Finite Group Databasebeta

← #7688886

Subgroups — #7688886

Order 512.

5119 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59921C213yesmaximal, complemented
2#59919C213yesmaximal, complemented
3#59897C213yesmaximal, complemented
4#59457C213yesmaximal, complemented
5#59214C213yesmaximal, complemented
6#45362C213yesmaximal, complemented
7#45360C213yesmaximal, complemented
8#44951C213yesmaximal, complemented
9#44908C213yesmaximal, complemented
10#39692C213yesmaximal, complemented
11#39672C213yesmaximal, complemented
12#38107C213yesmaximal, complemented
13#37879C213yesmaximal, complemented
14#36570C213yesmaximal, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36445C211yesmaximal, characteristic, complemented
17#36431C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#36431C211yesmaximal, characteristic, complemented
20#36363C213yesmaximal, complemented
21#35971C211yesmaximal, characteristic, complemented
22#35957C211yesmaximal, characteristic, complemented
23#35816C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic, complemented
25#34840C213yesmaximal, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34295C211yesmaximal, characteristic
28#34295C211yesmaximal, characteristic
29#34250C211yesmaximal, characteristic, complemented
30C4×#550C211yesmaximal, characteristic
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42#2864C2213yes—
43#2857C2213yes—
44#2851C2213yes—
45#2851C2213yes—
46#2851C2213yes—
47#2807C2216yes—
48#2790C2216yes—
49#2788C2216yes—
50#2784C2216yes—
51#2784C2216yes—
52#2780C2216yes—
53#2780C2216yes—
54#2780C2216yes—
55#2780C2216yes—
56#2780C2216yes—
57#2768C2216yes—
58#2748C2216yes—
59#2732C2216yes—
60#2692C2216yes—
61#2660C2213yes—
62#2647C2213yes—
63#2629C2213yes—
64#2629C2213yes—
65#2590C2213yes—
66#2589C2213yes—
67#2588C2213yes—
68#2587C2213yes—
69#2587C2216yes—
70#2586C2213yes—
71#2585C2216yes—
72#2585C2211yescharacteristic
73#2584C2213yes—
74#2583C2213yes—
75#2580C2213yes—
76#2580C2216yes—
77#2580C2213yes—
78#2580C2213yes—
79#2579C2216yes—
80#2579C2216yes—
81#2579C2213yes—
82#2574C2216yes—
83#2574C2213yes—
84#2571C2213yes—
85#2570C2213yes—
86#2570C2213yes—
87#2570C2213yes—
88#2567C2213yes—
89#2566C2216yes—
90#2566C2213yes—
91#2566C2213yes—
92#2566C2213yes—
93#2566C2213yes—
94#2566C2213yes—
95#2564C2216yes—
96#2564C2213yes—
97#2556C2213yes—
98#2552C2213yes—
99#2552C2213yes—
100#2550C2213yes—
101#2550C2213yes—
102#2549C2213yes—
103#2542C2213yes—
104#2538C2213yes—
105#2538C2213yes—
106#2538C2216yes—
107#2538C2213yes—
108#2522C2216yes—
109#2522C2216yes—
110#2509C2213yes—
111#2509C2213yes—
112#2508C2213yes—
113#2508C2213yes—
114#2508C2213yes—
115#2507C2213yes—
116#2507C2213yes—
117#2506C2213yes—
118#2505C2213yes—
119#2497C2216yes—
120#2487C2216yes—
121#2473C2213yes—
122#2465C2216yes—
123#2454C2213yes—
124#2454C2213yes—
125#2454C2213yes—
126#2454C2213yes—
127#2454C2213yes—
128#2454C2213yes—
129#2454C2213yes—
130#2452C2213yes—
131#2452C2213yes—
132#2452C2213yes—
133#2452C2213yes—
134#2452C2213yes—
135#2450C2216yes—
136#2450C2213yes—
137#2450C2216yes—
138#2449C2216yes—
139#2449C2213yes—
140#2449C2216yes—
141#2442C2213yes—
142#2442C2213yes—
143#2441C2213yes—
144#2441C2213yes—
145#2441C2213yes—
146#2441C2213yes—
147#2441C2213yes—
148#2440C2213yes—
149#2440C2213yes—
150#2439C2213yes—
151#2439C2213yes—
152#2439C2213yes—
153#2402C2213yes—
154#2399C2213yes—
155#2396C2213yes—
156#2396C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2368C2216yes—
160#2366C2213yes—
161#2366C2213yes—
162#2366C2213yes—
