Finite Group Databasebeta

← #7697425

Subgroups — #7697425

Order 512.

4743 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59928C211yesmaximal, characteristic, complemented
2#59914C212yesmaximal, complemented
3#59836C212yesmaximal
4#59558C214yesmaximal, complemented
5#52301C211yesmaximal, characteristic
6#52267C212yesmaximal, complemented
7#44727C214yesmaximal, complemented
8#43803C212yesmaximal, complemented
9#43728C214yesmaximal, complemented
10#43408C214yesmaximal, complemented
11#43349C214yesmaximal, complemented
12#39702C212yesmaximal, complemented
13#39214C214yesmaximal, complemented
14#38788C212yesmaximal, complemented
15#38647C214yesmaximal, complemented
16#38541C214yesmaximal, complemented
17#38472C212yesmaximal, complemented
18#36394C211yesmaximal, characteristic, complemented
19#36338C212yesmaximal, complemented
20#36072C212yesmaximal, complemented
21#35946C214yesmaximal, complemented
22#34322C212yesmaximal, complemented
23#34296C214yesmaximal, complemented
24C2×#556C2212yes—
25C2×#551C2214yes—
26#2864C2211yescharacteristic, complemented
27#2863C2212yescomplemented
28#2851C2214yescomplemented
29#2848C2212yescomplemented
30#2811C2211yescharacteristic, complemented
31#2809C2211yescharacteristic, complemented
32#2807C2212yescomplemented
33#2807C2214yescomplemented
34#2806C2212yescomplemented
35#2805C2212yescomplemented
36#2804C2212yes—
37#2804C2211yescharacteristic
38#2802C2214yescomplemented
39#2790C2214yescomplemented
40#2788C2214yescomplemented
41#2787C2214yescomplemented
42#2787C2214yescomplemented
43#2782C2212yes—
44#2782C2214yes—
45#2782C2214yes—
46#2782C2212yes—
47#2780C2214yes—
48#2767C2214yescomplemented
49#2767C2214yescomplemented
50#2763C2212yescomplemented
51#2746C2214yes—
52#2745C2214yescomplemented
53#2739C2214yescomplemented
54#2732C2212yes—
55#2732C2212yes—
56#2729C2214yescomplemented
57#2729C2214yescomplemented
58#2728C2214yes—
59#2724C2212yes—
60#2722C2214yescomplemented
61#2720C2214yescomplemented
62#2719C2214yescomplemented
63#2717C2214yes—
64#2698C2214yescomplemented
65#2695C2214yes—
66#2684C2214yes—
67#2684C2212yes—
68#2680C2212yes—
69#2679C2211yescharacteristic
70#2666C2214yescomplemented
71#2655C2214yescomplemented
72#2655C2214yescomplemented
73#2652C2214yescomplemented
74#2633C2212yes—
75#2612C2212yescomplemented
76#2612C2212yescomplemented
77#2611C2214yescomplemented
78#2609C2214yes—
79#2606C2212yescomplemented
80#2599C2214yescomplemented
81#2599C2214yescomplemented
82#2589C2214yescomplemented
83#2589C2214yescomplemented
84#2588C2214yescomplemented
85#2587C2214yescomplemented
86#2583C2214yescomplemented
87#2581C2211yescharacteristic, complemented
88#2580C2211yescharacteristic
89#2577C2214yescomplemented
90#2576C2214yes—
91#2575C2214yescomplemented
92#2575C2214yescomplemented
93#2575C2214yescomplemented
94#2574C2214yescomplemented
95#2571C2212yescomplemented
96#2569C2212yescomplemented
97#2565C2212yescomplemented
98#2564C2212yes—
99#2556C2214yescomplemented
100#2556C2214yescomplemented
101#2553C2214yes—
102#2553C2214yes—
103#2553C2214yes—
104#2536C2214yes—
105#2534C2214yes—
106#2530C2214yescomplemented
107#2530C2214yescomplemented
108#2530C2214yescomplemented
109#2528C2214yescomplemented
110#2528C2214yescomplemented
111#2527C2214yescomplemented
112#2527C2214yescomplemented
113#2517C2214yescomplemented
114#2508C2212yescomplemented
115#2508C2214yescomplemented
116#2505C2214yescomplemented
117#2505C2214yescomplemented
118#2496C2214yescomplemented
119#2494C2214yescomplemented
120#2493C2214yescomplemented
121#2489C2214yescomplemented
122#2487C2214yes—
123#2482C2214yescomplemented
124#2480C2214yescomplemented
125#2480C2214yescomplemented
126#2478C2214yescomplemented
127#2477C2214yes—
128#2475C2214yescomplemented
129#2475C2214yescomplemented
130#2473C2214yescomplemented
131#2470C2214yes—
