Finite Group Databasebeta

← #7683868

Subgroups — #7683868

Order 512.

4954 conjugacy classes of subgroups.

The subgroup lattice has 1259 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59998C214yesmaximal, complemented
2#59982C214yesmaximal, complemented
3#59961C214yesmaximal, complemented
4#59948C212yesmaximal, complemented
5#59923C211yesmaximal, characteristic, complemented
6#59885C211yesmaximal, characteristic, complemented
7#59719C214yesmaximal, complemented
8#59339C212yesmaximal, complemented
9#59312C212yesmaximal, complemented
10#44464C214yesmaximal, complemented
11#44451C214yesmaximal, complemented
12#43883C212yesmaximal, complemented
13#43848C214yesmaximal, complemented
14#43788C212yesmaximal, complemented
15#43488C212yesmaximal, complemented
16#43437C214yesmaximal, complemented
17#43400C212yesmaximal, complemented
18#35464C214yesmaximal, complemented
19#35397C212yesmaximal, complemented
20#34877C212yesmaximal, complemented
21C2×#2499C211yesmaximal, characteristic, complemented
22#34297C214yesmaximal, complemented
23#34277C212yesmaximal, complemented
24C2×#552C2214yes—
25C2×#539C2212yes—
26C2×#538C2212yes—
27C2×#529C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#2811C2211yescharacteristic, complemented
31#2809C2212yescomplemented
32#2809C2211yescharacteristic, complemented
33#2808C2214yes—
34#2808C2214yes—
35#2808C2212yescomplemented
36#2806C2212yescomplemented
37#2785C2212yescomplemented
38#2783C2214yes—
39#2783C2214yes—
40#2783C2214yescomplemented
41#2775C2214yes—
42#2775C2214yes—
43#2775C2214yescomplemented
44#2769C2212yescomplemented
45#2737C2214yes—
46#2737C2214yes—
47#2734C2211yescharacteristic, complemented
48#2733C2211yescharacteristic, complemented
49#2731C2212yescomplemented
50#2730C2214yes—
51#2730C2214yes—
52#2721C2214yes—
53#2721C2214yes—
54#2721C2214yescomplemented
55#2721C2214yescomplemented
56#2714C2214yes—
57#2714C2214yes—
58#2694C2214yes—
59#2694C2214yes—
60#2612C2212yescomplemented
61#2612C2214yescomplemented
62#2611C2212yes—
63#2611C2212yes—
64#2611C2214yescomplemented
65#2610C2212yes—
66#2610C2212yes—
67#2609C2212yescomplemented
68#2604C2214yescomplemented
69#2602C2214yescomplemented
70#2601C2214yes—
71#2601C2214yes—
72#2601C2214yescomplemented
73#2591C2212yes—
74#2586C2214yescomplemented
75#2586C2212yescomplemented
76#2583C2212yes—
77#2574C2214yescomplemented
78#2574C2214yescomplemented
79#2572C2212yescomplemented
80#2565C2214yescomplemented
81#2564C2214yescomplemented
82#2561C2212yes—
83#2561C2212yes—
84#2560C2214yes—
85#2560C2214yes—
86#2560C2214yescomplemented
87#2557C2214yescomplemented
88#2556C2214yes—
89#2556C2214yes—
90#2556C2214yescomplemented
91#2553C2214yescomplemented
92#2552C2214yescomplemented
93#2552C2212yescomplemented
94#2549C2214yes—
95#2543C2214yes—
96#2539C2212yes—
97#2539C2212yes—
98#2538C2212yescomplemented
99#2532C2214yes—
100#2532C2214yes—
101#2532C2214yescomplemented
102#2532C2214yescomplemented
103#2531C2214yes—
104#2531C2214yes—
105#2529C2214yes—
106#2529C2214yes—
107#2529C2214yescomplemented
108#2521C2214yescomplemented
109#2519C2214yescomplemented
110#2518C2214yescomplemented
111#2513C2214yes—
112#2513C2214yes—
113#2512C2214yes—
114#2512C2214yes—
115#2512C2214yescomplemented
116#2508C2214yescomplemented
117#2506C2214yescomplemented
118#2501C2214yes—
119#2499C2212yes—
120#2499C2214yes—
121#2499C2212yes—
122#2499C2214yes—
