Finite Group Databasebeta

← #7688785

Subgroups — #7688785

Order 512.

5013 conjugacy classes of subgroups.

The subgroup lattice has 1303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59922C213yesmaximal, complemented
2#59756C213yesmaximal, complemented
3#59569C213yesmaximal, complemented
4#59462C213yesmaximal, complemented
5#59324C213yesmaximal, complemented
6#45434C213yesmaximal, complemented
7#45359C213yesmaximal, complemented
8#45086C213yesmaximal, complemented
9#44940C213yesmaximal, complemented
10#39690C213yesmaximal, complemented
11#39675C213yesmaximal, complemented
12#38104C213yesmaximal, complemented
13#37878C213yesmaximal, complemented
14#36564C213yesmaximal, complemented
15Q8×#125C211yesmaximal, characteristic, complemented
16Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
17#36456C211yesmaximal, characteristic, complemented
18#36445C211yesmaximal, characteristic, complemented
19#36445C211yesmaximal, characteristic, complemented
20#36407C213yesmaximal, complemented
21#35937C211yesmaximal, characteristic, complemented
22#35868C211yesmaximal, characteristic, complemented
23#35845C211yesmaximal, characteristic, complemented
24#35786C211yesmaximal, characteristic, complemented
25#34840C213yesmaximal, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34293C211yesmaximal, characteristic
28#34293C211yesmaximal, characteristic
29#34249C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2859C2213yes—
43#2857C2213yes—
44#2857C2213yes—
45#2857C2213yes—
46#2857C2213yes—
47#2807C2216yes—
48#2790C2216yes—
49#2780C2216yes—
50#2768C2216yes—
51#2768C2216yes—
52#2748C2216yes—
53#2742C2216yes—
54#2742C2216yes—
55#2732C2216yes—
56#2729C2216yes—
57#2720C2216yes—
58#2704C2216yes—
59#2704C2216yes—
60#2692C2216yes—
61#2660C2213yes—
62#2647C2213yes—
63#2629C2213yes—
64#2628C2213yes—
65#2590C2216yes—
66#2590C2213yes—
67#2589C2216yes—
68#2589C2213yes—
69#2588C2213yes—
70#2587C2216yes—
71#2587C2213yes—
72#2586C2213yes—
73#2586C2216yes—
74#2585C2213yes—
75#2584C2213yes—
76#2583C2213yes—
77#2582C2213yes—
78#2582C2213yes—
79#2581C2213yes—
80#2579C2213yes—
81#2574C2213yes—
82#2574C2216yes—
83#2574C2216yes—
84#2570C2213yes—
85#2567C2213yes—
86#2567C2213yes—
87#2565C2213yes—
88#2564C2213yes—
89#2563C2213yes—
90#2556C2211yescharacteristic
91#2556C2216yes—
92#2556C2216yes—
93#2556C2216yes—
94#2552C2213yes—
95#2552C2213yes—
96#2552C2213yes—
97#2551C2213yes—
98#2551C2213yes—
99#2550C2213yes—
100#2550C2213yes—
101#2549C2216yes—
102#2549C2213yes—
103#2549C2216yes—
104#2546C2213yes—
105#2542C2213yes—
106#2542C2213yes—
107#2538C2213yes—
108#2538C2213yes—
109#2538C2213yes—
110#2522C2216yes—
111#2522C2216yes—
112#2520C2216yes—
113#2509C2213yes—
114#2507C2213yes—
115#2507C2213yes—
116#2507C2213yes—
117#2507C2213yes—
118#2507C2216yes—
119#2507C2213yes—
120#2506C2213yes—
121#2506C2213yes—
122#2505C2213yes—
123#2473C2213yes—
124#2454C2216yes—
125#2454C2213yes—
126#2454C2213yes—
127#2454C2213yes—
128#2454C2213yes—
129#2453C2213yes—
130#2453C2213yes—
131#2453C2213yes—
132#2452C2213yes—
133#2452C2216yes—
134#2452C2213yes—
135#2451C2213yes—
136#2451C2213yes—
137#2451C2213yes—
138#2450C2213yes—
139#2449C2213yes—
140#2441C2213yes—
141#2441C2213yes—
142#2441C2213yes—
143#2441C2213yes—
144#2441C2213yes—
145#2441C2213yes—
146#2441C2213yes—
147#2440C2216yes—
148#2440C2213yes—
149#2440C2213yes—
150#2439C2213yes—
151#2439C2213yes—
152#2439C2213yes—
153#2402C2213yes—
154#2399C2213yes—
155#2396C2213yes—
156#2396C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2370C2216yes—
160#2369C2213yes—
161#2369C2216yes—
162#2367C2213yes—
163#2367C2213yes—
164#2367C2213yes—
165#2363C2213yes—
166#2363C2213yes—
167#2362C2213yes—
168#2362C2213yes—
169#2362C2213yes—
170#2361C2213yes—
171#2355C2213yes—
172#2354C2213yes—
173#2354C2213yes—
174#2352C2213yes—
175#2351C2211yescharacteristic
176#2351C2213yes—
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2213yes—
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2213yes—
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2213yes—
195#2349C2213yes—
196#2349C2213yes—
197D4×C4⋊C4C2213yes—
198D4×C4⋊C4C2213yes—
199#2345C2216yes—
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2331C2213yes—
207#2330C2213yes—
208#2326C2213yes—
209#2326C2213yes—
210#2324C2213yes—
