Finite Group Databasebeta

← #7687307

Subgroups — #7687307

Order 512.

5015 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59918C213yesmaximal, complemented
2#59771C213yesmaximal, complemented
3#59642C213yesmaximal, complemented
4#59461C213yesmaximal, complemented
5#59460C213yesmaximal, complemented
6#45409C213yesmaximal, complemented
7#44946C213yesmaximal, complemented
8#44923C213yesmaximal, complemented
9#44908C213yesmaximal, complemented
10#39695C213yesmaximal, complemented
11#39690C213yesmaximal, complemented
12#39493C213yesmaximal, complemented
13#38960C213yesmaximal, complemented
14#36566C213yesmaximal, complemented
15Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
16#36475C211yesmaximal, characteristic, complemented
17#36475C211yesmaximal, characteristic, complemented
18#36474C211yesmaximal, characteristic, complemented
19#36431C211yesmaximal, characteristic, complemented
20#36363C213yesmaximal, complemented
21#35786C211yesmaximal, characteristic, complemented
22#35748C211yesmaximal, characteristic, complemented
23#35748C211yesmaximal, characteristic, complemented
24#35711C211yesmaximal, characteristic, complemented
25#34893C213yesmaximal, complemented
26#34312C211yesmaximal, characteristic
27#34312C211yesmaximal, characteristic
28#34250C211yesmaximal, characteristic, complemented
29#34249C211yesmaximal, characteristic, complemented
30C4×Q82C211yesmaximal, characteristic, complemented
31C4×#548C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2864C2213yes—
43#2864C2213yes—
44#2862C2213yes—
45#2857C2213yes—
46#2851C2213yes—
47#2807C2216yes—
48#2807C2216yes—
49#2806C2216yes—
50#2805C2216yes—
51#2804C2216yes—
52#2792C2216yes—
53#2780C2216yes—
54#2768C2216yes—
55#2763C2216yes—
56#2755C2216yes—
57#2732C2216yes—
58#2720C2216yes—
59#2704C2216yes—
60#2692C2216yes—
61#2629C2213yes—
62#2628C2213yes—
63#2628C2213yes—
64#2628C2213yes—
65#2589C2216yes—
66#2589C2216yes—
67#2589C2213yes—
68#2589C2216yes—
69#2589C2213yes—
70#2587C2213yes—
71#2587C2213yes—
72#2587C2216yes—
73#2586C2216yes—
74#2585C2216yes—
75#2584C2213yes—
76#2583C2216yes—
77#2582C2213yes—
78#2582C2213yes—
79#2581C2213yes—
80#2580C2213yes—
81#2580C2213yes—
82#2580C2213yes—
83#2580C2213yes—
84#2574C2216yes—
85#2574C2216yes—
86#2570C2213yes—
87#2570C2213yes—
88#2570C2213yes—
89#2570C2213yes—
90#2568C2213yes—
91#2567C2213yes—
92#2567C2213yes—
93#2566C2213yes—
94#2566C2213yes—
95#2565C2213yes—
96#2550C2213yes—
97#2550C2213yes—
98#2550C2213yes—
99#2550C2213yes—
100#2550C2213yes—
101#2549C2216yes—
102#2546C2213yes—
103#2542C2213yes—
104#2542C2213yes—
105#2522C2213yes—
106#2522C2213yes—
107#2509C2213yes—
108#2509C2213yes—
109#2509C2213yes—
110#2508C2213yes—
111#2508C2213yes—
112#2507C2213yes—
113#2507C2213yes—
114#2507C2213yes—
115#2506C2213yes—
116#2506C2213yes—
117#2502C2216yes—
118#2492C2216yes—
119#2465C2216yes—
120#2465C2216yes—
121#2465C2211yescharacteristic
122#2465C2213yes—
123#2465C2216yes—
124#2454C2213yes—
125#2454C2213yes—
126#2453C2213yes—
127#2452C2213yes—
128#2452C2213yes—
129#2452C2213yes—
130#2452C2213yes—
131#2452C2213yes—
132#2452C2213yes—
133#2451C2213yes—
134#2451C2213yes—
135#2451C2213yes—
136#2451C2213yes—
137#2451C2213yes—
138#2450C2216yes—
139#2449C2216yes—
140#2441C2213yes—
141#2441C2213yes—
142#2440C2213yes—
143#2440C2213yes—
144#2440C2213yes—
145#2440C2213yes—
146#2440C2213yes—
147#2440C2213yes—
148#2439C2213yes—