163#2365C2213yes—
164#2363C2213yes—
165#2363C2213yes—
166#2363C2213yes—
167#2363C2213yes—
168#2361C2213yes—
169#2361C2213yes—
170#2360C2216yes—
171#2354C2213yes—
172#2352C2213yes—
173#2352C2213yes—
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2213yes—
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191#2349C2213yes—
192#2349C2213yes—
193#2349C2213yes—
194#2349C2216yes—
195#2349C2213yes—
196D4×C4⋊C4C2213yes—
197D4×C4⋊C4C2213yes—
198D4×C4⋊C4C2213yes—
199D4×C4⋊C4C2213yes—
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2330C2213yes—
207#2330C2213yes—
208#2328C2213yes—
209#2328C2213yes—
210#2324C2213yes—
211#2324C2213yes—
212#2317C2213yes—
213#2316C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×#127C2213yes—
216C4×#125C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×#121C2213yes—
222C4×#121C2213yes—
223C4×#121C2213yes—
224C4×#121C2213yes—
225#2296C2213yes—
226#2296C2213yes—
227#2296C2213yes—
228#2295C2213yes—
229C2×#389C2213yes—
230#2290C2213yes—
231#2290C2213yes—
232#2285C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#557—28no—
241#557—44no—
242#557—44no—
243#550Q8116yescomplemented
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#127C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×C22⋊Q8C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2316yes—
258C2×C22⋊Q8C2316yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2316yes—
262C2×#121C2313yes—
263C2×#121C2313yes—
264#520—28no—
265#520—44no—
266C4×#41—28no—
267C4×#41—44no—
268C4×#41—44no—
269C4×#41—44no—
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×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2316yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4C2313yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2316yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2316yes—
303C2×C4×D4C2316yes—
304C2×C4×D4C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C4⋊C4C2316yes—
316C22×C42C2313yes—
317C22×C42C2313yes—
318C22×C42C2313yes—
319C22×C42C2313yes—
320#400C2311yescharacteristic
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2316yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2313yes—
330#399C2316yes—
331#399C2313yes—
332#399C2316yes—
333#399C2316yes—
334#399C2316yes—
335#399C2313yes—
336#399C2316yes—
337#398C2313yes—
338#398C2316yes—
339#398C2316yes—
340#398C2313yes—
341#398C2311yescharacteristic
342#398C2313yes—
343#398C2316yes—
344#398C2316yes—
345#398C2311yescharacteristic
346#398C2313yes—
347#398C2316yes—
348#398C2316yes—
349#398C2311yescharacteristic
350#398C2316yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#396C2313yes—
357#396C2313yes—
358#396C2316yes—
359#396C2316yes—
360#396C2316yes—
361#396C2316yes—
362#396C2316yes—
363#396C2316yes—
364#396C2316yes—
365#396C2316yes—
366#396C2316yes—
367#396C2316yes—
368#396C2313yes—
369#396C2316yes—
370#396C2313yes—
371#396C2316yes—
372#395C2316yes—
373#395C2313yes—
374#395C2313yes—
375#395C2313yes—
376#395C2313yes—
377#395C2313yes—
378#395C2313yes—
379#393C2313yes—
380#393C2316yes—
381#393C2316yes—
382#393C2313yes—
383#393C2316yes—
384#391C2313yes—
385#391C2316yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2316yes—
394#390C2316yes—
395#390C2313yes—
396#390C2316yes—
397#390C2313yes—
398#390C2313yes—
399#390C2316yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2313yes—
405#390C2313yes—
406#390C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2316yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2316yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2316yes—