132#2468C2214yes—
133#2468C2214yes—
134#2468C2214yes—
135#2466C2214yes—
136#2465C2214yescomplemented
137#2462C2214yescomplemented
138#2460C2214yes—
139#2460C2214yes—
140#2453C2214yescomplemented
141#2450C2214yes—
142#2449C2214yes—
143#2449C2214yes—
144#2447C2212yes—
145#2442C2214yescomplemented
146#2438C2214yescomplemented
147#2437C2212yescomplemented
148#2437C2212yescomplemented
149#2423C2214yescomplemented
150#2421C2214yescomplemented
151#2419C2214yes—
152#2418C2214yes—
153#2418C2214yes—
154#2402C2214yescomplemented
155#2398C2212yes—
156#2398C2214yes—
157#2396C2214yescomplemented
158#2396C2214yescomplemented
159#2373C2214yescomplemented
160#2373C2214yescomplemented
161#2373C2214yescomplemented
162#2373C2214yescomplemented
163#2372C2212yes—
164#2371C2212yescomplemented
165#2368C2214yescomplemented
166#2368C2212yescomplemented
167#2367C2212yes—
168#2367C2212yes—
169#2365C2212yescomplemented
170#2360C2214yescomplemented
171#2360C2214yescomplemented
172#2359C2214yes—
173#2359C2214yes—
174#2359C2214yes—
175#2358C2214yes—
176#2358C2214yes—
177#2356C2211yescharacteristic, complemented
178#2355C2212yescomplemented
179#2352C2214yes—
180#2351C2212yescomplemented
181#2351C2212yescomplemented
182#2349C2214yes—
183#2349C2211yescharacteristic
184D4×C4⋊C4C2212yes—
185#2346C2214yescomplemented
186#2343C2214yescomplemented
187#2343C2214yescomplemented
188#2342C2214yescomplemented
189#2342C2214yescomplemented
190#2337C2214yes—
191#2335C2214yes—
192#2334C2214yescomplemented
193#2334C2214yescomplemented
194#2334C2214yescomplemented
195#2334C2214yescomplemented
196#2329C2214yescomplemented
197#2323C2214yescomplemented
198#2322C2214yes—
199C4×C4⋊Q8C2212yescomplemented
200C4×#124C2212yes—
201C4×#124C2212yes—
202C4×#124C2211yescharacteristic
203C4×C22⋊Q8C2214yescomplemented
204C4×#123C2214yes—
205C4×#120C2212yes—
206C4×#120C2214yes—
207#2296C2214yescomplemented
208#2295C2212yescomplemented
209#2295C2212yescomplemented
210#2293C2212yes—
211#2293C2212yes—
212#2290C2214yes—
213#2290C2214yes—
214C2×#385C2214yescomplemented
215#2275C2212yes—
216#2274C2214yescomplemented
217C42×Q8C2211yescharacteristic, complemented
218C2×C4×C22⋊C4C2212yescomplemented
219C24×C4C2312yes—
220#556—216no—
221#551—232no—
222C2×C4⋊Q8C2312yes—
223C2×#126C2314yes—
224C2×#126C2314yes—
225C2×#126C2314yes—
226C2×#126C2314yes—
227C2×#125C2312yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#124C2312yes—
231C2×#124C2311yescharacteristic
232C2×#124C2312yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×#123C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×#120C2312yes—
243C2×#120C2314yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×#117C2314yes—
264C2×#117C2314yes—
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2314yes—
270C22×C22⋊C4C2314yes—
271C22×C22⋊C4C2314yes—
272C22×C22⋊C4C2314yes—
273C22×C42C2314yes—
274#401C2314yes—
275#401C2314yes—
276#400C2312yes—
277#400C2314yes—
278#400C2312yes—
279#400C2314yes—
280#400C2312yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#400C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2312yes—
294#400C2314yes—
295#400C2314yes—
296#400C2314yes—
297#399C2312yes—
298#399C2312yes—
299#399C2314yes—
300#399C2314yes—
301#399C2314yes—
302#399C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#397C2314yes—
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#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#395C2312yes—
341#395C2314yes—
342#395C2312yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#394C2314yes—
347#394C2314yes—
348#394C2314yes—
349#394C2312yes—
350#394C2312yes—
351#394C2314yes—
352#394C2314yes—
353#393C2312yes—
354#393C2312yes—
355#393C2314yes—
356#393C2314yes—
357#393C2314yes—
358#391C2312yes—
359#391C2312yes—
360#391C2312yes—
361#391C2312yes—
362#391C2314yes—
363#391C2314yes—
