Finite Group Databasebeta

← #7698293

Subgroups — #7698293

Order 512.

5588 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59826C213yesmaximal, complemented
2#59693C213yesmaximal, complemented
3#59680C213yesmaximal, complemented
4#52262C213yesmaximal, complemented
5#45373C213yesmaximal, complemented
6#45257C213yesmaximal, complemented
7#45074C213yesmaximal, complemented
8#45046C213yesmaximal, complemented
9#45038C213yesmaximal, complemented
10#44922C213yesmaximal, complemented
11#39818C213yesmaximal, complemented
12#39552C213yesmaximal, complemented
13#39282C213yesmaximal, complemented
14#39185C213yesmaximal, complemented
15#38214C213yesmaximal, complemented
16#38123C213yesmaximal, complemented
17#36475C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36455C211yesmaximal, characteristic, complemented
20#36076C211yesmaximal, characteristic, complemented
21#36029C211yesmaximal, characteristic, complemented
22#36029C211yesmaximal, characteristic, complemented
23#36029C211yesmaximal, characteristic, complemented
24#36005C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic, complemented
26#34313C211yesmaximal, characteristic, complemented
27#34313C211yesmaximal, characteristic, complemented
28#34313C211yesmaximal, characteristic, complemented
29#34295C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31#34250C211yesmaximal, characteristic, complemented
32C2×#553C2216yes—
33C2×#550C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#550C2211yescharacteristic
39C2×#520C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#520C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45#2864C2213yes—
46#2860C2213yes—
47#2856C2213yes—
48#2803C2213yes—
49#2803C2216yes—
50#2802C2211yescharacteristic
51#2801C2213yes—
52#2800C2213yes—
53#2800C2213yes—
54#2797C2216yes—
55#2797C2213yes—
56#2796C2213yes—
57#2796C2216yes—
58#2787C2213yes—
59#2780C2216yes—
60#2779C2213yes—
61#2778C2216yes—
62#2777C2213yes—
63#2772C2213yes—
64#2757C2213yes—
65#2753C2213yes—
66#2750C2216yes—
67#2725C2213yes—
68#2714C2216yes—
69#2714C2216yes—
70#2714C2213yes—
71#2711C2213yes—
72#2708C2216yes—
73#2703C2216yes—
74#2701C2216yes—
75#2691C2216yes—
76#2688C2216yes—
77#2644C2213yes—
78#2624C2213yes—
79#2624C2213yes—
80#2619C2213yes—
81#2619C2213yes—
82#2619C2213yes—
83#2602C2216yes—
84#2600C2216yes—
85#2598C2216yes—
86#2579C2216yes—
87#2570C2213yes—
88#2570C2213yes—
89#2559C2216yes—
90#2543C2216yes—
91#2541C2213yes—
92#2541C2213yes—
93#2541C2213yes—
94#2541C2213yes—
95#2537C2213yes—
96#2535C2213yes—
97#2535C2213yes—
98#2535C2213yes—
99#2535C2216yes—
100#2513C2213yes—
101#2513C2213yes—
102#2512C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2512C2213yes—
106#2509C2213yes—
107#2508C2213yes—
108#2507C2213yes—
109#2506C2213yes—
110#2504C2213yes—
111#2501C2213yes—
112#2497C2213yes—
113#2497C2213yes—
114#2496C2213yes—
115#2496C2213yes—
116#2495C2213yes—
117#2494C2213yes—
118#2487C2213yes—
119#2486C2213yes—
120#2470C2216yes—
121#2467C2216yes—
122#2467C2216yes—
123#2466C2216yes—
124#2464C2216yes—
125#2456C2216yes—
126#2456C2216yes—
127#2456C2216yes—
128#2445C2213yes—
129#2445C2213yes—
130#2445C2213yes—
131#2445C2213yes—
132#2444C2216yes—
133#2444C2216yes—
134#2444C2216yes—
135#2443C2216yes—
136#2428C2213yes—
137#2428C2213yes—
138#2428C2213yes—
139#2428C2213yes—
140#2428C2213yes—
141#2428C2213yes—