149#2439C2213yes—
150#2439C2213yes—
151#2439C2213yes—
152#2423C2216yes—
153#2396C2213yes—
154#2396C2213yes—
155#2396C2213yes—
156#2396C2213yes—
157#2369C2213yes—
158#2369C2213yes—
159#2369C2213yes—
160#2368C2216yes—
161#2368C2216yes—
162#2367C2213yes—
163#2367C2213yes—
164#2367C2213yes—
165#2363C2213yes—
166#2363C2213yes—
167#2362C2213yes—
168#2361C2213yes—
169#2360C2213yes—
170#2360C2213yes—
171#2360C2216yes—
172#2352C2213yes—
173#2352C2213yes—
174#2352C2213yes—
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2213yes—
178#2351C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186Q8×C4⋊C4C2213yes—
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2213yes—
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2213yes—
196#2349C2213yes—
197#2349C2213yes—
198D4×C4⋊C4C2213yes—
199D4×C4⋊C4C2213yes—
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2324C2213yes—
207#2324C2213yes—
208#2323C2213yes—
209#2323C2213yes—
210#2317C2213yes—
211#2317C2213yes—
212#2317C2213yes—
213#2316C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×C4⋊Q8C2213yes—
217C4×C4⋊Q8C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#124C2213yes—
221C4×#124C2213yes—
222C4×#124C2213yes—
223C4×C22⋊Q8C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×#121C2213yes—
227#2296C2213yes—
228#2296C2213yes—
229#2296C2213yes—
230#2293C2213yes—
231#2293C2213yes—
232C2×#389C2213yes—
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2213yes—
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—28no—
241Q82—44no—
242#557—44no—
243#548Q8116yescomplemented
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#124C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2316yes—
260C2×C22⋊Q8C2316yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2316yes—
264C2×C22⋊Q8C2313yes—
265C2×#121C2313yes—
266#520—28no—
267#520—44no—
268#519—28no—
269#519—44no—
270C4×#41—44no—
271C2×C4×Q8—44no—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2316yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C4⋊C4C2313yes—
316C22×C4⋊C4C2316yes—
317C22×C42C2313yes—
318C22×C42C2313yes—
319#400C2313yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2316yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#399C2316yes—
329#399C2316yes—
330#399C2313yes—
331#399C2313yes—
332#399C2316yes—
333#399C2313yes—
334#399C2313yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2313yes—
344#398C2316yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2316yes—
349#398C2313yes—
350#398C2313yes—
351#398C2316yes—
352#398C2313yes—
353#396C2311yescharacteristic
354#396C2313yes—
355#396C2316yes—
356#396C2313yes—
357#396C2313yes—
358#396C2316yes—
359#396C2313yes—
360#396C2313yes—
361#396C2313yes—
362#396C2313yes—
363#396C2316yes—
364#395C2316yes—
365#395C2316yes—
366#395C2316yes—
367#395C2316yes—
368#395C2313yes—
369#395C2313yes—
370#395C2311yescharacteristic
371#395C2316yes—
372#395C2316yes—
373#395C2316yes—
374#395C2311yescharacteristic
375#393C2316yes—
376#393C2316yes—
377#393C2311yescharacteristic
378#393C2313yes—
379#393C2313yes—
380#393C2316yes—
381#393C2313yes—
382#393C2316yes—
383#391C2311yescharacteristic
384#391C2316yes—
385#391C2313yes—
386#391C2316yes—
387#391C2316yes—
388#391C2313yes—
389#391C2313yes—
390#391C2316yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
394#391C2316yes—
395#391C2316yes—
396#391C2316yes—
397#391C2313yes—
398#391C2313yes—