364#391C2312yes—
365#391C2312yes—
366#391C2314yes—
367#391C2314yes—
368#391C2312yes—
369#391C2314yes—
370#391C2311yescharacteristic
371#391C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2311yescharacteristic
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2312yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2312yes—
491#385C2314yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2312yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#384C2312yes—
528#384C2312yes—
529#383C2312yes—
530#383C2314yes—
531#382C2312yes—
532#382C2314yes—
533#382C2314yes—
534#382C2314yes—
535#382C2314yes—
536#382C2311yescharacteristic
537#382C2311yescharacteristic
538#382C2314yes—
539#382C2314yes—
540#382C2312yes—
541#382C2312yes—
542#382C2311yescharacteristic
543#381C2314yes—
544#381C2314yes—
545#381C2314yes—
546#381C2314yes—
547#380C2314yes—
548#380C2312yes—
549#380C2314yes—
550#380C2314yes—
551#380C2314yes—
552#380C2314yes—
553#380C2314yes—
554#380C2314yes—
555#380C2314yes—
556#380C2314yes—
557#380C2314yes—
558#379C2314yes—
559#379C2314yes—
560#379C2312yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2312yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2312yes—
566C4×C4⋊C4C2312yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C22⋊C4C2312yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2314yes—
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⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605#376C2312yes—
606#376C2314yes—
607#376C2314yes—
608#376C2314yes—
609#376C2312yes—
610C2×#95C2312yes—
611C2×#95C2314yes—
612C2×#95C2312yes—
613C2×#95C2314yes—
614C43C2312yes—
615C43C2311yescharacteristic
616C25C2412yes—
617C22×Q8C2411yescharacteristic
618C22×Q8C2412yes—
619C22×Q8C2411yescharacteristic
620C22×Q8C2412yes—
621C22×Q8C2412yes—
622C22×D4C2412yes—
623C22×D4C2414yes—
624C22×D4C2412yes—
625C22×D4C2411yescharacteristic
626C23×C4—44no—
627C23×C4—84no—
628C23×C4C2414yes—
629C23×C4C2414yes—
630C23×C4C2414yes—
631C23×C4C2414yes—
632C23×C4C2414yes—
633C23×C4C2414yes—
634C23×C4C2412yes—
635C23×C4C2414yes—
636C23×C4C2414yes—
637C23×C4C2412yes—
638C4⋊Q8—28no—
639#126—216no—
640#126—216no—
641#126—216no—
642#126—216no—
643#125—44no—
644#125—84no—
645#125—84no—
646#124—28no—
647#124—24no—
648#124#41116yes—
649#123—216no—
650#123—216no—
651#123—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—44no—
656C22⋊Q8—84no—
657C22⋊Q8—84no—
658#120—216no—
659#120—28no—
660C4×Q8—28no—
661C4×Q8—28no—
662C4×Q8—28no—
663C4×Q8—42no—
664C4×Q8—42no—
665C4×Q8—82no—
666C4×Q8—82no—
667C4×Q8—82no—
668C4×Q8—82no—
669C4×D4—28no—
670C4×D4—28no—
671C4×D4—216no—
672C4×D4—216no—
673C4×D4—42no—
674C4×D4—44no—
675C4×D4—84no—
676C4×D4—82no—
677C4×D4—84no—
678C4×D4—82no—
679#117—216no—
680#117—216no—
681#117—216no—
682#117—84no—
683#117—84no—
684C2×C4⋊C4—48no—
685C2×C4⋊C4—84no—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C22⋊C4—216no—
740C2×C22⋊C4—216no—
741C2×C22⋊C4—84no—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C42—84no—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780C2×C42C2411yescharacteristic
781C2×C42C2412yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2411yescharacteristic
786C2×C42C2414yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2412yes—
795C2×C42C2412yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
798C2×C42C2411yescharacteristic
799C2×C42C2412yes—
800C2×C42C2412yes—
801C2×C42C2412yes—
802#95C2411yescharacteristic
803#95C2412yes—
804#95C2414yes—
805#95C2414yes—
806#95C2412yes—
807#95C2412yes—
808#95C2414yes—
809#95C2412yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2412yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2412yes—
828#95C2414yes—
829#95C2412yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
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#95C2411yescharacteristic