142#2428C2213yes—
143#2428C2213yes—
144#2422C2213yes—
145#2422C2213yes—
146#2420C2213yes—
147#2420C2213yes—
148#2416C2213yes—
149#2416C2216yes—
150#2416C2213yes—
151#2416C2213yes—
152#2416C2213yes—
153#2416C2213yes—
154#2416C2213yes—
155#2414C2216yes—
156#2414C2213yes—
157#2414C2213yes—
158#2401C2213yes—
159#2395C2213yes—
160#2395C2213yes—
161#2392C2213yes—
162#2392C2213yes—
163#2392C2213yes—
164#2366C2213yes—
165#2366C2213yes—
166#2366C2213yes—
167#2366C2213yes—
168#2363C2213yes—
169#2361C2213yes—
170#2361C2213yes—
171#2361C2213yes—
172#2361C2213yes—
173#2361C2213yes—
174#2361C2213yes—
175#2361C2213yes—
176#2357C2213yes—
177#2354C2213yes—
178#2352C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189#2349C2213yes—
190#2349C2213yes—
191D4×C4⋊C4C2213yes—
192D4×C4⋊C4C2213yes—
193D4×C4⋊C4C2213yes—
194D4×C4⋊C4C2213yes—
195D4×C4⋊C4C2213yes—
196#2345C2213yes—
197#2344C2213yes—
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2328C2213yes—
209#2324C2213yes—
210#2324C2213yes—
211#2324C2213yes—
212#2324C2213yes—
213#2324C2213yes—
214#2324C2213yes—
215#2324C2213yes—
216#2319C2213yes—
217#2317C2213yes—
218#2316C2213yes—
219#2314C2213yes—
220C4×#127C2213yes—
221C4×#127C2213yes—
222C4×#127C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#121C2213yes—
226C4×#121C2213yes—
227#2298C2213yes—
228#2296C2213yes—
229#2293C2213yes—
230#2293C2213yes—
231#2293C2213yes—
232#2293C2213yes—
233C2×#389C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242#553—424no—
243#550—28no—
244#550—28no—
245#550—28no—
246#550—28no—
247#550—44no—
248#550—44no—
249C2×#127C2313yes—
250C2×#127C2313yes—
251C2×#127C2313yes—
252C2×#127C2313yes—
253C2×#127C2313yes—
254C2×#127C2313yes—
255C2×#126C2313yes—
256C2×#126C2316yes—
257C2×#126C2316yes—
258C2×#125C2313yes—
259C2×#123C2316yes—
260C2×#123C2316yes—
261C2×#123C2316yes—
262C2×#121C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#121C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2316yes—
276C2×#121C2316yes—
277C2×#121C2316yes—
278C2×#121C2316yes—
279C2×#121C2316yes—
280C2×#121C2316yes—
281C2×#121C2316yes—
282C2×#121C2316yes—
283#520—28no—
284#520—28no—
285#520—44no—
286#520—44no—
287#520—44no—
288C4×#41—44no—
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
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×C4×D4C2316yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2316yes—
323C2×C4×D4C2316yes—
324C2×C4×D4C2316yes—
325C2×#117C2313yes—
326C2×#117C2313yes—
327C2×#117C2313yes—
328C2×#117C2313yes—
329C2×#117C2313yes—
330C2×#117C2313yes—
331C2×#117C2316yes—
332C22×C4⋊C4C2313yes—
333C22×C4⋊C4C2313yes—
334C22×C4⋊C4C2313yes—
335C22×C4⋊C4C2316yes—
336C22×C4⋊C4C2313yes—
337C22×C4⋊C4C2313yes—
338C22×C42C2313yes—
339#401C2313yes—
340#400C2316yes—
341#400C2316yes—
342#400C2311yescharacteristic
343#400C2313yes—
344#400C2311yescharacteristic
345#400C2313yes—
346#400C2313yes—
347#400C2316yes—
348#399C2313yes—
349#399C2313yes—
350#399C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2313yes—
354#398C2311yescharacteristic
355#398C2311yescharacteristic
356#398C2311yescharacteristic
357#398C2311yescharacteristic
358#397C2316yes—
359#397C2316yes—
360#397C2313yes—
361#397C2316yes—
362#397C2313yes—
363#397C2316yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2316yes—
375#396C2313yes—
376#396C2316yes—
377#396C2316yes—
378#396C2313yes—
379#396C2313yes—
