Finite Group Databasebeta

← #7688699

Subgroups — #7688699

Order 512.

5317 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59860C213yesmaximal, complemented
2#59859C213yesmaximal, complemented
3#59702C213yesmaximal, complemented
4#59401C213yesmaximal, complemented
5#59212C213yesmaximal, complemented
6#45257C213yesmaximal, complemented
7#45224C213yesmaximal, complemented
8#45038C213yesmaximal, complemented
9#44970C213yesmaximal, complemented
10#39284C213yesmaximal, complemented
11#39256C213yesmaximal, complemented
12#38131C213yesmaximal, complemented
13#37899C213yesmaximal, complemented
14#36606C213yesmaximal, complemented
15#36585C211yesmaximal, characteristic, complemented
16#36578C211yesmaximal, characteristic, complemented
17#36455C211yesmaximal, characteristic, complemented
18#36430C211yesmaximal, characteristic, complemented
19#36430C211yesmaximal, characteristic, complemented
20#36369C213yesmaximal, complemented
21#36076C211yesmaximal, characteristic, complemented
22#35971C211yesmaximal, characteristic, complemented
23#35883C211yesmaximal, characteristic, complemented
24#35831C211yesmaximal, characteristic, complemented
25#34856C213yesmaximal, complemented
26#34295C211yesmaximal, characteristic, complemented
27#34295C211yesmaximal, characteristic, complemented
28#34294C211yesmaximal, characteristic, complemented
29#34263C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic, complemented
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2860C2213yes—
45#2856C2213yes—
46#2854C2213yes—
47#2850C2213yes—
48#2850C2213yes—
49#2796C2216yes—
50#2787C2216yes—
51#2786C2216yes—
52#2779C2216yes—
53#2778C2216yes—
54#2778C2216yes—
55#2778C2216yes—
56#2778C2216yes—
57#2756C2216yes—
58#2753C2216yes—
59#2750C2216yes—
60#2746C2216yes—
61#2708C2216yes—
62#2688C2216yes—
63#2647C2213yes—
64#2645C2213yes—
65#2624C2213yes—
66#2620C2213yes—
67#2600C2216yes—
68#2598C2216yes—
69#2597C2213yes—
70#2596C2213yes—
71#2595C2216yes—
72#2595C2213yes—
73#2594C2213yes—
74#2593C2216yes—
75#2593C2213yes—
76#2591C2213yes—
77#2591C2216yes—
78#2585C2213yes—
79#2579C2213yes—
80#2578C2216yes—
81#2576C2216yes—
82#2573C2216yes—
83#2573C2211yescharacteristic
84#2571C2213yes—
85#2570C2213yes—
86#2569C2213yes—
87#2559C2216yes—
88#2554C2213yes—
89#2544C2213yes—
90#2544C2213yes—
91#2544C2213yes—
92#2543C2213yes—
93#2541C2213yes—
94#2537C2213yes—
95#2537C2213yes—
96#2535C2216yes—
97#2535C2213yes—
98#2535C2213yes—
99#2516C2216yes—
100#2514C2213yes—
101#2514C2213yes—
102#2513C2213yes—
103#2513C2213yes—
104#2513C2213yes—
105#2511C2213yes—
106#2510C2213yes—
107#2509C2213yes—
108#2508C2213yes—
109#2508C2213yes—
110#2507C2213yes—
111#2504C2213yes—
112#2504C2213yes—
113#2497C2213yes—
114#2495C2213yes—
115#2494C2213yes—
116#2494C2213yes—
117#2494C2216yes—
118#2494C2213yes—
119#2494C2213yes—
120#2487C2213yes—
121#2486C2213yes—
122#2485C2216yes—
123#2481C2213yes—
124#2476C2216yes—
125#2464C2216yes—
126#2456C2216yes—
127#2448C2213yes—
128#2448C2213yes—
129#2445C2213yes—
130#2445C2213yes—
131#2444C2213yes—
132#2444C2216yes—
133#2443C2213yes—
134#2443C2216yes—
135#2428C2213yes—
136#2428C2213yes—
137#2428C2213yes—
138#2428C2213yes—
139#2428C2213yes—
140#2427C2213yes—
141#2427C2213yes—
142#2427C2213yes—
143#2421C2213yes—
144#2421C2213yes—
145#2420C2213yes—
146#2420C2213yes—
147#2417C2213yes—
148#2416C2213yes—
149#2415C2213yes—
150#2415C2213yes—
151#2414C2213yes—
152#2414C2213yes—
153#2414C2213yes—
154#2414C2213yes—
155#2402C2213yes—
156#2401C2213yes—
157#2395C2213yes—
158#2392C2213yes—
159#2374C2216yes—
160#2367C2213yes—
161#2367C2213yes—
162#2366C2213yes—
163#2366C2213yes—
164#2364C2216yes—
165#2363C2213yes—
166#2363C2216yes—
167#2363C2213yes—
168#2362C2213yes—
169#2361C2213yes—
170#2361C2213yes—
171#2361C2213yes—
172#2361C2213yes—
173#2360C2213yes—
174#2357C2213yes—
175#2354C2213yes—
176#2352C2213yes—
177#2352C2213yes—