852#95C2412yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2412yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865C24—28no—
866C24—24no—
867C24—44no—
868C24—42no—
869C24—42no—
870C24C2514yes—
871C24C2512yes—
872C2×Q8—24no—
873C2×Q8—24no—
874C2×Q8—22no—
875C2×Q8—41no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—42no—
879C2×Q8—42no—
880C2×Q8—41no—
881C2×Q8—41no—
882C2×Q8—42no—
883C2×Q8—44no—
884C2×Q8C2×#4118yes—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—41no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—44no—
892C2×D4—41no—
893C2×D4—42no—
894C2×D4C2×#4118yes—
895C2×D42−1+414yes—
896C22×C4—28no—
897C22×C4—28no—
898C22×C4—28no—
899C22×C4—28no—
900C22×C4—28no—
901C22×C4—28no—
902C22×C4—28no—
903C22×C4—28no—
904C22×C4—24no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—42no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—816no—
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2514yes—
933C22×C4C2512yes—
934C22×C4C2511yescharacteristic
935C22×C4C2514yes—
936C22×C4C2512yes—
937C22×C4C2514yes—
938C22×C4C2512yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2512yes—
942C22×C4C2512yes—
943C22×C4C2514yes—
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C4⋊C4—24no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—28no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—24no—
953C4⋊C4—28no—
954C4⋊C4—28no—
955C4⋊C4—28no—
956C4⋊C4—28no—
957C4⋊C4—24no—
958C4⋊C4—24no—
959C4⋊C4—28no—
960C4⋊C4—28no—
961C4⋊C4—28no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—28no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—44no—
971C4⋊C4—42no—
972C4⋊C4—44no—
973C4⋊C4—42no—
974C4⋊C4—44no—
975C4⋊C4—44no—
976C4⋊C4—44no—
977C4⋊C4—44no—
978C4⋊C4—41no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—41no—
987C4⋊C4—42no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—42no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—24no—
1008C22⋊C4—28no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—42no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—42no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4C2×#41116yes—
1031C22⋊C4C2×#41116yes—
1032C42—28no—
1033C42—28no—
1034C42—28no—
1035C42—28no—
1036C42—24no—
1037C42—24no—
1038C42—24no—
1039C42—22no—
1040C42—22no—
1041C42—24no—
1042C42—44no—
1043C42—44no—
1044C42—44no—
1045C42—44no—
1046C42—41no—
1047C42—42no—
1048C42—42no—
1049C42—44no—
1050C42—44no—
1051C42—44no—
1052C42—42no—
1053C42—42no—
1054C42—44no—
1055C42—42no—
1056C42—42no—
1057C42C2×#4118yes—
1058C23—24no—
1059C23—24no—
1060C23—24no—
1061C23—22no—
1062C23—24no—
1063C23—24no—
1064C23—24no—
1065C23—24no—
1066C23—24no—
1067C23—22no—
1068C23—416no—
1069C23—48no—
1070C23—88no—
1071C23—84no—
1072C23—84no—
1073C23C22×#4118yes—
1074C23C2×2−1+414yes—
1075C23C2611yescharacteristic
1076Q8—48no—
1077Q8—44no—
1078Q8—48no—
1079Q8—82no—
1080Q8—162no—
1081D4—48no—
1082D4—44no—
1083D4—416no—
1084D4—48no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—416no—
1139C2×C4—416no—
1140C2×C4—48no—
1141C2×C4—88no—
1142C2×C4—88no—
1143C2×C4—88no—
1144C2×C4—84no—
1145C2×C4—88no—
1146C2×C4—88no—
1147C2×C4—164no—
1148C2×C4C22×#4114yes—
1149C2×C4C22×#4114yes—
1150C2×C4C22×#4114yes—
1151C2×C4C22×#4118yes—
1152C2×C4C2×2−1+412yes—
1153C2×C4#58512yes—
1154C22—28no—
1155C22—28no—
1156C22—28no—
1157C22—24no—
1158C22—28no—
1159C22—44no—
1160C22—42no—
1161C22—44no—
1162C22—44no—
1163C22—44no—
1164C22—44no—
1165C22—42no—
1166C22—816no—
1167C22C23×#4112yes—
1168C22C22×2−1+411yescharacteristic
1169C22C2×#58511yescharacteristic
1170C22H(7,𝔽2)12yes—
1171C222−1+611yescharacteristic
1172C4—24no—
1173C4—22no—
1174C4—28no—
1175C4—24no—
1176C4—22no—
1177C4—24no—
1178C4—42no—
1179C4—42no—
1180C4—44no—
1181C4—44no—
1182C4—44no—
1183C4—42no—
1184C4—42no—
1185C4—44no—