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2313yes—
384#394C2313yes—
385#394C2313yes—
386#394C2316yes—
387#394C2313yes—
388#394C2316yes—
389#394C2313yes—
390#394C2316yes—
391#394C2316yes—
392#394C2316yes—
393#394C2316yes—
394#394C2316yes—
395#394C2316yes—
396#394C2313yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2313yes—
403#394C2313yes—
404#394C2313yes—
405#394C2316yes—
406#392C2316yes—
407#392C2316yes—
408#392C2316yes—
409#392C2316yes—
410#392C2316yes—
411#392C2316yes—
412#392C2316yes—
413#392C2313yes—
414#392C2313yes—
415#392C2313yes—
416#392C2316yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2316yes—
422#390C2316yes—
423#390C2316yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2316yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2316yes—
446#390C2313yes—
447#390C2313yes—
448#390C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2316yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
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#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2311yescharacteristic
479#389C2311yescharacteristic
480#389C2311yescharacteristic
481#389C2311yescharacteristic
482#389C2311yescharacteristic
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2316yes—
487#388C2316yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2316yes—
496#388C2316yes—
497#388C2316yes—
498#388C2316yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2313yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#388C2316yes—
511#388C2313yes—
512#388C2313yes—
513#387C2311yescharacteristic
514#387C2313yes—
515#387C2313yes—
516#387C2311yescharacteristic
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2313yes—
525#387C2313yes—
526#387C2313yes—
527#387C2316yes—
528#387C2316yes—
529#387C2311yescharacteristic
530#387C2311yescharacteristic
531#386C2316yes—
532#386C2316yes—
533#386C2316yes—
534#386C2316yes—
535#386C2316yes—
536#386C2316yes—
537#386C2316yes—
538#386C2316yes—
539#386C2316yes—
540#386C2313yes—
541#386C2316yes—
542#386C2316yes—
543#386C2316yes—
544#386C2316yes—
545#386C2316yes—
546#386C2313yes—
547#386C2316yes—
548#386C2316yes—
549#386C2316yes—
550#386C2313yes—
551#386C2313yes—
552#386C2316yes—
553#385C2316yes—
554#385C2316yes—
555#385C2316yes—
556#385C2316yes—
557#385C2316yes—
558#385C2316yes—
559#385C2313yes—
560#385C2316yes—
561#385C2316yes—
562#385C2316yes—
563#385C2313yes—
564#385C2313yes—
565#385C2313yes—
566#385C2313yes—
567#385C2313yes—
568#384C2313yes—
569#384C2313yes—
570#384C2313yes—
571#384C2313yes—
572#384C2313yes—
573#383C2313yes—
574#382C2313yes—
575#382C2313yes—
576#382C2313yes—
577#382C2313yes—
578#382C2313yes—
579#382C2313yes—
580#381C2316yes—
581#381C2316yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
585#380C2316yes—
586#380C2316yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2316yes—
626C4×C22⋊C4C2316yes—
627#376C2313yes—
628C2×#95C2316yes—
629C43C2313yes—
630C43C2313yes—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C2×#41—24no—
640C2×#41—24no—
641C2×#41—24no—
642C2×#41#4118yes—
643C22×Q8C2411yescharacteristic
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2416yes—
652C22×D4C2413yes—
653C22×D4C2416yes—
654C22×D4C2416yes—
655C22×D4C2413yes—
656C22×D4C2416yes—
657C22×D4C2413yes—
658C22×D4C2416yes—
659C22×D4C2416yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2413yes—