178#2352C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189#2349C2213yes—
190#2349C2213yes—
191D4×C4⋊C4C2213yes—
192D4×C4⋊C4C2213yes—
193D4×C4⋊C4C2213yes—
194#2345C2213yes—
195#2344C2213yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2328C2213yes—
207#2328C2213yes—
208#2326C2213yes—
209#2324C2213yes—
210#2324C2213yes—
211#2323C2213yes—
212#2319C2213yes—
213#2314C2213yes—
214C4×#126C2213yes—
215C4×#124C2213yes—
216C4×C22⋊Q8C2213yes—
217C4×#123C2213yes—
218C4×#121C2213yes—
219C4×#121C2213yes—
220C4×#121C2213yes—
221C4×#121C2213yes—
222C4×#121C2213yes—
223C4×#121C2213yes—
224C4×#121C2213yes—
225#2298C2213yes—
226#2296C2213yes—
227#2296C2213yes—
228#2293C2213yes—
229#2290C2213yes—
230#2290C2213yes—
231#2290C2213yes—
232#2285C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242#550—28no—
243#550—28no—
244#550—44no—
245#548—28no—
246#548—28no—
247#548—44no—
248C2×#127C2313yes—
249C2×#127C2313yes—
250C2×#127C2313yes—
251C2×#126C2313yes—
252C2×#124C2313yes—
253C2×#124C2313yes—
254C2×#124C2313yes—
255C2×#123C2313yes—
256C2×#123C2316yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×#121C2313yes—
261C2×#121C2313yes—
262C2×#121C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266C2×#121C2316yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2316yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2316yes—
275#520—28no—
276#520—44no—
277C4×#41—28no—
278C4×#41—44no—
279C4×#41—44no—
280C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2311yescharacteristic
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×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2316yes—
313C2×C4×D4C2316yes—
314C2×C4×D4C2316yes—
315C2×#117C2313yes—
316C2×#117C2313yes—
317C2×#117C2313yes—
318C2×#117C2313yes—
319C2×#117C2313yes—
320C2×#117C2316yes—
321C22×C4⋊C4C2313yes—
322C22×C4⋊C4C2313yes—
323C22×C4⋊C4C2313yes—
324C22×C4⋊C4C2313yes—
325C22×C4⋊C4C2313yes—
326C22×C42C2313yes—
327C22×C42C2313yes—
328C22×C42C2313yes—
329C22×C42C2313yes—
330#401C2316yes—
331#401C2313yes—
332#401C2316yes—
333#400C2311yescharacteristic
334#400C2313yes—
335#400C2316yes—
336#400C2313yes—
337#400C2316yes—
338#400C2311yescharacteristic
339#400C2316yes—
340#400C2313yes—
341#400C2316yes—
342#400C2316yes—
343#400C2313yes—
344#400C2313yes—
345#400C2313yes—
346#399C2313yes—
347#399C2316yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2316yes—
354#398C2313yes—
355#397C2311yescharacteristic
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2316yes—
364#397C2316yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2316yes—
369#397C2316yes—
370#396C2316yes—
371#396C2311yescharacteristic
372#396C2313yes—
373#396C2313yes—
374#394C2316yes—
375#394C2316yes—
376#394C2313yes—
377#394C2316yes—
378#394C2316yes—
379#394C2313yes—
380#394C2316yes—
381#394C2316yes—
382#394C2313yes—
383#394C2313yes—
384#394C2313yes—
385#394C2316yes—
386#394C2316yes—
387#394C2316yes—
388#394C2316yes—
389#392C2316yes—
390#392C2316yes—
391#392C2313yes—
392#392C2316yes—
393#392C2316yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2316yes—
405#390C2316yes—
406#390C2313yes—
407#390C2313yes—
408#390C2313yes—
409#390C2316yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2316yes—
425#389C2313yes—
426#389C2311yescharacteristic
427#389C2313yes—
428#389C2313yes—
429#389C2316yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2316yes—
449#388C2316yes—
450#388C2313yes—
451#388C2316yes—
452#388C2311yescharacteristic
453#388C2311yescharacteristic
454#388C2313yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2313yes—
462#388C2313yes—
463#388C2313yes—
464#388C2313yes—
465#388C2313yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2316yes—
471#388C2313yes—
472#388C2313yes—
473#388C2316yes—
474#388C2316yes—
475#388C2313yes—
476#388C2313yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2313yes—
494#387C2311yescharacteristic
495#387C2316yes—
496#387C2311yescharacteristic
497#387C2311yescharacteristic