443#389C2316yes—
444#389C2311yescharacteristic
445#389C2311yescharacteristic
446#389C2311yescharacteristic
447#389C2316yes—
448#389C2313yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2316yes—
462#388C2313yes—
463#388C2316yes—
464#388C2316yes—
465#388C2313yes—
466#388C2316yes—
467#387C2311yescharacteristic
468#387C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2316yes—
473#387C2313yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2313yes—
478#387C2313yes—
479#387C2316yes—
480#387C2316yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2311yescharacteristic
487#387C2316yes—
488#387C2311yescharacteristic
489#387C2311yescharacteristic
490#387C2311yescharacteristic
491#387C2316yes—
492#387C2311yescharacteristic
493#387C2316yes—
494#387C2313yes—
495#387C2313yes—
496#387C2316yes—
497#386C2316yes—
498#386C2313yes—
499#386C2316yes—
500#386C2313yes—
501#386C2316yes—
502#386C2316yes—
503#386C2313yes—
504#386C2316yes—
505#386C2313yes—
506#386C2316yes—
507#386C2316yes—
508#386C2316yes—
509#385C2313yes—
510#385C2313yes—
511#385C2316yes—
512#385C2313yes—
513#385C2313yes—
514#385C2313yes—
515#385C2313yes—
516#385C2313yes—
517#385C2316yes—
518#385C2316yes—
519#385C2316yes—
520#385C2316yes—
521#385C2316yes—
522#385C2316yes—
523#385C2316yes—
524#385C2316yes—
525#385C2316yes—
526#385C2316yes—
527#385C2313yes—
528#385C2313yes—
529#385C2313yes—
530#385C2316yes—
531#385C2313yes—
532#385C2316yes—
533#385C2313yes—
534#385C2313yes—
535#385C2313yes—
536#385C2313yes—
537#385C2316yes—
538#385C2316yes—
539#385C2316yes—
540#385C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2316yes—
544#384C2313yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2316yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#380C2316yes—
561#380C2316yes—
562#380C2313yes—
563#380C2313yes—
564#380C2316yes—
565#380C2316yes—
566#380C2313yes—
567#380C2316yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2316yes—
576#380C2316yes—
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⋊C4C2311yescharacteristic
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2313yes—
622#376C2313yes—
623#376C2313yes—
624C2×#95C2316yes—
625C2×#95C2313yes—
626C2×#95C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41C2×Q818yes—
633C2×#41C2×Q818yes—
634C22×Q8C2413yes—
635C22×Q8C2413yes—
636C22×Q8C2413yes—
637C22×Q8C2411yescharacteristic
638C22×D4C2413yes—
639C22×D4C2413yes—
640C22×D4C2416yes—
641C22×D4C2413yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C23×C4C2416yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2416yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2413yes—
654C4⋊Q8—212no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657#127C2×Q8124yes—
658#125—212no—
659#125—212no—
660#125—46no—
661#125—46no—
662#125—46no—
663#125—46no—
664#125—46no—
665C22⋊Q8—46no—
666C22⋊Q8—412no—
667C22⋊Q8—412no—
668C22⋊Q8—46no—
669C22⋊Q8—46no—
670C22⋊Q8—46no—
671C22⋊Q8—86no—
672#121C2×Q8124yes—
673#121C2×Q8124yes—
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—24no—
685C4×Q8—212no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—86no—
689C4×Q8C2×Q818yes—
690C4×Q8#4118yes—
691C4×D4—212no—
692C4×D4—212no—
693C4×D4—212no—
694C4×D4—212no—
695C4×D4—46no—
696C4×D4—46no—
697C4×D4—46no—
698C4×D4—46no—
699C4×D4—46no—
700C4×D4—46no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—46no—
704C4×D4—412no—
705C4×D4—46no—
706C4×D4—86no—
707C4×D4—86no—
708C4×D4C2×Q8124yes—
709#117—212no—
710#117—212no—
711#117—46no—
712#117—46no—
713#117—46no—