664C23×C4C2413yes—
665C23×C4C2416yes—
666C23×C4C2416yes—
667C23×C4C2416yes—
668C23×C4C2416yes—
669C23×C4C2416yes—
670C23×C4C2413yes—
671#127—212no—
672#127—212no—
673#127—212no—
674#127—212no—
675#127—46no—
676#127—46no—
677#126—212no—
678#126—412no—
679#126—86no—
680#125—212no—
681#123—412no—
682#123—412no—
683#123—86no—
684#121—212no—
685#121—212no—
686#121—212no—
687#121—212no—
688#121—212no—
689#121—212no—
690#121—212no—
691#121—212no—
692#121—212no—
693#121—412no—
694#121—412no—
695#121—412no—
696#121—46no—
697#121—46no—
698#121—46no—
699#121—46no—
700#121—86no—
701#121—86no—
702#121—86no—
703#121—86no—
704#121—86no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—24no—
713C4×Q8—24no—
714C4×Q8—24no—
715C4×Q8#4118yes—
716C4×D4—212no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—212no—
721C4×D4—212no—
722C4×D4—212no—
723C4×D4—212no—
724C4×D4—412no—
725C4×D4—46no—
726C4×D4—46no—
727C4×D4—46no—
728C4×D4—46no—
729C4×D4—46no—
730C4×D4—46no—
731C4×D4—46no—
732C4×D4—46no—
733C4×D4—412no—
734C4×D4—412no—
735C4×D4—46no—
736C4×D4—46no—
737C4×D4—412no—
738C4×D4—86no—
739C4×D4—86no—
740C4×D4—86no—
741#117—212no—
742#117—212no—
743#117—46no—
744#117—46no—
745#117—46no—
746#117—412no—
747#117—46no—
748C2×C4⋊C4—212no—
749C2×C4⋊C4—212no—
750C2×C4⋊C4—46no—
751C2×C4⋊C4—46no—
752C2×C4⋊C4—46no—
753C2×C4⋊C4—412no—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2416yes—
783C2×C4⋊C4C2416yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2416yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2413yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2413yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2416yes—
831C2×C22⋊C4C2416yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2413yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2416yes—
841C2×C22⋊C4C2416yes—
842C2×C22⋊C4C2416yes—
843C2×C22⋊C4C2416yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2413yes—
849C2×C22⋊C4C2416yes—
850C2×C22⋊C4C2416yes—
851C2×C22⋊C4C2416yes—
852C2×C22⋊C4C2416yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C42—46no—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2416yes—
874C2×C42C2413yes—
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2413yes—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881C2×C42C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2416yes—
885#95C2416yes—
886#95C2411yescharacteristic
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2411yescharacteristic
892#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2411yescharacteristic
899#95C2411yescharacteristic
900#95C2411yescharacteristic
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2416yes—
912#95C2416yes—
913#95C2416yes—
914#95C2411yescharacteristic
915#95C2416yes—
916#95C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2411yescharacteristic
919#95C2411yescharacteristic
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2416yes—
933C24C2513yes—
934C24C2513yes—
935C24C2513yes—
936C24C2513yes—
937#41—232no—
938#41—416no—
939#41—416no—
940#41—416no—
941C2×Q8C2×#4114yes—
942C2×Q8C2×#4114yes—
943C2×Q8H(5,𝔽2)14yes—
944C2×D4—26no—
945C2×D4—26no—
946C2×D4—26no—
947C2×D4—212no—
948C2×D4—212no—
949C2×D4—212no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—212no—
959C2×D4—26no—
960C2×D4—26no—
961C2×D4—26no—
