Finite Group Databasebeta

← #7697201

Subgroups — #7697201

Order 512.

5141 conjugacy classes of subgroups.

The subgroup lattice has 1275 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59928C212yesmaximal, complemented
2#59836C211yesmaximal, characteristic, complemented
3#59744C212yesmaximal, complemented
4#59048C214yesmaximal, complemented
5#52307C211yesmaximal, characteristic, complemented
6#52160C212yesmaximal, complemented
7#44378C212yesmaximal, complemented
8#44272C214yesmaximal, complemented
9#44178C214yesmaximal, complemented
10#44073C214yesmaximal, complemented
11#43282C214yesmaximal, complemented
12#40315C214yesmaximal, complemented
13#40099C214yesmaximal, complemented
14#39444C212yesmaximal, complemented
15#38810C212yesmaximal, complemented
16#38494C212yesmaximal, complemented
17#38140C214yesmaximal, complemented
18#36403C211yesmaximal, characteristic, complemented
19#36135C212yesmaximal, complemented
20#35907C212yesmaximal, complemented
21#35698C214yesmaximal, complemented
22#34331C212yesmaximal, complemented
23#34283C214yesmaximal, complemented
24C2×#559C2212yes—
25C2×#551C2212yes—
26C2×#538C2214yes—
27C2×#529C2214yescomplemented
28#2864C2211yescharacteristic, complemented
29#2860C2212yes—
30#2859C2212yescomplemented
31#2851C2214yescomplemented
32#2811C2211yescharacteristic, complemented
33#2809C2212yescomplemented
34#2797C2214yescomplemented
35#2789C2212yescomplemented
36#2785C2212yescomplemented
37#2785C2214yescomplemented
38#2782C2212yes—
39#2777C2214yescomplemented
40#2777C2214yescomplemented
41#2765C2214yescomplemented
42#2753C2214yescomplemented
43#2752C2212yescomplemented
44#2751C2214yescomplemented
45#2733C2212yes—
46#2733C2212yes—
47#2733C2214yescomplemented
48#2733C2211yescharacteristic, complemented
49#2732C2212yes—
50#2732C2212yes—
51#2730C2214yescomplemented
52#2730C2214yescomplemented
53#2727C2212yescomplemented
54#2724C2211yescharacteristic
55#2721C2214yescomplemented
56#2721C2214yescomplemented
57#2718C2214yes—
58#2718C2214yescomplemented
59#2714C2214yescomplemented
60#2711C2214yes—
61#2710C2214yes—
62#2705C2214yescomplemented
63#2703C2214yes—
64#2696C2214yes—
65#2694C2214yes—
66#2694C2214yescomplemented
67#2682C2212yes—
68#2679C2211yescharacteristic
69#2673C2214yes—
70#2670C2212yescomplemented
71#2669C2214yes—
72#2667C2212yescomplemented
73#2667C2214yescomplemented
74#2653C2214yes—
75#2649C2214yescomplemented
76#2636C2214yes—
77#2612C2214yescomplemented
78#2609C2212yes—
79#2607C2212yescomplemented
80#2604C2214yescomplemented
81#2603C2214yescomplemented
82#2600C2214yescomplemented
83#2596C2214yescomplemented
84#2595C2214yescomplemented
85#2594C2214yescomplemented
86#2593C2212yescomplemented
87#2589C2214yescomplemented
88#2581C2211yescharacteristic, complemented
89#2580C2211yescharacteristic
90#2576C2214yescomplemented
91#2576C2214yescomplemented
92#2575C2214yescomplemented
93#2575C2214yescomplemented
94#2574C2214yescomplemented
95#2574C2214yescomplemented
96#2570C2214yescomplemented
97#2565C2214yescomplemented
98#2564C2214yes—
99#2559C2214yes—
100#2556C2214yescomplemented
101#2556C2214yescomplemented
102#2555C2212yes—
103#2554C2214yes—
104#2553C2214yes—
105#2553C2214yescomplemented
106#2553C2214yescomplemented
107#2543C2214yes—
108#2539C2214yes—
109#2539C2214yescomplemented
110#2536C2212yes—
111#2535C2212yes—
112#2534C2212yes—
113#2525C2214yescomplemented
114#2521C2214yescomplemented
115#2512C2214yescomplemented
116#2510C2214yescomplemented
117#2509C2212yescomplemented
118#2501C2214yes—
119#2479C2214yescomplemented
120#2479C2214yescomplemented
121#2478C2214yescomplemented
122#2478C2214yescomplemented
123#2471C2214yes—
124#2468C2214yes—
125#2467C2214yes—
126#2467C2214yescomplemented
127#2464C2214yes—
128#2464C2214yes—
129#2460C2214yescomplemented
130#2457C2214yescomplemented
131#2456C2214yes—
132#2455C2214yes—
133#2455C2214yes—
134#2455C2214yescomplemented