123#2499C2212yes—
124#2499C2212yes—
125#2499C2214yescomplemented
126#2498C2214yescomplemented
127#2496C2214yescomplemented
128#2490C2214yes—
129#2490C2214yes—
130#2488C2214yes—
131#2488C2214yes—
132#2486C2214yes—
133#2474C2214yescomplemented
134#2471C2214yes—
135#2471C2214yes—
136#2461C2214yes—
137#2461C2214yes—
138#2459C2214yescomplemented
139#2452C2214yes—
140#2452C2214yes—
141#2451C2214yescomplemented
142#2448C2214yes—
143#2448C2214yes—
144#2441C2214yescomplemented
145#2439C2214yescomplemented
146#2436C2212yes—
147#2434C2212yes—
148#2425C2214yes—
149#2425C2214yes—
150#2423C2214yescomplemented
151#2413C2214yes—
152#2413C2214yes—
153#2411C2214yes—
154#2411C2214yes—
155#2396C2212yes—
156#2396C2212yes—
157#2392C2212yes—
158#2392C2212yes—
159C2×#397C2214yes—
160#2374C2214yes—
161#2373C2214yes—
162#2373C2214yes—
163#2373C2214yescomplemented
164#2373C2214yescomplemented
165#2372C2214yes—
166#2372C2212yescomplemented
167#2372C2212yescomplemented
168#2371C2214yescomplemented
169#2371C2214yescomplemented
170#2370C2214yescomplemented
171#2369C2212yescomplemented
172#2369C2212yescomplemented
173#2368C2214yes—
174#2368C2214yescomplemented
175#2367C2214yes—
176#2364C2214yes—
177#2363C2214yes—
178#2359C2214yes—
179#2359C2214yes—
180#2359C2214yes—
181#2356C2214yescomplemented
182#2354C2212yescomplemented
183#2353C2214yes—
184Q8×C4⋊C4C2212yescomplemented
185#2346C2214yescomplemented
186#2344C2214yes—
187#2343C2214yes—
188#2343C2214yes—
189#2343C2214yescomplemented
190#2336C2214yescomplemented
191#2336C2214yescomplemented
192#2334C2214yescomplemented
193#2332C2214yescomplemented
194#2329C2212yes—
195#2325C2212yes—
196#2322C2214yes—
197#2321C2214yes—
198#2312C2212yes—
199C4×#125C2214yescomplemented
200C4×#126C2214yescomplemented
201C4×C22⋊Q8C2212yes—
202C4×#123C2214yes—
203C4×#121C2212yes—
204C4×#120C2214yes—
205#2298C2214yescomplemented
206#2295C2214yescomplemented
207C2×#391C2211yescharacteristic
208C2×#391C2211yescharacteristic
209#2293C2214yes—
210#2293C2214yes—
211#2290C2214yes—
212C2×#387C2214yes—
213C2×#384C2211yescharacteristic
214C2×#382C2211yescharacteristic
215#2275C2214yes—
216#2274C2212yes—
217C4×#117C2212yes—
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C24×C4C2311yescharacteristic
221#552—232no—
222#539—48no—
223#538—216no—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2312yes—
226#529—48no—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#125C2314yes—
233C2×#125C2314yes—
234C2×#125C2314yes—
235C2×#125C2314yes—
236C2×#125C2312yes—
237C2×#124C2314yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2312yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×C22⋊Q8—44no—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×#121C2312yes—
257C2×#121C2314yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#120C2314yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×#117—44no—
272C2×#117C2314yes—
273C2×#117C2314yes—
274C2×#117C2314yes—
275C2×#117C2312yes—
276C2×#117C2312yes—
277C2×#117C2314yes—
278C2×#117C2314yes—
279C2×#117C2312yes—
280C2×#117C2312yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2314yes—
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2312yes—
289C22×C42C2312yes—
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292#400C2314yes—
293#400C2312yes—
294#400C2312yes—
295#400C2314yes—
296#400C2314yes—
297#400C2314yes—
298#399C2314yes—
299#399C2314yes—
300#399C2312yes—