962C2×D4—26no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—43no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—43no—
970C2×D4—46no—
971C2×D4—46no—
972C2×D4—43no—
973C2×D4—43no—
974C2×D4—46no—
975C2×D4—46no—
976C2×D4—46no—
977C2×D4—43no—
978C2×D4—46no—
979C2×D4—46no—
980C2×D4—43no—
981C2×D4—43no—
982C2×D4—43no—
983C2×D4—46no—
984C2×D4—43no—
985C2×D4—46no—
986C2×D4—46no—
987C2×D4—46no—
988C2×D4—46no—
989C2×D4—46no—
990C2×D4—46no—
991C2×D4C2×#41112yes—
992C22×C4—26no—
993C22×C4—26no—
994C22×C4—26no—
995C22×C4—26no—
996C22×C4—26no—
997C22×C4—26no—
998C22×C4—26no—
999C22×C4—26no—
1000C22×C4—26no—
1001C22×C4—26no—
1002C22×C4—26no—
1003C22×C4—212no—
1004C22×C4—212no—
1005C22×C4—26no—
1006C22×C4—43no—
1007C22×C4—43no—
1008C22×C4—46no—
1009C22×C4—46no—
1010C22×C4—46no—
1011C22×C4—46no—
1012C22×C4—43no—
1013C22×C4—43no—
1014C22×C4—43no—
1015C22×C4—46no—
1016C22×C4—46no—
1017C22×C4—46no—
1018C22×C4—46no—
1019C22×C4—46no—
1020C22×C4—46no—
1021C22×C4—46no—
1022C22×C4—46no—
1023C22×C4—46no—
1024C22×C4C2×#41112yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2513yes—
1027C22×C4C2511yescharacteristic
1028C22×C4C2511yescharacteristic
1029C22×C4C2513yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2513yes—
1036C22×C4C2513yes—
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2513yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2513yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2513yes—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—26no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—43no—
1078C4⋊C4—43no—
1079C4⋊C4—43no—
1080C4⋊C4—46no—
1081C4⋊C4—46no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—43no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—43no—
1093C4⋊C4—46no—
1094C4⋊C4—46no—
1095C4⋊C4—43no—
1096C4⋊C4—43no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—46no—
1100C4⋊C4—43no—
1101C4⋊C4—43no—
1102C4⋊C4C2×#41112yes—
1103C4⋊C4H(5,𝔽2)14yes—
1104C22⋊C4—26no—
1105C22⋊C4—26no—
1106C22⋊C4—26no—
1107C22⋊C4—26no—
1108C22⋊C4—26no—
1109C22⋊C4—26no—
1110C22⋊C4—26no—
1111C22⋊C4—26no—
1112C22⋊C4—26no—
1113C22⋊C4—26no—
1114C22⋊C4—26no—
1115C22⋊C4—26no—
1116C22⋊C4—26no—
1117C22⋊C4—26no—
1118C22⋊C4—26no—
1119C22⋊C4—26no—
1120C22⋊C4—26no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—46no—
1131C22⋊C4—46no—
1132C22⋊C4—46no—
1133C22⋊C4—43no—
1134C22⋊C4—43no—
1135C22⋊C4—43no—
1136C22⋊C4—43no—
1137C22⋊C4—46no—
1138C22⋊C4—46no—
1139C22⋊C4—43no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—46no—
1144C22⋊C4—46no—
1145C22⋊C4—46no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—46no—
1152C22⋊C4—46no—
1153C22⋊C4—46no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C42—26no—
1158C42—26no—
1159C42—26no—
1160C42—26no—
1161C42—26no—
1162C42—26no—
1163C42—26no—
1164C42—26no—
1165C42—26no—
1166C42—26no—
1167C42—26no—
1168C42—26no—
1169C42—41no—
1170C42—43no—
1171C42—41no—
1172C42—41no—
1173C42—46no—
1174C42—43no—
1175C42—43no—
1176C42—43no—
1177C42—43no—
1178C42C2×#41112yes—
1179C23—23no—
1180C23—23no—
1181C23—23no—
1182C23—23no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—23no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23—23no—
1191C23—23no—
1192C23—23no—
1193C23—23no—
1194C23—23no—
1195C23—23no—
1196C23—23no—
1197C23—23no—
1198C23—23no—
1199C23—23no—
1200C23—23no—
1201C23—23no—
1202C23—23no—
1203C23—23no—
1204C23—23no—
1205C23—23no—
1206C23C22×#4116yes—