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2316yes—
503#387C2316yes—
504#386C2313yes—
505#386C2316yes—
506#386C2313yes—
507#386C2316yes—
508#386C2313yes—
509#386C2313yes—
510#386C2316yes—
511#386C2316yes—
512#386C2313yes—
513#386C2313yes—
514#386C2316yes—
515#386C2316yes—
516#386C2316yes—
517#386C2316yes—
518#386C2313yes—
519#386C2313yes—
520#386C2313yes—
521#386C2316yes—
522#386C2316yes—
523#386C2316yes—
524#386C2313yes—
525#386C2313yes—
526#386C2316yes—
527#386C2316yes—
528#386C2316yes—
529#386C2316yes—
530#386C2313yes—
531#386C2316yes—
532#386C2313yes—
533#385C2313yes—
534#385C2313yes—
535#385C2316yes—
536#385C2311yescharacteristic
537#385C2316yes—
538#385C2313yes—
539#385C2313yes—
540#385C2313yes—
541#385C2313yes—
542#385C2316yes—
543#385C2316yes—
544#385C2316yes—
545#385C2316yes—
546#385C2316yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#383C2311yescharacteristic
551#383C2316yes—
552#382C2313yes—
553#382C2313yes—
554#382C2316yes—
555#382C2313yes—
556#382C2313yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#381C2316yes—
561#381C2311yescharacteristic
562#381C2316yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2316yes—
569#380C2316yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2316yes—
579#380C2316yes—
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⋊C4C2311yescharacteristic
589C4×C4⋊C4C2316yes—
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×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2311yescharacteristic
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2316yes—
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⋊C4C2313yes—
623C4×C22⋊C4C2316yes—
624C4×C22⋊C4C2313yes—
625#376C2313yes—
626#376C2313yes—
627C2×#95C2313yes—
628C2×#95C2313yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41#4118yes—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2411yescharacteristic
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2416yes—
651C22×D4C2416yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2416yes—
656C23×C4C2413yes—
657C23×C4C2413yes—
658C23×C4C2413yes—
659C23×C4C2411yescharacteristic
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2416yes—
663C23×C4C2413yes—
664C23×C4C2413yes—
665C23×C4C2413yes—
666C23×C4C2413yes—
667C23×C4C2416yes—
668C23×C4C2413yes—
669C23×C4C2413yes—
670#127—212no—
671#127—212no—
672#127—46no—
673#126—46no—
674#124—212no—
675#124—212no—
676#124—46no—
677#123—46no—
678#123—412no—
679C22⋊Q8—212no—
680C22⋊Q8—212no—
681C22⋊Q8—46no—
682#121—212no—
683#121—212no—
684#121—212no—
685#121—212no—
686#121—212no—
687#121—212no—
688#121—412no—
689#121—412no—
690#121—46no—
691#121—46no—
692#121—46no—
693#121—46no—
694#121—46no—
695#121—46no—
696#121—86no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—24no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—46no—
708C4×Q8—46no—
709C4×Q8#4118yes—
710C4×D4—212no—
711C4×D4—212no—
712C4×D4—212no—
713C4×D4—212no—
714C4×D4—212no—
715C4×D4—212no—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—46no—
719C4×D4—46no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—46no—
727C4×D4—46no—
728C4×D4—86no—
729C4×D4—86no—
730C4×D4—86no—
731#117—212no—
732#117—212no—
733#117—46no—
734#117—46no—
735#117—46no—
736#117—86no—
737C2×C4⋊C4—212no—
738C2×C4⋊C4—46no—
739C2×C4⋊C4—46no—
740C2×C4⋊C4—46no—
741C2×C4⋊C4—46no—
742C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C22⋊C4C2416yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2416yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2416yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2411yescharacteristic
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2416yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2416yes—
831C2×C22⋊C4C2416yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C42—212no—
837C2×C42—46no—
838C2×C42—46no—
839C2×C42—46no—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2411yescharacteristic