135#2454C2214yescomplemented
136#2450C2214yescomplemented
137#2448C2212yes—
138#2448C2214yescomplemented
139#2443C2214yes—
140#2442C2214yescomplemented
141#2437C2212yescomplemented
142#2426C2214yes—
143#2425C2214yes—
144#2424C2214yes—
145#2424C2214yes—
146#2423C2214yescomplemented
147#2423C2214yescomplemented
148#2422C2214yescomplemented
149#2420C2214yes—
150#2418C2214yes—
151#2418C2214yescomplemented
152#2413C2214yescomplemented
153#2412C2214yescomplemented
154#2407C2214yes—
155#2404C2212yescomplemented
156#2397C2214yescomplemented
157#2392C2214yescomplemented
158#2392C2214yescomplemented
159#2388C2212yes—
160#2388C2214yescomplemented
161#2374C2214yescomplemented
162#2373C2214yescomplemented
163#2373C2214yescomplemented
164#2372C2214yes—
165#2368C2214yescomplemented
166#2368C2214yescomplemented
167#2367C2212yes—
168#2367C2212yescomplemented
169#2367C2214yescomplemented
170#2366C2212yes—
171#2364C2214yes—
172#2364C2214yes—
173#2363C2214yes—
174#2361C2214yes—
175#2360C2214yescomplemented
176#2359C2214yescomplemented
177#2359C2214yescomplemented
178#2359C2214yescomplemented
179#2358C2214yes—
180#2358C2214yes—
181#2358C2214yescomplemented
182#2358C2214yescomplemented
183#2357C2211yescharacteristic
184#2355C2212yescomplemented
185#2354C2214yescomplemented
186#2351C2211yescharacteristic, complemented
187Q8×C4⋊C4C2212yescomplemented
188#2349C2212yes—
189#2349C2212yescomplemented
190#2349C2212yescomplemented
191#2339C2212yescomplemented
192#2337C2214yescomplemented
193#2335C2214yes—
194#2335C2214yescomplemented
195#2335C2214yescomplemented
196#2334C2214yescomplemented
197#2333C2214yes—
198#2326C2214yescomplemented
199#2318C2214yes—
200C4×#127C2212yes—
201C4×#126C2214yescomplemented
202C4×#124C2212yes—
203C4×#124C2211yescharacteristic
204C4×#124C2212yescomplemented
205C4×#124C2212yescomplemented
206C4×#124C2214yescomplemented
207C4×#123C2214yes—
208C4×#121C2214yes—
209#2295C2212yescomplemented
210#2295C2212yescomplemented
211#2293C2212yes—
212#2293C2212yescomplemented
213#2290C2214yescomplemented
214C2×#388C2214yescomplemented
215#2275C2214yescomplemented
216#2273C2212yescomplemented
217C42×Q8C2211yescharacteristic, complemented
218C42×D4C2212yes—
219C22×#41C2312yes—
220#559—216no—
221#551—48no—
222#538—232no—
223C2×#127C2312yes—
224#529—416no—
225C2×#126C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#125C2314yes—
231C2×#125C2314yes—
232C2×#124C2314yes—
233C2×#124C2314yes—
234C2×#124C2312yes—
235C2×#124C2312yes—
236C2×#124C2311yescharacteristic
237C2×#124C2312yes—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2312yes—
246C2×#123C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×#121C2314yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#120C2314yes—
257C2×#120C2314yes—
258C2×#120C2312yes—
259C2×#120C2314yes—
260C2×C4×Q8C2312yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×#117C2314yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C22×C4⋊C4C2314yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2314yes—
294C22×C22⋊C4C2314yes—
295C22×C42C2314yes—
296#401C2314yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2312yes—
303#399C2314yes—
304#399C2314yes—
305#399C2314yes—
306#399C2312yes—
307#399C2314yes—
308#399C2314yes—
309#399C2314yes—
310#399C2314yes—
311#399C2314yes—
312#399C2314yes—
313#399C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2312yes—
322#398C2314yes—
323#398C2312yes—
324#398C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#395C2314yes—
344#395C2312yes—
345#395C2312yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2312yes—
353#394C2314yes—
354#394C2312yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2312yes—
365#393C2314yes—
366#393C2312yes—
367#393C2314yes—
368#393C2312yes—
369#392C2314yes—
370#392C2314yes—
371#392C2314yes—
372#392C2312yes—
373#392C2314yes—
374#392C2314yes—
375#392C2314yes—
376#392C2314yes—
377#392C2314yes—
378#392C2314yes—