301#399C2312yes—
302#399C2314yes—
303#399C2314yes—
304#399C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2312yes—
313#398C2312yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2312yes—
321#397C2312yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#395C2314yes—
347#395C2312yes—
348#395C2314yes—
349#395C2312yes—
350#395C2314yes—
351#395C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2312yes—
356#394C2312yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#393C2314yes—
362#393C2314yes—
363#393C2314yes—
364#393C2312yes—
365#393C2312yes—
366#393C2314yes—
367#393C2314yes—
368#392C2314yes—
369#392C2312yes—
370#392C2312yes—
371#392C2314yes—
372#391C2312yes—
373#391C2312yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2311yescharacteristic
378#391C2312yes—
379#391C2314yes—
380#391C2311yescharacteristic
381#391C2314yes—
382#391C2314yes—
383#391C2312yes—
384#391C2312yes—
385#391C2314yes—
386#391C2311yescharacteristic
387#391C2312yes—
388#391C2312yes—
389#391C2314yes—
390#391C2312yes—
391#391C2311yescharacteristic
392#391C2312yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2314yes—
398#390C2314yes—
399#390C2314yes—
400#390C2314yes—
401#390C2314yes—
402#390C2314yes—
403#390C2312yes—
404#390C2314yes—
405#390C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#389C2314yes—
426#389C2312yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#384C2314yes—
536#384C2312yes—
537#384C2314yes—
538#384C2312yes—
539#384C2312yes—
540#384C2312yes—
541#383C2314yes—
542#383C2314yes—
543#383C2314yes—
544#382C2314yes—
545#382C2314yes—
546#382C2314yes—
547#382C2314yes—
548#382C2312yes—
549#382C2314yes—
550#382C2312yes—
551#381C2314yes—
552#381C2314yes—
553#381C2314yes—
554#380C2314yes—
555#380C2314yes—
556#380C2312yes—
557#380C2312yes—
558#380C2314yes—
559#380C2314yes—
560#379C2314yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2314yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2312yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2314yes—
607#376C2314yes—
608#376C2314yes—
609#376C2312yes—
610#376C2314yes—
611#376C2314yes—
612#376C2314yes—
613#376C2312yes—
614C2×#95C2314yes—
615C2×#95C2312yes—
616C2×#95C2314yes—
617C2×#95C2314yes—
618C2×#95C2314yes—
619C43C2314yes—
620C25C2411yescharacteristic
621C22×Q8—42no—
622C22×Q8—42no—
623C22×Q8—42no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2412yes—
626C22×Q8C2411yescharacteristic
627C22×Q8C2412yes—
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×D4C2414yes—
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2412yes—
636C23×C4—24no—
637C23×C4—42no—
638C23×C4—42no—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2411yescharacteristic
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2414yes—
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C4⋊Q8—44no—
653C4⋊Q8—44no—
654#126—216no—
655#126—216no—
656#126—216no—
657#126—48no—
658#126—48no—
659#125—216no—
660#125—216no—
661#125—216no—
662#125—44no—
663#125—48no—
664#124—216no—
665#124—44no—
666#124—44no—
667#124—44no—
668#123—216no—
669#123—216no—
670#123—216no—
671#123—48no—
672#123—48no—
673#123—48no—
674C22⋊Q8—216no—
675C22⋊Q8—44no—
676C22⋊Q8—44no—
677C22⋊Q8—44no—
678C22⋊Q8—48no—
679C22⋊Q8—44no—
680C22⋊Q8—48no—
681C22⋊Q8#41116yes—
682#121—28no—
683#121—216no—
684#121—44no—
685#121—44no—
686#120—216no—
687C4×Q8—216no—
688C4×Q8—44no—
689C4×Q8—44no—