714#117—46no—
715C2×C4⋊C4—212no—
716C2×C4⋊C4—46no—
717C2×C4⋊C4—46no—
718C2×C4⋊C4—46no—
719C2×C4⋊C4—86no—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2416yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2416yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2416yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2416yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C42—212no—
819C2×C42—46no—
820C2×C42—46no—
821C2×C42—46no—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2411yescharacteristic
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2411yescharacteristic
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2416yes—
841C2×C42C2416yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846C2×C42C2411yescharacteristic
847C2×C42C2413yes—
848C2×C42C2413yes—
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2411yescharacteristic
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2416yes—
859#95C2416yes—
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2413yes—
871#95C2413yes—
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2416yes—
883#95C2416yes—
884#95C2413yes—
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2416yes—
892#95C2413yes—
893#95C2416yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2416yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2416yes—
909#95C2416yes—
910C24C2513yes—
911C24C2513yes—
912#41—232no—
913#41—232no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—26no—
917C2×Q8—43no—
918C2×Q8—43no—
919C2×Q8—43no—
920C2×Q8—43no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8C22×Q814yes—
924C2×Q8C2×#4114yes—
925C2×Q8H(5,𝔽2)14yes—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—46no—
931C2×D4—43no—
932C2×D4—43no—
933C2×D4—46no—
934C2×D4C22×Q8112yes—
935C2×D4C22×Q8112yes—
936C2×D4C22×Q8112yes—
937C2×D4C22×Q8124yes—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—26no—
944C22×C4—212no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—43no—
949C22×C4—43no—
950C22×C4—43no—
951C22×C4—43no—
952C22×C4—43no—
953C22×C4—43no—
954C22×C4—43no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—46no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4—43no—
963C22×C4—43no—
964C22×C4—43no—
965C22×C4—46no—
966C22×C4—43no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—46no—
970C22×C4—46no—
971C22×C4—46no—
972C22×C4C22×Q8112yes—
973C22×C4C22×Q8112yes—
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2513yes—
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2513yes—
989C22×C4C2513yes—
990C22×C4C2513yes—
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2513yes—
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2513yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2513yes—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—22no—
1006C4⋊C4—26no—
1007C4⋊C4—22no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—212no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—26no—
1030C4⋊C4—22no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—46no—
1039C4⋊C4—46no—
1040C4⋊C4—41no—
1041C4⋊C4—46no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—46no—
1053C4⋊C4—46no—
1054C4⋊C4—43no—
1055C4⋊C4—46no—
1056C4⋊C4—46no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—46no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—46no—
1069C4⋊C4—46no—
1070C4⋊C4C22×Q814yes—
1071C4⋊C4C22×Q8112yes—
1072C4⋊C4C2×#41112yes—
1073C22⋊C4—26no—
1074C22⋊C4—212no—
1075C22⋊C4—26no—
1076C22⋊C4—26no—
1077C22⋊C4—26no—
1078C22⋊C4—26no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—46no—