211#2324C2213yes—
212#2317C2213yes—
213#2317C2213yes—
214C4×#125C2213yes—
215C4×#125C2213yes—
216C4×#124C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×C22⋊Q8C2213yes—
223C4×C22⋊Q8C2213yes—
224C4×#121C2213yes—
225#2296C2213yes—
226#2296C2213yes—
227#2296C2213yes—
228#2296C2213yes—
229#2295C2213yes—
230#2290C2213yes—
231#2290C2213yes—
232#2285C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—44no—
241#557—28no—
242#557—44no—
243#548Q8116yescomplemented
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2316yes—
249C2×C4⋊Q8C2313yes—
250C2×#125C2311yescharacteristic
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2316yes—
256C2×#125C2316yes—
257C2×#124C2313yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2316yes—
264C2×C22⋊Q8C2316yes—
265C2×C22⋊Q8C2316yes—
266C2×C22⋊Q8C2313yes—
267C2×#121C2313yes—
268#519—28no—
269#519—44no—
270C4×#41—28no—
271C4×#41—44no—
272C4×#41—44no—
273C2×C4×Q8—44no—
274C2×C4×Q8C2313yes—
275C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
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×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×D4C2313yes—
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×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C42C2313yes—
316C22×C42C2313yes—
317C22×C42C2313yes—
318C22×C42C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2316yes—
324#400C2313yes—
325#400C2313yes—
326#400C2316yes—
327#399C2311yescharacteristic
328#399C2313yes—
329#399C2316yes—
330#399C2316yes—
331#399C2316yes—
332#399C2316yes—
333#399C2316yes—
334#398C2313yes—
335#398C2316yes—
336#398C2316yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2316yes—
342#398C2316yes—
343#398C2311yescharacteristic
344#398C2313yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2316yes—
353#398C2316yes—
354#398C2316yes—
355#398C2316yes—
356#398C2316yes—
357#396C2313yes—
358#396C2316yes—
359#396C2316yes—
360#396C2311yescharacteristic
361#396C2313yes—
362#396C2313yes—
363#396C2316yes—
364#396C2316yes—
365#396C2316yes—
366#396C2316yes—
367#396C2316yes—
368#395C2313yes—
369#395C2313yes—
370#395C2316yes—
371#395C2316yes—
372#395C2316yes—
373#395C2313yes—
374#395C2316yes—
375#395C2313yes—
376#395C2313yes—
377#395C2316yes—
378#395C2311yescharacteristic
379#393C2316yes—
380#393C2316yes—
381#393C2313yes—
382#393C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2316yes—
390#391C2316yes—
391#391C2313yes—
392#391C2313yes—
393#391C2316yes—
394#391C2313yes—
395#391C2316yes—
396#391C2316yes—
397#391C2313yes—
398#391C2313yes—
399#391C2311yescharacteristic
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2316yes—
404#390C2316yes—
405#390C2313yes—
406#390C2313yes—
407#390C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2316yes—
414#389C2316yes—
415#389C2316yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2316yes—
420#389C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2311yescharacteristic
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2316yes—
446#389C2313yes—
447#389C2316yes—
448#389C2313yes—
449#389C2316yes—
450#389C2311yescharacteristic
451#389C2316yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2316yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2313yes—
470#388C2313yes—
471#388C2316yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2311yescharacteristic
476#388C2311yescharacteristic
477#388C2316yes—
478#388C2316yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2316yes—
484#387C2313yes—
485#387C2313yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2316yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2316yes—
501#387C2313yes—
502#387C2313yes—
503#387C2316yes—
504#387C2313yes—
505#387C2316yes—
506#387C2313yes—
507#387C2313yes—
508#387C2311yescharacteristic
509#386C2313yes—
510#386C2313yes—
511#386C2313yes—
512#386C2313yes—
513#386C2316yes—
514#385C2313yes—
515#385C2313yes—
516#385C2313yes—
517#385C2316yes—
518#385C2313yes—
519#385C2316yes—
520#385C2313yes—
521#385C2313yes—
522#385C2313yes—
523#385C2316yes—
524#385C2316yes—
525#385C2313yes—
526#385C2313yes—
527#385C2313yes—
528#385C2313yes—
529#385C2313yes—
530#385C2313yes—
531#385C2313yes—
532#385C2316yes—
533#385C2316yes—
534#385C2316yes—
535#385C2316yes—
536#385C2313yes—
537#385C2311yescharacteristic
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2313yes—