399#391C2316yes—
400#391C2316yes—
401#391C2316yes—
402#391C2313yes—
403#390C2313yes—
404#390C2313yes—
405#390C2313yes—
406#390C2313yes—
407#390C2313yes—
408#390C2313yes—
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2316yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2316yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2311yescharacteristic
475#388C2313yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2311yescharacteristic
483#388C2313yes—
484#388C2316yes—
485#388C2313yes—
486#388C2311yescharacteristic
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#387C2311yescharacteristic
491#387C2311yescharacteristic
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2313yes—
510#387C2316yes—
511#387C2313yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2311yescharacteristic
516#386C2316yes—
517#386C2316yes—
518#386C2316yes—
519#385C2313yes—
520#385C2313yes—
521#385C2313yes—
522#385C2316yes—
523#385C2313yes—
524#385C2313yes—
525#385C2313yes—
526#385C2316yes—
527#385C2316yes—
528#385C2316yes—
529#385C2316yes—
530#385C2316yes—
531#385C2316yes—
532#385C2316yes—
533#385C2316yes—
534#385C2313yes—
535#385C2313yes—
536#385C2316yes—
537#385C2316yes—
538#385C2316yes—
539#385C2313yes—
540#385C2313yes—
541#385C2313yes—
542#385C2311yescharacteristic
543#384C2313yes—
544#384C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2316yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2316yes—
562#382C2313yes—
563#382C2313yes—
564#380C2316yes—
565#380C2316yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
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⋊C4C2313yes—
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⋊C4C2316yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2311yescharacteristic
624C2×#95C2316yes—
625C43C2313yes—
626C43C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41C2×Q818yes—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8C2×Q818yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2411yescharacteristic
636C22×Q8C2413yes—
637C22×Q8C2416yes—
638C22×Q8C2413yes—
639C22×Q8C2416yes—
640C22×Q8C2411yescharacteristic
641C22×D4C2413yes—
642C22×D4C2413yes—
643C23×C4C2411yescharacteristic
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2416yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2416yes—
650C23×C4C2413yes—
651C4⋊Q8—212no—
652C4⋊Q8—212no—
653C4⋊Q8—212no—
654C4⋊Q8—46no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657C4⋊Q8—46no—
658C4⋊Q8—46no—
659#125—46no—
660#125—46no—
661#125—46no—
662#125—46no—
663#124C2×Q8124yes—
664C22⋊Q8—24no—
665C22⋊Q8—212no—
666C22⋊Q8—412no—
667C22⋊Q8—412no—
668C22⋊Q8—86no—
669C22⋊Q8—86no—
670C22⋊Q8—86no—
671C22⋊Q8C2×Q8124yes—
672#121C2×Q8124yes—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—212no—
685C4×Q8—24no—
686C4×Q8—212no—
687C4×Q8—212no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×Q8—86no—
696C4×Q8C2×Q818yes—
697C4×Q8#4118yes—
698C4×D4—212no—
699C4×D4—212no—
700C4×D4—46no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706C4×D4C2×Q8124yes—
707#117—212no—
708#117—212no—
709#117—212no—
710#117—46no—
711#117—46no—
712#117—46no—
713#117—46no—
714C2×C4⋊C4—212no—
715C2×C4⋊C4—46no—
716C2×C4⋊C4—46no—
717C2×C4⋊C4—86no—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2411yescharacteristic
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2416yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2411yescharacteristic