690C4×D4—216no—
691C4×D4—216no—
692C4×D4—216no—
693C4×D4—44no—
694C4×D4—44no—
695C4×D4—48no—
696C4×D4—48no—
697#117—216no—
698#117—216no—
699#117—216no—
700#117—44no—
701#117—44no—
702#117—44no—
703#117—44no—
704#117—48no—
705#117—48no—
706C2×C4⋊C4—216no—
707C2×C4⋊C4—28no—
708C2×C4⋊C4—42no—
709C2×C4⋊C4—42no—
710C2×C4⋊C4—42no—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C22⋊C4—28no—
762C2×C22⋊C4—44no—
763C2×C22⋊C4—44no—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C42—28no—
804C2×C42—42no—
805C2×C42—42no—
806C2×C42C2412yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2411yescharacteristic
831C2×C42C2412yes—
832C2×C42C2414yes—
833C2×C42C2411yescharacteristic
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2412yes—
859#95C2412yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886C24—22no—
887C24—24no—
888C24—41no—
889C24—41no—
890C24—42no—
891C24C2512yes—
892C24C2514yes—
893C24C2511yescharacteristic
894C2×Q8—22no—
895C2×Q8—24no—
896C2×Q8—22no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×Q8—41no—
901C2×Q8—42no—
902C2×Q8—41no—
903C2×Q8—42no—
904C2×Q8—41no—
905C2×Q8—41no—
906C2×Q8—44no—
907C2×Q8—42no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—88no—
911C2×Q8C2×#4118yes—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—24no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—28no—
933C22×C4—28no—
934C22×C4—24no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—28no—
946C22×C4—42no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—416no—
964C22×C4C2×#4118yes—
965C22×C4H(5,𝔽2)14yes—
966C22×C4C2514yes—
967C22×C4C2512yes—
968C22×C4C2514yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2514yes—
974C22×C4C2514yes—
975C22×C4C2512yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2514yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—42no—
1009C4⋊C4—41no—
1010C4⋊C4—42no—
1011C4⋊C4—41no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—44no—
1015C4⋊C4—42no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—42no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—42no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4C2×#4118yes—
1035C4⋊C4C2×#41116yes—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4C2×#41116yes—
1075C42—28no—
1076C42—28no—
1077C42—28no—
1078C42—28no—
1079C42—28no—
1080C42—28no—
1081C42—24no—
1082C42—24no—
1083C42—24no—
1084C42—24no—
1085C42—28no—
1086C42—24no—
1087C42—24no—
1088C42—41no—
1089C42—41no—
1090C42—42no—
1091C42—44no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—24no—
1110C23—22no—
1111C23—24no—
1112C23—24no—
1113C23—22no—
1114C23—22no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—44no—
1119C23—44no—
1120C23—44no—
1121C23—84no—
1122C23—84no—
1123C23C22×#4114yes—
1124C23C2×H(5,𝔽2)12yes—
1125C23C2611yescharacteristic
1126Q8—48no—
1127Q8—82no—
1128Q8—84no—
1129Q8—82no—
1130Q8—84no—
1131Q8—162no—
1132D4—416no—
1133D4—84no—
1134D4—88no—
1135D4—88no—
1136D4—84no—
1137D4—162no—
1138C2×C4—28no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—44no—
1189C2×C4—48no—
1190C2×C4—48no—
1191C2×C4—48no—
1192C2×C4—48no—
1193C2×C4—48no—
1194C2×C4—88no—
1195C2×C4—88no—
1196C2×C4—88no—
1197C2×C4—84no—
1198C2×C4—84no—
1199C2×C4—84no—
1200C2×C4C22×#4118yes—
1201C2×C4C22×#4114yes—
1202C2×C4C22×#4118yes—
1203C2×C4C22×#4114yes—
1204C2×C4C2×H(5,𝔽2)14yes—
1205C2×C4#58512yes—
1206C2×C4#58512yes—
1207C22—24no—
1208C22—24no—