544#384C2316yes—
545#384C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2316yes—
555#382C2313yes—
556#382C2313yes—
557#380C2313yes—
558#380C2316yes—
559#380C2313yes—
560#380C2316yes—
561#380C2313yes—
562#380C2316yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2316yes—
571#380C2316yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2316yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2316yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2316yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2311yescharacteristic
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2316yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2316yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2316yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C22⋊C4C2311yescharacteristic
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2316yes—
623#376C2313yes—
624#376C2313yes—
625C2×#95C2313yes—
626C2×#95C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41C2×Q818yes—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8C2×Q818yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2413yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2416yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C23×C4C2413yes—
643C23×C4C2411yescharacteristic
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C4⋊Q8—212no—
653C4⋊Q8—46no—
654C4⋊Q8—46no—
655C4⋊Q8—46no—
656C4⋊Q8—46no—
657C4⋊Q8—412no—
658#125—212no—
659#125—212no—
660#125—24no—
661#125—46no—
662#125—46no—
663#125—412no—
664#125—86no—
665#124C2×Q8124yes—
666C22⋊Q8—24no—
667C22⋊Q8—46no—
668C22⋊Q8—46no—
669C22⋊Q8—46no—
670C22⋊Q8—86no—
671C22⋊Q8—86no—
672C22⋊Q8—86no—
673C22⋊Q8—86no—
674C22⋊Q8C2×Q8124yes—
675#121C2×Q8124yes—
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—24no—
686C4×Q8—24no—
687C4×Q8—212no—
688C4×Q8—212no—
689C4×Q8—212no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×Q8—46no—
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⋊C4C2411yescharacteristic
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2416yes—
784C2×C4⋊C4C2416yes—
785C2×C4⋊C4C2416yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
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⋊C4C2411yescharacteristic
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2416yes—
815C2×C42—212no—
816C2×C42—46no—
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×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2416yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2416yes—
843C2×C42C2416yes—
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846C2×C42C2413yes—
847C2×C42C2413yes—
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2413yes—
867#95C2413yes—
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2416yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2416yes—
885#95C2413yes—
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2413yes—
889#95C2416yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2416yes—
895#95C2416yes—
896#95C2413yes—
897#95C2416yes—
898#95C2413yes—
899#95C2413yes—
900#95C2416yes—
901#95C2416yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909C24C2511yescharacteristic
910C24C2513yes—
911#41—232no—
912C2×Q8—232no—
913C2×Q8—26no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—22no—
917C2×Q8—22no—
918C2×Q8—26no—
919C2×Q8—41no—
920C2×Q8—43no—
921C2×Q8—43no—
922C2×Q8—43no—
923C2×Q8—43no—
924C2×Q8—46no—
925C2×Q8—46no—
926C2×Q8—46no—
927C2×Q8C22×Q8112yes—
928C2×Q8C22×Q814yes—
929C2×Q8C2×#4114yes—
930C2×Q8H(5,𝔽2)14yes—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—43no—
934C2×D4—43no—
935C2×D4C22×Q8112yes—
936C2×D4C22×Q8112yes—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—41no—
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—43no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4—43no—
963C22×C4—43no—
964C22×C4—43no—
965C22×C4C22×Q8112yes—
966C22×C4C22×Q8112yes—
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2513yes—
971C22×C4C2511yescharacteristic
972C22×C4C2513yes—
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2511yescharacteristic
989C22×C4C2513yes—
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2513yes—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—22no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—212no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—46no—