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2416yes—
817C2×C42—46no—
818C2×C42—46no—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2416yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835C2×C42C2413yes—
836C2×C42C2416yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2411yescharacteristic
848C2×C42C2413yes—
849C2×C42C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2416yes—
853#95C2416yes—
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2413yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871#95C2416yes—
872#95C2416yes—
873#95C2416yes—
874#95C2413yes—
875#95C2413yes—
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2413yes—
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2413yes—
883#95C2411yescharacteristic
884#95C2413yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2416yes—
899#95C2413yes—
900#95C2416yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2416yes—
908#95C2416yes—
909C24C2511yescharacteristic
910C24C2513yes—
911#41—232no—
912C2×Q8—232no—
913C2×Q8—22no—
914C2×Q8—26no—
915C2×Q8—212no—
916C2×Q8—26no—
917C2×Q8—22no—
918C2×Q8—22no—
919C2×Q8—26no—
920C2×Q8—22no—
921C2×Q8—22no—
922C2×Q8—41no—
923C2×Q8—43no—
924C2×Q8—46no—
925C2×Q8—46no—
926C2×Q8—43no—
927C2×Q8—46no—
928C2×Q8—46no—
929C2×Q8—46no—
930C2×Q8C22×Q8112yes—
931C2×Q8C22×Q814yes—
932C2×Q8C2×#4114yes—
933C2×Q8H(5,𝔽2)14yes—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—43no—
937C2×D4—43no—
938C2×D4C22×Q8112yes—
939C2×D4C22×Q8112yes—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—26no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—212no—
947C22×C4—26no—
948C22×C4—41no—
949C22×C4—43no—
950C22×C4—43no—
951C22×C4—43no—
952C22×C4—43no—
953C22×C4—46no—
954C22×C4—43no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—46no—
958C22×C4—43no—
959C22×C4—46no—
960C22×C4—46no—
961C22×C4—46no—
962C22×C4C22×Q8112yes—
963C22×C4C22×Q8112yes—
964C22×C4C2511yescharacteristic
965C22×C4C2513yes—
966C22×C4C2513yes—
967C22×C4C2511yescharacteristic
968C22×C4C2513yes—
969C22×C4C2513yes—
970C22×C4C2513yes—
971C22×C4C2513yes—
972C22×C4C2513yes—
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2511yescharacteristic
979C22×C4C2513yes—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2513yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—22no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—43no—
1025C4⋊C4—46no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—46no—
1029C4⋊C4—46no—
1030C4⋊C4—41no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—41no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—46no—
1043C4⋊C4—46no—
1044C4⋊C4—46no—
1045C4⋊C4—46no—
1046C4⋊C4—43no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—46no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—46no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4C22×Q8112yes—
1062C4⋊C4C22×Q8112yes—
1063C4⋊C4C2×#41112yes—
1064C4⋊C42−1+414yes—
1065C22⋊C4—26no—
1066C22⋊C4—22no—
1067C22⋊C4—26no—
1068C22⋊C4—26no—
1069C22⋊C4—22no—
1070C22⋊C4—26no—
1071C22⋊C4—22no—
1072C22⋊C4—26no—
1073C22⋊C4—22no—
1074C22⋊C4—26no—
1075C22⋊C4—26no—
1076C22⋊C4—41no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—46no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C22⋊C4—46no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—46no—
1087C22⋊C4—43no—
1088C22⋊C4—43no—
1089C22⋊C4C22×Q814yes—