379#392C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#391C2312yes—
385#391C2314yes—
386#391C2312yes—
387#391C2312yes—
388#391C2311yescharacteristic
389#391C2312yes—
390#390C2314yes—
391#390C2314yes—
392#390C2312yes—
393#390C2312yes—
394#390C2312yes—
395#390C2314yes—
396#390C2312yes—
397#390C2314yes—
398#390C2314yes—
399#390C2312yes—
400#390C2314yes—
401#390C2314yes—
402#390C2311yescharacteristic
403#390C2312yes—
404#390C2314yes—
405#390C2314yes—
406#390C2312yes—
407#390C2314yes—
408#390C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2312yes—
412#389C2312yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2312yes—
427#389C2314yes—
428#389C2312yes—
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#388C2314yes—
472#388C2314yes—
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#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#384C2312yes—
543#384C2314yes—
544#384C2314yes—
545#383C2314yes—
546#382C2314yes—
547#382C2314yes—
548#382C2312yes—
549#382C2312yes—
550#382C2311yescharacteristic
551#382C2311yescharacteristic
552#382C2312yes—
553#382C2312yes—
554#382C2312yes—
555#382C2311yescharacteristic
556#381C2314yes—
557#381C2312yes—
558#381C2314yes—
559#381C2312yes—
560#380C2314yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2312yes—
566#380C2314yes—
567#380C2314yes—
568#379C2312yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2311yescharacteristic
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2312yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2314yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610#376C2314yes—
611#376C2314yes—
612C2×#95C2314yes—
613C2×#95C2314yes—
614C2×#95C2314yes—
615C43C2312yes—
616C43C2312yes—
617C43C2311yescharacteristic
618C25C2412yes—
619C2×#41—44no—
620C2×#41—84no—
621C22×Q8C2411yescharacteristic
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2411yescharacteristic
625C22×D4C2412yes—
626C22×D4C2414yes—
627C22×D4C2412yes—
628C22×D4C2412yes—
629C22×D4C2414yes—
630C22×D4C2411yescharacteristic
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2412yes—
638C23×C4C2414yes—
639C23×C4C2414yes—
640C23×C4C2414yes—
641C23×C4C2414yes—
642C23×C4C2412yes—
643C23×C4C2414yes—
644C23×C4C2414yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2412yes—
649#127—28no—
650#126—216no—
651#126—216no—
652#126—48no—
653#126—48no—
654#126—48no—
655#125—48no—
656#125—84no—
657#124—216no—
658#124—28no—
659#124—28no—
660#124—24no—
661#124—216no—
662#124#41116yescomplemented
663#123—216no—
664#123—216no—
665#123—216no—
666#123—216no—
667#123—48no—
668#123—48no—
669#123—48no—
670#123—44no—
671#123—84no—
672C22⋊Q8—216no—
673C22⋊Q8—216no—
674C22⋊Q8—84no—
675#121—216no—
676#121—216no—
677#121—216no—
678#121—48no—
679#121—84no—
680#121—84no—
681#120—216no—
682#120—216no—
683#120—44no—
684#120—84no—
685C4×Q8—28no—
686C4×Q8—28no—
687C4×Q8—28no—
688C4×Q8—42no—
689C4×Q8—42no—
690C4×Q8—82no—
691C4×Q8—82no—
692C4×D4—28no—
693C4×D4—216no—
694C4×D4—216no—
695C4×D4—216no—
696C4×D4—28no—
697C4×D4—44no—
698C4×D4—48no—
699C4×D4—48no—
700C4×D4—48no—
701C4×D4—44no—
702C4×D4—42no—
703C4×D4—48no—
704C4×D4—48no—
705C4×D4—82no—
706C4×D4—84no—
707C4×D4—82no—
708C4×D4—84no—
709C4×D4—84no—
710C4×D4—82no—
711C4×D4—82no—
712#117—48no—
713#117—48no—
714#117—48no—
715C2×C4⋊C4—84no—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C22⋊C4—216no—
761C2×C22⋊C4—44no—
762C2×C22⋊C4—48no—
763C2×C22⋊C4—84no—
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⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
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×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C42—48no—
813C2×C42C2411yescharacteristic
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2411yescharacteristic
818C2×C42C2412yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2412yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2411yescharacteristic