852C2×C42C2411yescharacteristic
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2416yes—
857C2×C42C2416yes—
858C2×C42C2413yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2411yescharacteristic
863C2×C42C2411yescharacteristic
864C2×C42C2413yes—
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2411yescharacteristic
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2416yes—
899#95C2413yes—
900#95C2416yes—
901#95C2413yes—
902#95C2413yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907#95C2413yes—
908#95C2413yes—
909#95C2416yes—
910#95C2411yescharacteristic
911#95C2411yescharacteristic
912#95C2411yescharacteristic
913#95C2411yescharacteristic
914#95C2416yes—
915#95C2416yes—
916#95C2413yes—
917#95C2413yes—
918#95C2413yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2416yes—
923#95C2416yes—
924C24C2513yes—
925C24C2513yes—
926C24C2513yes—
927C24C2511yescharacteristic
928#41—232no—
929#41—416no—
930#41—416no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—416no—
935C2×Q8C2×#4114yes—
936C2×Q8C2×#4114yes—
937C2×Q8H(5,𝔽2)14yes—
938C2×D4—26no—
939C2×D4—26no—
940C2×D4—26no—
941C2×D4—26no—
942C2×D4—26no—
943C2×D4—212no—
944C2×D4—212no—
945C2×D4—26no—
946C2×D4—26no—
947C2×D4—26no—
948C2×D4—26no—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—43no—
957C2×D4—43no—
958C2×D4—43no—
959C2×D4—43no—
960C2×D4—46no—
961C2×D4—46no—
962C2×D4—46no—
963C2×D4—46no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4—46no—
971C2×D4—46no—
972C2×D4—46no—
973C2×D4C2×#41112yes—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—22no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—22no—
988C22×C4—26no—
989C22×C4—212no—
990C22×C4—26no—
991C22×C4—26no—
992C22×C4—41no—
993C22×C4—43no—
994C22×C4—43no—
995C22×C4—43no—
996C22×C4—43no—
997C22×C4—43no—
998C22×C4—43no—
999C22×C4—43no—
1000C22×C4—43no—
1001C22×C4—43no—
1002C22×C4—46no—
1003C22×C4—43no—
1004C22×C4—43no—
1005C22×C4—43no—
1006C22×C4—43no—
1007C22×C4—43no—
1008C22×C4—46no—
1009C22×C4—43no—
1010C22×C4—43no—
1011C22×C4—43no—
1012C22×C4—46no—
1013C22×C4—46no—
1014C22×C4—46no—
1015C22×C4C2×#41112yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2513yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2513yes—
1022C22×C4C2513yes—
1023C22×C4C2513yes—
1024C22×C4C2513yes—
1025C22×C4C2513yes—
1026C22×C4C2513yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2513yes—
1033C22×C4C2513yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C22×C4C2513yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2513yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2513yes—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—22no—
1046C4⋊C4—26no—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—26no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—26no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—22no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—46no—
1071C4⋊C4—41no—
1072C4⋊C4—43no—
1073C4⋊C4—46no—
1074C4⋊C4—43no—
1075C4⋊C4—41no—
1076C4⋊C4—43no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—46no—
1081C4⋊C4—43no—
1082C4⋊C4—46no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4C2×#41112yes—
1088C22⋊C4—26no—
1089C22⋊C4—26no—
1090C22⋊C4—26no—
1091C22⋊C4—212no—
1092C22⋊C4—26no—
1093C22⋊C4—22no—
1094C22⋊C4—22no—
1095C22⋊C4—26no—
1096C22⋊C4—212no—
1097C22⋊C4—26no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—26no—
1101C22⋊C4—26no—
1102C22⋊C4—26no—
1103C22⋊C4—212no—
1104C22⋊C4—22no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—46no—
1110C22⋊C4—46no—
1111C22⋊C4—43no—
1112C22⋊C4—46no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—41no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—46no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—46no—
1124C22⋊C4—46no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—46no—
1130C22⋊C4—46no—
1131C22⋊C4—46no—
1132C22⋊C4—43no—