1090C22⋊C4C22×Q8112yes—
1091C22⋊C4C22×Q8124yes—
1092C42—26no—
1093C42—212no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—22no—
1105C42—22no—
1106C42—22no—
1107C42—26no—
1108C42—41no—
1109C42—43no—
1110C42—43no—
1111C42—43no—
1112C42—46no—
1113C42—43no—
1114C42—43no—
1115C42—43no—
1116C42—43no—
1117C42—43no—
1118C42—43no—
1119C42—43no—
1120C42—43no—
1121C42C22×Q8112yes—
1122C42C2×#41112yes—
1123C23—21no—
1124C23—23no—
1125C23—21no—
1126C23—23no—
1127C23—21no—
1128C23—23no—
1129C23—23no—
1130C23—23no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—23no—
1135C23C23×Q816yes—
1136C23C23×Q812yes—
1137C23C2611yescharacteristic
1138Q8—28no—
1139Q8—224no—
1140Q8—44no—
1141Q8—812no—
1142Q8—86no—
1143Q8—166no—
1144Q8#554116yes—
1145D4—224no—
1146D4—412no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—224no—
1170C2×C4—224no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—21no—
1222C2×C4—44no—
1223C2×C4—812no—
1224C2×C4—86no—
1225C2×C4—86no—
1226C2×C4—86no—
1227C2×C4—166no—
1228C2×C4C23×Q812yes—
1229C2×C4C23×Q816yes—
1230C2×C4C23×Q816yes—
1231C2×C4C23×Q812yes—
1232C2×C4C23×Q816yes—
1233C2×C4C22×#4116yes—
1234C2×C4C22×#4112yes—
1235C2×C4C22×#4116yes—
1236C2×C4C2×H(5,𝔽2)16yes—
1237C2×C4C2×2−1+412yes—
1238C2×C4C2×2−1+412yes—
1239C2×C4C2×2−1+412yes—
1240C2×C4#58512yes—
1241C2×C4#58512yes—
1242C22—22no—
1243C22—26no—
1244C22—22no—
1245C22—26no—
1246C22—22no—
1247C22—26no—
1248C22—43no—
1249C22—41no—
1250C22—41no—
1251C22—43no—
1252C22—41no—
1253C22—43no—
1254C22—41no—
1255C22—43no—
1256C22C24×Q811yescharacteristic
1257C22C23×#4111yescharacteristic
1258C22C22×H(5,𝔽2)11yescharacteristic
1259C22C22×2−1+411yescharacteristic
1260C22C2×#58511yescharacteristic
1261C22C2×#58511yescharacteristic
1262C22H(7,𝔽2)11yescharacteristic
1263C4—22no—
1264C4—26no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—22no—
1271C4—26no—
1272C4—22no—
1273C4—26no—
1274C4—41no—
1275C4—43no—
1276C4—43no—
1277C4—43no—
1278C4—41no—
1279C4—43no—
1280C4—41no—
1281C4—43no—
1282C4—41no—
1283C4—43no—
1284C4—41no—
1285C4—43no—
1286C4—41no—
1287C4—43no—
1288C4—43no—
1289C4—43no—
1290C4—43no—
1291C4C2×#554112yes—
1292C2—42no—
1293C2—46no—
1294C2C22×#55411yescharacteristic
1295C2#6278811yescharacteristic
1296C2#6281311yescharacteristic
1297C2#6292311yescharacteristic
1298C2Q8×2−1+411yescharacteristic
1299C2#6301011yescharacteristic
1300C2#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. #59918C2semidirect
2. #59771C2semidirect
3. #59642C2semidirect
4. #59461C2semidirect
5. #59460C2semidirect
6. #45409C2semidirect
7. #44946C2semidirect
8. #44923C2semidirect
9. #44908C2semidirect
10. #39695C2semidirect
11. #39690C2semidirect
12. #39493C2semidirect
13. #38960C2semidirect
14. #36566C2semidirect
15. Q8×C22⋊Q8C2semidirect
16. #36475C2semidirect
17. #36475C2semidirect
18. #36474C2semidirect
19. #36431C2semidirect
20. #36363C2semidirect
21. #35786C2semidirect
22. #35748C2semidirect
23. #35748C2semidirect
24. #35711C2semidirect
25. #34893C2semidirect
28. #34250C2semidirect
29. #34249C2semidirect
30. C4×Q82C2semidirect
243. #548Q8semidirect

Maximal subgroups

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

subgroupindex
#599182
#597712
#596422
#594612
#594602
#454092
#449462
#449232
#449082
#396952
#396902
#394932
#389602
#365662
Q8×C22⋊Q82
#364752
#364742
#364312
#363632
#357862
#357482
#357112
#348932
#343122
#342502
#342492
C4×Q822
C4×#5482