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2412yes—
838#95C2411yescharacteristic
839#95C2414yes—
840#95C2412yes—
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#95C2412yes—
857#95C2412yes—
858#95C2414yes—
859#95C2412yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2412yes—
874#95C2411yescharacteristic
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2412yes—
887C24—28no—
888C24—42no—
889C24—42no—
890C24—44no—
891C24—42no—
892C24C2512yes—
893C24C2514yes—
894C24C2514yes—
895#41—816no—
896C2×Q8—24no—
897C2×Q8—41no—
898C2×Q8—41no—
899C2×Q8—42no—
900C2×Q8—42no—
901C2×Q8—41no—
902C2×Q8—44no—
903C2×Q8—42no—
904C2×Q8C2×#4118yes—
905C2×Q8H(5,𝔽2)14yes—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—24no—
914C2×D4—28no—
915C2×D4—24no—
916C2×D4—22no—
917C2×D4—42no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—41no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—41no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4C2×#4118yes—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—28no—
946C22×C4—28no—
947C22×C4—28no—
948C22×C4—28no—
949C22×C4—28no—
950C22×C4—24no—
951C22×C4—28no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—42no—
970C22×C4—44no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—42no—
975C22×C4C2514yes—
976C22×C4C2514yes—
977C22×C4C2514yes—
978C22×C4C2511yescharacteristic
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2514yes—
986C22×C4C2514yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—41no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—41no—
1032C4⋊C4—42no—
1033C4⋊C4—41no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
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—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
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—42no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—42no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—42no—
1085C22⋊C4C2×#41116yes—
1086C22⋊C4C2×#41116yes—
1087C42—28no—
1088C42—24no—
1089C42—28no—
1090C42—24no—
1091C42—24no—
1092C42—28no—
1093C42—22no—
1094C42—24no—
1095C42—24no—
1096C42—22no—
1097C42—44no—
1098C42—44no—
1099C42—42no—
1100C42—44no—
1101C42—41no—
1102C42—44no—
1103C42—44no—
1104C42—42no—
1105C42—44no—
1106C42—42no—
1107C42—42no—
1108C42—44no—
1109C42—42no—
1110C42—44no—
1111C42C2×#4118yes—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23—24no—
1122C23—22no—
1123C23—24no—
1124C23—22no—
1125C23—24no—
1126C23—24no—
1127C23—24no—
1128C23—24no—
1129C23—22no—
1130C23—48no—
1131C23—88no—
1132C23—88no—
1133C23—162no—
1134C23—162no—
1135C23C22×#4118yes—
1136C23C2611yescharacteristic
1137Q8—48no—
1138Q8—44no—
1139Q8—44no—
1140Q8—84no—
1141D4—48no—
1142D4—416no—
1143D4—48no—
1144D4—48no—
1145D4—48no—
1146D4—48no—
1147D4—88no—
1148D4—82no—
1149D4—88no—
1150D4—88no—
1151D4—88no—
1152D4—88no—
1153D4—88no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—88no—
1204C2×C4—88no—
1205C2×C4—88no—
1206C2×C4—88no—
1207C2×C4—88no—
1208C2×C4—88no—
1209C2×C4—84no—
1210C2×C4—88no—
1211C2×C4—88no—
1212C2×C4—164no—
1213C2×C4—162no—
1214C2×C4C22×#4114yes—
1215C2×C4C22×#4118yes—
1216C2×C4C22×#4114yes—
1217C2×C4C22×#4114yes—
1218C2×C4C2×H(5,𝔽2)12yes—
1219C2×C4C2×H(5,𝔽2)14yes—
1220C2×C4#58512yes—
1221C22—28no—
1222C22—28no—
1223C22—28no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—42no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—42no—
1240C22—168no—
1241C22C23×#4112yes—
1242C22C22×H(5,𝔽2)11yescharacteristic
1243C22C2×#58511yescharacteristic
1244C22H(7,𝔽2)12yes—
1245C222−1+611yescharacteristic
1246C4—24no—
1247C4—22no—
1248C4—28no—
1249C4—24no—
1250C4—24no—
1251C4—22no—
1252C4—24no—
1253C4—44no—
1254C4—42no—
1255C4—44no—
1256C4—44no—
1257C4—44no—
1258C4—42no—
1259C4—44no—
1260C4—42no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—42no—
1265C4—41no—
1266C2—48no—
1267C2—84no—
1268C2—82no—
