C2semidirect
17. Q8×C22⋊Q8C2semidirect
18. #36456C2semidirect
19. #36447C2semidirect
20. #36261C2semidirect
21. #35937C2semidirect
22. #35868C2semidirect
23. #35816C2semidirect
24. #35748C2semidirect
25. #34840C2semidirect
26. #34335C2semidirect
29. #34250C2semidirect
31. C2×#2351C2semidirect
244. #548Q8semidirect
1155. Q8#554semidirect

Maximal subgroups

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

subgroupindex
#598312
#596632
#594602
#594552
#593262
#454342
#454092
#452752
#452132
#396912
#396742
#380992
#378752
#365772
#365612
Q8×C22⋊Q82
#364562
#364472
#362612
#359372
#358682
#358162
#357482
#348402
#343352
#342942
#342502
C4×#5482
C2×#23512