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—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—46no—
1051C4⋊C4—46no—
1052C4⋊C4—43no—
1053C4⋊C4—46no—
1054C4⋊C4—46no—
1055C4⋊C4—46no—
1056C4⋊C4—46no—
1057C4⋊C4—46no—
1058C4⋊C4—46no—
1059C4⋊C4—46no—
1060C4⋊C4—46no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—46no—
1064C4⋊C4—46no—
1065C4⋊C4C22×Q8112yes—
1066C4⋊C4C22×Q8112yes—
1067C4⋊C4C2×#41112yes—
1068C4⋊C42−1+414yes—
1069C22⋊C4—26no—
1070C22⋊C4—22no—
1071C22⋊C4—212no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—26no—
1076C22⋊C4—41no—
1077C22⋊C4—43no—
1078C22⋊C4—46no—
1079C22⋊C4—46no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—46no—
1087C22⋊C4—46no—
1088C22⋊C4—43no—
1089C22⋊C4—46no—
1090C22⋊C4—43no—
1091C22⋊C4C22×Q814yes—
1092C22⋊C4C22×Q8112yes—
1093C22⋊C4C22×Q8124yes—
1094C42—22no—
1095C42—26no—
1096C42—26no—
1097C42—212no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—22no—
1109C42—41no—
1110C42—41no—
1111C42—43no—
1112C42—43no—
1113C42—43no—
1114C42—43no—
1115C42—46no—
1116C42—43no—
1117C42—43no—
1118C42—46no—
1119C42—43no—
1120C42—46no—
1121C42C22×Q8112yes—
1122C42C2×#41112yes—
1123C23—21no—
1124C23—23no—
1125C23—21no—
1126C23—23no—
1127C23—21no—
1128C23—23no—
1129C23—23no—
1130C23—21no—
1131C23—23no—
1132C23—21no—
1133C23—23no—
1134C23—21no—
1135C23C23×Q816yes—
1136C23C23×Q812yes—
1137C23C2611yescharacteristic
1138Q8—224no—
1139Q8—44no—
1140Q8—86no—
1141Q8—86no—
1142Q8—166no—
1143Q8#554116yes—
1144D4—224no—
1145D4—412no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—21no—
1156C2×C4—23no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—224no—
1169C2×C4—224no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—21no—
1221C2×C4—44no—
1222C2×C4—412no—
1223C2×C4—86no—
1224C2×C4—86no—
1225C2×C4—86no—
1226C2×C4—86no—
1227C2×C4—86no—
1228C2×C4—86no—
1229C2×C4C23×Q812yes—
1230C2×C4C23×Q816yes—
1231C2×C4C23×Q816yes—
1232C2×C4C23×Q812yes—
1233C2×C4C23×Q816yes—
1234C2×C4C22×#4116yes—
1235C2×C4C22×#4112yes—
1236C2×C4C22×#4116yes—
1237C2×C4C2×H(5,𝔽2)16yes—
1238C2×C4C2×2−1+412yes—
1239C2×C4C2×2−1+412yes—
1240C2×C4C2×2−1+412yes—
1241C2×C4#58512yes—
1242C2×C4#58512yes—
1243C22—22no—
1244C22—26no—
1245C22—22no—
1246C22—26no—
1247C22—22no—
1248C22—26no—
1249C22—43no—
1250C22—41no—
1251C22—41no—
1252C22—43no—
1253C22—43no—
1254C22—41no—
1255C22—41no—
1256C22—43no—
1257C22C24×Q811yescharacteristic
1258C22C23×#4111yescharacteristic
1259C22C22×H(5,𝔽2)11yescharacteristic
1260C22C22×2−1+411yescharacteristic
1261C22C2×#58511yescharacteristic
1262C22C2×#58511yescharacteristic
1263C22H(7,𝔽2)11yescharacteristic
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—26no—
1271C4—26no—
1272C4—22no—
1273C4—22no—
1274C4—26no—
1275C4—43no—
1276C4—43no—
1277C4—43no—
1278C4—43no—
1279C4—41no—
1280C4—43no—
1281C4—43no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—43no—
1287C4—41no—
1288C4—43no—
1289C4—43no—
1290C4—43no—
1291C4—43no—
1292C4C2×#554112yes—
1293C2—42no—
1294C2—46no—
1295C2C22×#55411yescharacteristic
1296C2#6280511yescharacteristic
1297C2#6281311yescharacteristic
1298C2#6289911yescharacteristic
1299C2Q8×2−1+411yescharacteristic
1300C2#6300611yescharacteristic
1301C2#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. #59922C2semidirect
2. #59756C2semidirect
3. #59569C2semidirect
4. #59462C2semidirect
5. #59324C2semidirect
6. #45434C2semidirect
7. #45359C2semidirect
8. #45086C2semidirect
9. #44940C2semidirect
10. #39690C2semidirect
11. #39675C2semidirect
12. #38104C2semidirect
13. #37878C2semidirect
14. #36564C2semidirect
15. Q8×#125C2semidirect
16. Q8×C22⋊Q8C2semidirect
17. #36456C2semidirect
18. #36445C2semidirect
19. #36445C2semidirect
20. #36407C2semidirect
21. #35937C2semidirect
22. #35868C2semidirect
23. #35845C2semidirect
24. #35786C2semidirect
25. #34840C2semidirect
26. #34336C2semidirect
29. #34249C2semidirect
31. C4⋊C4×#41C2semidirect
243. #548Q8semidirect

Maximal subgroups

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

subgroupindex
#599222
#597562
#595692
#594622
#593242
#454342
#453592
#450862
#449402
#396902
#396752
#381042
#378782
#365642
Q8×#1252
Q8×C22⋊Q82
#364562
#364452
#364072
#359372
#358682
#358452
#357862
#348402
#343362
#342932
#342492
C4×#5482
C4⋊C4×#412