1133C22⋊C4—46no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C42—22no—
1138C42—26no—
1139C42—26no—
1140C42—26no—
1141C42—26no—
1142C42—26no—
1143C42—26no—
1144C42—26no—
1145C42—26no—
1146C42—26no—
1147C42—26no—
1148C42—26no—
1149C42—22no—
1150C42—41no—
1151C42—41no—
1152C42—43no—
1153C42—43no—
1154C42—43no—
1155C42—43no—
1156C42—43no—
1157C42—46no—
1158C42—43no—
1159C42—43no—
1160C42—46no—
1161C42C2×#41112yes—
1162C23—23no—
1163C23—21no—
1164C23—21no—
1165C23—23no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—23no—
1170C23—23no—
1171C23—23no—
1172C23—21no—
1173C23—23no—
1174C23—23no—
1175C23—23no—
1176C23—23no—
1177C23—23no—
1178C23—23no—
1179C23—23no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23C22×#4116yes—
1189C23#58512yes—
1190C23C2611yescharacteristic
1191Q8—412no—
1192Q8#553116yes—
1193D4—224no—
1194D4—412no—
1195D4—412no—
1196D4—412no—
1197D4—412no—
1198D4—86no—
1199D4—812no—
1200D4—812no—
1201D4—86no—
1202D4—86no—
1203D4—86no—
1204D4—166no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—224no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—23no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—44no—
1280C2×C4—412no—
1281C2×C4—412no—
1282C2×C4—412no—
1283C2×C4—412no—
1284C2×C4—812no—
1285C2×C4—86no—
1286C2×C4—86no—
1287C2×C4—86no—
1288C2×C4—86no—
1289C2×C4—86no—
1290C2×C4—86no—
1291C2×C4—166no—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4116yes—
1294C2×C4C22×#4112yes—
1295C2×C4C22×#4116yes—
1296C2×C4C22×#4116yes—
1297C2×C4C2×H(5,𝔽2)16yes—
1298C2×C4#58512yes—
1299C2×C4#58512yes—
1300C22—22no—
1301C22—26no—
1302C22—22no—
1303C22—22no—
1304C22—26no—
1305C22—26no—
1306C22—43no—
1307C22—41no—
1308C22—43no—
1309C22—43no—
1310C22—41no—
1311C22—41no—
1312C22—43no—
1313C22—41no—
1314C22—43no—
1315C22—43no—
1316C22—43no—
1317C22—43no—
1318C22—43no—
1319C22—43no—
1320C22—43no—
1321C22—43no—
1322C22—43no—
1323C22—43no—
1324C22—43no—
1325C22—43no—
1326C22—43no—
1327C22—43no—
1328C22C23×#4111yescharacteristic
1329C22C23×#4111yescharacteristic
1330C22C22×H(5,𝔽2)11yescharacteristic
1331C22C2×#58511yescharacteristic
1332C22C2×#58511yescharacteristic
1333C22C2×#58511yescharacteristic
1334C22H(7,𝔽2)11yescharacteristic
1335C4—26no—
1336C4—22no—
1337C4—22no—
1338C4—22no—
1339C4—22no—
1340C4—43no—
1341C4—41no—
1342C4—41no—
1343C4—43no—
1344C4—43no—
1345C4—41no—
1346C4—41no—
1347C4—43no—
1348C4—43no—
1349C4—41no—
1350C4—43no—
1351C4—43no—
1352C4—41no—
1353C4—41no—
1354C4—43no—
1355C4—41no—
1356C4—43no—
1357C4—43no—
1358C4—41no—
1359C4—41no—
1360C4—43no—
1361C4C2×#553112yes—
1362C2—42no—
1363C2—46no—
1364C2—83no—
1365C2—83no—
1366C2C22×#55311yescharacteristic
1367C2#6279311yescharacteristic
1368C2#6281611yescharacteristic
1369C2#6289911yescharacteristic
1370C2#6300811yescharacteristic
1371C2#6301011yescharacteristic
1372C2#6302011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59860C2semidirect
2. #59859C2semidirect
3. #59702C2semidirect
4. #59401C2semidirect
5. #59212C2semidirect
6. #45257C2semidirect
7. #45224C2semidirect
8. #45038C2semidirect
9. #44970C2semidirect
10. #39284C2semidirect
11. #39256C2semidirect
12. #38131C2semidirect
13. #37899C2semidirect
14. #36606C2semidirect
15. #36585C2semidirect
16. #36578C2semidirect
17. #36455C2semidirect
18. #36430C2semidirect
19. #36430C2semidirect
20. #36369C2semidirect
21. #36076C2semidirect
22. #35971C2semidirect
23. #35883C2semidirect
24. #35831C2semidirect
25. #34856C2semidirect
26. #34295C2semidirect
27. #34295C2semidirect
28. #34294C2semidirect
29. #34263C2semidirect
30. C4×#548C2semidirect
31. C4⋊C4×#41C2semidirect

Maximal subgroups

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

subgroupindex
#598602
#598592
#597022
#594012
#592122
#452572
#452242
#450382
#449702
#392842
#392562
#381312
#378992
#366062
#365852
#365782
#364552
#364302
#363692
#360762
#359712
#358832
#358312
#348562
#342952
#342942
#342632
C4×#5482
C4⋊C4×#412