1209C22—22no—
1210C22—22no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—42no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—44no—
1222C22—42no—
1223C22—88no—
1224C22#348314yes—
1225C22C23×#4112yes—
1226C22C22×H(5,𝔽2)11yescharacteristic
1227C22C2×#58511yescharacteristic
1228C22C2×#58511yescharacteristic
1229C222−1+612yes—
1230C4—24no—
1231C4—24no—
1232C4—28no—
1233C4—28no—
1234C4—22no—
1235C4—22no—
1236C4—24no—
1237C4—44no—
1238C4—44no—
1239C4—44no—
1240C4—42no—
1241C4—42no—
1242C4—44no—
1243C4—42no—
1244C4—42no—
1245C4—44no—
1246C4—42no—
1247C4—44no—
1248C4—42no—
1249C4—44no—
1250C2—24no—
1251C2—84no—
1252C2—82no—
1253C2C2×#348311yescharacteristic
1254C2#6282011yescharacteristic
1255C2#6288611yescharacteristic
1256C2#6299112yes—
1257C2#6299512yes—
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. #59998C2semidirect
2. #59982C2semidirect
3. #59961C2semidirect
4. #59948C2semidirect
5. #59923C2semidirect
6. #59885C2semidirect
7. #59719C2semidirect
8. #59339C2semidirect
9. #59312C2semidirect
10. #44464C2semidirect
11. #44451C2semidirect
12. #43883C2semidirect
13. #43848C2semidirect
14. #43788C2semidirect
15. #43488C2semidirect
16. #43437C2semidirect
17. #43400C2semidirect
18. #35464C2semidirect
19. #35397C2semidirect
20. #34877C2semidirect
21. C2×#2499C2semidirect
22. #34297C2semidirect
23. #34277C2semidirect
30. #2811C22semidirect
31. #2809C22semidirect
32. #2809C22semidirect
35. #2808C22semidirect
36. #2806C22semidirect
37. #2785C22semidirect
40. #2783C22semidirect
43. #2775C22semidirect
44. #2769C22semidirect
47. #2734C22semidirect
48. #2733C22semidirect
49. #2731C22semidirect
54. #2721C22semidirect
55. #2721C22semidirect
60. #2612C22semidirect
61. #2612C22semidirect
64. #2611C22semidirect
67. #2609C22semidirect
68. #2604C22semidirect
69. #2602C22semidirect
72. #2601C22semidirect
74. #2586C22semidirect
75. #2586C22semidirect
77. #2574C22semidirect
78. #2574C22semidirect
79. #2572C22semidirect
80. #2565C22semidirect
81. #2564C22semidirect
86. #2560C22semidirect
87. #2557C22semidirect
90. #2556C22semidirect
91. #2553C22semidirect
92. #2552C22semidirect
93. #2552C22semidirect
98. #2538C22semidirect
101. #2532C22semidirect
102. #2532C22semidirect
107. #2529C22semidirect
108. #2521C22semidirect
109. #2519C22semidirect
110. #2518C22semidirect
115. #2512C22semidirect
116. #2508C22semidirect
117. #2506C22semidirect
125. #2499C22semidirect
126. #2498C22semidirect
127. #2496C22semidirect
133. #2474C22semidirect
138. #2459C22semidirect
141. #2451C22semidirect
144. #2441C22semidirect
145. #2439C22semidirect
150. #2423C22semidirect
163. #2373C22semidirect
164. #2373C22semidirect
166. #2372C22semidirect
167. #2372C22semidirect
168. #2371C22semidirect
169. #2371C22semidirect
170. #2370C22semidirect
171. #2369C22semidirect
172. #2369C22semidirect
174. #2368C22semidirect
181. #2356C22semidirect
182. #2354C22semidirect
184. Q8×C4⋊C4C22semidirect
185. #2346C22semidirect
189. #2343C22semidirect
190. #2336C22semidirect
191. #2336C22semidirect
192. #2334C22semidirect
193. #2332C22semidirect
199. C4×#125C22semidirect
200. C4×#126C22semidirect
205. #2298C22semidirect
206. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#599982
#599822
#599612
#599482
#599232
#598852
#597192
#593392
#593122
#444642
#444512
#438832
#438482
#437882
#434882
#434372
#434002
#354642
#353972
#348772
C2×#24992
#342972
#342772