1207C23C2611yescharacteristic
1208Q8#553116yescomplemented
1209D4—224no—
1210D4—412no—
1211D4—412no—
1212D4—412no—
1213D4—412no—
1214D4—412no—
1215D4—412no—
1216D4—812no—
1217D4—86no—
1218D4—812no—
1219D4—812no—
1220D4—812no—
1221D4—86no—
1222D4—86no—
1223D4—166no—
1224D4—166no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—23no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—224no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—23no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—23no—
1289C2×C4—23no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—412no—
1299C2×C4—412no—
1300C2×C4—412no—
1301C2×C4—812no—
1302C2×C4—812no—
1303C2×C4—86no—
1304C2×C4—86no—
1305C2×C4—166no—
1306C2×C4—166no—
1307C2×C4—166no—
1308C2×C4C22×#4112yes—
1309C2×C4C22×#4116yes—
1310C2×C4C22×#4112yes—
1311C2×C4C22×#4116yes—
1312C2×C4C22×#4116yes—
1313C2×C4C2×H(5,𝔽2)12yes—
1314C2×C4C2×H(5,𝔽2)12yes—
1315C2×C4C2×H(5,𝔽2)12yes—
1316C2×C4C2×H(5,𝔽2)16yes—
1317C22—26no—
1318C22—26no—
1319C22—26no—
1320C22—43no—
1321C22—43no—
1322C22—43no—
1323C22—43no—
1324C22—43no—
1325C22—43no—
1326C22—43no—
1327C22—43no—
1328C22—43no—
1329C22—43no—
1330C22—43no—
1331C22—43no—
1332C22—43no—
1333C22—43no—
1334C22—43no—
1335C22—43no—
1336C22—43no—
1337C22—43no—
1338C22—43no—
1339C22—43no—
1340C22—43no—
1341C22—43no—
1342C22—43no—
1343C22—43no—
1344C22—43no—
1345C22C23×#4111yescharacteristic
1346C22C23×#4111yescharacteristic
1347C22C22×H(5,𝔽2)11yescharacteristic
1348C22C22×H(5,𝔽2)11yescharacteristic
1349C22H(7,𝔽2)11yescharacteristic
1350C22H(7,𝔽2)11yescharacteristic
1351C222−1+611yescharacteristic
1352C4—22no—
1353C4—22no—
1354C4—26no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—43no—
1359C4—43no—
1360C4—43no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—43no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—43no—
1369C4—43no—
1370C4—41no—
1371C4—43no—
1372C4—43no—
1373C4—43no—
1374C4—43no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4C2×#553112yes—
1379C2—46no—
1380C2—83no—
1381C2—83no—
1382C2—83no—
1383C2C22×#55311yescharacteristic
1384C2#6285111yescharacteristic
1385C2#6285811yescharacteristic
1386C2#6291611yescharacteristic
1387C2#6298511yescharacteristic
1388C2#6298611yescharacteristic
1389C2#6305211yescharacteristic
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. #59826C2semidirect
2. #59693C2semidirect
3. #59680C2semidirect
4. #52262C2semidirect
5. #45373C2semidirect
6. #45257C2semidirect
7. #45074C2semidirect
8. #45046C2semidirect
9. #45038C2semidirect
10. #44922C2semidirect
11. #39818C2semidirect
12. #39552C2semidirect
13. #39282C2semidirect
14. #39185C2semidirect
15. #38214C2semidirect
16. #38123C2semidirect
17. #36475C2semidirect
18. #36458C2semidirect
19. #36455C2semidirect
20. #36076C2semidirect
21. #36029C2semidirect
22. #36029C2semidirect
23. #36029C2semidirect
24. #36005C2semidirect
25. #35898C2semidirect
26. #34313C2semidirect
27. #34313C2semidirect
28. #34313C2semidirect
29. #34295C2semidirect
30. #34263C2semidirect
31. #34250C2semidirect
1208. Q8#553semidirect

Maximal subgroups

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

subgroupindex
#598262
#596932
#596802
#522622
#453732
#452572
#450742
#450462
#450382
#449222
#398182
#395522
#392822
#391852
#382142
#381232
#364752
#364582
#364552
#360762
#360292
#360052
#358982
#343132
#342952
#342632
#342502