1269C2#41211yescharacteristic
1270C2#6284712yes—
1271C2#6290111yescharacteristic
1272C2#6298612yes—
1273C2#6304611yescharacteristic
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. #59928C2semidirect
2. #59836C2semidirect
3. #59744C2semidirect
4. #59048C2semidirect
5. #52307C2semidirect
6. #52160C2semidirect
7. #44378C2semidirect
8. #44272C2semidirect
9. #44178C2semidirect
10. #44073C2semidirect
11. #43282C2semidirect
12. #40315C2semidirect
13. #40099C2semidirect
14. #39444C2semidirect
15. #38810C2semidirect
16. #38494C2semidirect
17. #38140C2semidirect
18. #36403C2semidirect
19. #36135C2semidirect
20. #35907C2semidirect
21. #35698C2semidirect
22. #34331C2semidirect
23. #34283C2semidirect
27. C2×#529C22semidirect
28. #2864C22semidirect
30. #2859C22semidirect
31. #2851C22semidirect
32. #2811C22semidirect
33. #2809C22semidirect
34. #2797C22semidirect
35. #2789C22semidirect
36. #2785C22semidirect
37. #2785C22semidirect
39. #2777C22semidirect
40. #2777C22semidirect
41. #2765C22semidirect
42. #2753C22semidirect
43. #2752C22semidirect
44. #2751C22semidirect
47. #2733C22semidirect
48. #2733C22semidirect
51. #2730C22semidirect
52. #2730C22semidirect
53. #2727C22semidirect
55. #2721C22semidirect
56. #2721C22semidirect
58. #2718C22semidirect
59. #2714C22semidirect
62. #2705C22semidirect
66. #2694C22semidirect
70. #2670C22semidirect
72. #2667C22semidirect
73. #2667C22semidirect
75. #2649C22semidirect
77. #2612C22semidirect
79. #2607C22semidirect
80. #2604C22semidirect
81. #2603C22semidirect
82. #2600C22semidirect
83. #2596C22semidirect
84. #2595C22semidirect
85. #2594C22semidirect
86. #2593C22semidirect
87. #2589C22semidirect
88. #2581C22semidirect
90. #2576C22semidirect
91. #2576C22semidirect
92. #2575C22semidirect
93. #2575C22semidirect
94. #2574C22semidirect
95. #2574C22semidirect
96. #2570C22semidirect
97. #2565C22semidirect
100. #2556C22semidirect
101. #2556C22semidirect
105. #2553C22semidirect
106. #2553C22semidirect
109. #2539C22semidirect
113. #2525C22semidirect
114. #2521C22semidirect
115. #2512C22semidirect
116. #2510C22semidirect
117. #2509C22semidirect
119. #2479C22semidirect
120. #2479C22semidirect
121. #2478C22semidirect
122. #2478C22semidirect
126. #2467C22semidirect
129. #2460C22semidirect
130. #2457C22semidirect
134. #2455C22semidirect
135. #2454C22semidirect
136. #2450C22semidirect
138. #2448C22semidirect
140. #2442C22semidirect
141. #2437C22semidirect
146. #2423C22semidirect
147. #2423C22semidirect
148. #2422C22semidirect
151. #2418C22semidirect
152. #2413C22semidirect
153. #2412C22semidirect
155. #2404C22semidirect
156. #2397C22semidirect
157. #2392C22semidirect
158. #2392C22semidirect
160. #2388C22semidirect
161. #2374C22semidirect
162. #2373C22semidirect
163. #2373C22semidirect
165. #2368C22semidirect
166. #2368C22semidirect
168. #2367C22semidirect
169. #2367C22semidirect
175. #2360C22semidirect
176. #2359C22semidirect
177. #2359C22semidirect
178. #2359C22semidirect
181. #2358C22semidirect
182. #2358C22semidirect
184. #2355C22semidirect
185. #2354C22semidirect
186. #2351C22semidirect
187. Q8×C4⋊C4C22semidirect
189. #2349C22semidirect
190. #2349C22semidirect
191. #2339C22semidirect
192. #2337C22semidirect
194. #2335C22semidirect
195. #2335C22semidirect
196. #2334C22semidirect
198. #2326C22semidirect
201. C4×#126C22semidirect
204. C4×#124C22semidirect
205. C4×#124C22semidirect
206. C4×#124C22semidirect
209. #2295C22semidirect
210. #2295C22semidirect
212. #2293C22semidirect
213. #2290C22semidirect
214. C2×#388C22semidirect
215. #2275C22semidirect
216. #2273C22semidirect
217. C42×Q8C22semidirect
662. #124#41semidirect

Maximal subgroups

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

subgroupindex
#599282
#598362
#597442
#590482
#523072
#521602
#443782
#442722
#441782
#440732
#432822
#403152
#400992
#394442
#388102
#384942
#381402
#364032
#361352
#359072
#356982
#343312
#342832