1082C22⋊C4—46no—
1083C22⋊C4—46no—
1084C22⋊C4—46no—
1085C22⋊C4—46no—
1086C22⋊C4—43no—
1087C22⋊C4—43no—
1088C22⋊C4—43no—
1089C22⋊C4—46no—
1090C22⋊C4—46no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—46no—
1098C22⋊C4—46no—
1099C22⋊C4C22×Q8112yes—
1100C22⋊C4C22×Q8112yes—
1101C42—22no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—22no—
1115C42—26no—
1116C42—41no—
1117C42—41no—
1118C42—41no—
1119C42—43no—
1120C42—43no—
1121C42—43no—
1122C42—43no—
1123C42—46no—
1124C42—46no—
1125C42—43no—
1126C42C22×Q8112yes—
1127C42C2×#41112yes—
1128C23—23no—
1129C23—23no—
1130C23—23no—
1131C23—23no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23C23×Q816yes—
1141C23C23×Q816yes—
1142C23C2611yescharacteristic
1143Q8—412no—
1144Q8—86no—
1145Q8—86no—
1146Q8#554116yes—
1147D4—224no—
1148D4—224no—
1149D4—424no—
1150D4—412no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—21no—
1169C2×C4—224no—
1170C2×C4—224no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—21no—
1228C2×C4—412no—
1229C2×C4—812no—
1230C2×C4—86no—
1231C2×C4—86no—
1232C2×C4—86no—
1233C2×C4—86no—
1234C2×C4—86no—
1235C2×C4—86no—
1236C2×C4—86no—
1237C2×C4—166no—
1238C2×C4C23×Q812yes—
1239C2×C4C23×Q816yes—
1240C2×C4C23×Q812yes—
1241C2×C4C23×Q812yes—
1242C2×C4C23×Q816yes—
1243C2×C4C22×#4112yes—
1244C2×C4C22×#4116yes—
1245C2×C4C22×#4116yes—
1246C2×C4C2×H(5,𝔽2)16yes—
1247C2×C4#58512yes—
1248C2×C4#58512yes—
1249C2×C4#58512yes—
1250C22—26no—
1251C22—26no—
1252C22—26no—
1253C22—26no—
1254C22—26no—
1255C22—26no—
1256C22—43no—
1257C22—43no—
1258C22—43no—
1259C22—43no—
1260C22—43no—
1261C22—43no—
1262C22—43no—
1263C22—43no—
1264C22C24×Q811yescharacteristic
1265C22C23×#4111yescharacteristic
1266C22C22×H(5,𝔽2)11yescharacteristic
1267C22C2×#58511yescharacteristic
1268C22C2×#58511yescharacteristic
1269C22C2×#58511yescharacteristic
1270C22H(7,𝔽2)11yescharacteristic
1271C4—26no—
1272C4—26no—
1273C4—22no—
1274C4—22no—
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—43no—
1281C4—41no—
1282C4—43no—
1283C4—41no—
1284C4—43no—
1285C4—41no—
1286C4—43no—
1287C4—43no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—43no—
1292C4—43no—
1293C4—43no—
1294C4—41no—
1295C4—41no—
1296C4—43no—
1297C4—43no—
1298C4—43no—
1299C4C2×#554112yes—
1300C2—46no—
1301C2—46no—
1302C2C22×#55411yescharacteristic
1303C2#6279311yescharacteristic
1304C2#6281311yescharacteristic
1305C2#6289911yescharacteristic
1306C2#6298911yescharacteristic
1307C2#6300811yescharacteristic
1308C2#6301911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59921C2semidirect
2. #59919C2semidirect
3. #59897C2semidirect
4. #59457C2semidirect
5. #59214C2semidirect
6. #45362C2semidirect
7. #45360C2semidirect
8. #44951C2semidirect
9. #44908C2semidirect
10. #39692C2semidirect
11. #39672C2semidirect
12. #38107C2semidirect
13. #37879C2semidirect
14. #36570C2semidirect
15. #36475C2semidirect
16. #36445C2semidirect
17. #36431C2semidirect
18. #36431C2semidirect
19. #36431C2semidirect
20. #36363C2semidirect
21. #35971C2semidirect
22. #35957C2semidirect
23. #35816C2semidirect
24. #35816C2semidirect
25. #34840C2semidirect
26. #34337C2semidirect
29. #34250C2semidirect
31. C4⋊C4×#41C2semidirect
243. #550Q8semidirect

Maximal subgroups

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

subgroupindex
#599212
#599192
#598972
#594572
#592142
#453622
#453602
#449512
#449082
#396922
#396722
#381072
#378792
#365702
#364752
#364452
#364312
#363632
#359712
#359572
#358162
#348402
#343372
#342952
#342502
C4×#5502
C4⋊C4×#412