1186C4—44no—
1187C4—44no—
1188C4—44no—
1189C4—42no—
1190C4—44no—
1191C4—42no—
1192C4—41no—
1193C2—44no—
1194C2—48no—
1195C2#41211yescharacteristic
1196C2#6284712yes—
1197C2#6290411yescharacteristic
1198C2#6300012yes—
1199C2#6304611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2679C22
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. #59914C2semidirect
4. #59558C2semidirect
6. #52267C2semidirect
7. #44727C2semidirect
8. #43803C2semidirect
9. #43728C2semidirect
10. #43408C2semidirect
11. #43349C2semidirect
12. #39702C2semidirect
13. #39214C2semidirect
14. #38788C2semidirect
15. #38647C2semidirect
16. #38541C2semidirect
17. #38472C2semidirect
18. #36394C2semidirect
19. #36338C2semidirect
20. #36072C2semidirect
21. #35946C2semidirect
22. #34322C2semidirect
23. #34296C2semidirect
26. #2864C22semidirect
27. #2863C22semidirect
28. #2851C22semidirect
29. #2848C22semidirect
30. #2811C22semidirect
31. #2809C22semidirect
32. #2807C22semidirect
33. #2807C22semidirect
34. #2806C22semidirect
35. #2805C22semidirect
38. #2802C22semidirect
39. #2790C22semidirect
40. #2788C22semidirect
41. #2787C22semidirect
42. #2787C22semidirect
48. #2767C22semidirect
49. #2767C22semidirect
50. #2763C22semidirect
52. #2745C22semidirect
53. #2739C22semidirect
56. #2729C22semidirect
57. #2729C22semidirect
60. #2722C22semidirect
61. #2720C22semidirect
62. #2719C22semidirect
64. #2698C22semidirect
70. #2666C22semidirect
71. #2655C22semidirect
72. #2655C22semidirect
73. #2652C22semidirect
75. #2612C22semidirect
76. #2612C22semidirect
77. #2611C22semidirect
79. #2606C22semidirect
80. #2599C22semidirect
81. #2599C22semidirect
82. #2589C22semidirect
83. #2589C22semidirect
84. #2588C22semidirect
85. #2587C22semidirect
86. #2583C22semidirect
87. #2581C22semidirect
89. #2577C22semidirect
91. #2575C22semidirect
92. #2575C22semidirect
93. #2575C22semidirect
94. #2574C22semidirect
95. #2571C22semidirect
96. #2569C22semidirect
97. #2565C22semidirect
99. #2556C22semidirect
100. #2556C22semidirect
106. #2530C22semidirect
107. #2530C22semidirect
108. #2530C22semidirect
109. #2528C22semidirect
110. #2528C22semidirect
111. #2527C22semidirect
112. #2527C22semidirect
113. #2517C22semidirect
114. #2508C22semidirect
115. #2508C22semidirect
116. #2505C22semidirect
117. #2505C22semidirect
118. #2496C22semidirect
119. #2494C22semidirect
120. #2493C22semidirect
121. #2489C22semidirect
123. #2482C22semidirect
124. #2480C22semidirect
125. #2480C22semidirect
126. #2478C22semidirect
128. #2475C22semidirect
129. #2475C22semidirect
130. #2473C22semidirect
136. #2465C22semidirect
137. #2462C22semidirect
140. #2453C22semidirect
145. #2442C22semidirect
146. #2438C22semidirect
147. #2437C22semidirect
148. #2437C22semidirect
149. #2423C22semidirect
150. #2421C22semidirect
154. #2402C22semidirect
157. #2396C22semidirect
158. #2396C22semidirect
159. #2373C22semidirect
160. #2373C22semidirect
161. #2373C22semidirect
162. #2373C22semidirect
164. #2371C22semidirect
165. #2368C22semidirect
166. #2368C22semidirect
169. #2365C22semidirect
170. #2360C22semidirect
171. #2360C22semidirect
177. #2356C22semidirect
178. #2355C22semidirect
180. #2351C22semidirect
181. #2351C22semidirect
185. #2346C22semidirect
186. #2343C22semidirect
187. #2343C22semidirect
188. #2342C22semidirect
189. #2342C22semidirect
192. #2334C22semidirect
193. #2334C22semidirect
194. #2334C22semidirect
195. #2334C22semidirect
196. #2329C22semidirect
197. #2323C22semidirect
199. C4×C4⋊Q8C22semidirect
203. C4×C22⋊Q8C22semidirect
207. #2296C22semidirect
208. #2295C22semidirect
209. #2295C22semidirect
214. C2×#385C22semidirect
216. #2274C22semidirect
217. C42×Q8C22semidirect
218. C2×C4×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#599282
#599142
#598362
#595582
#523012
#522672
#447272
#438032
#437282
#434082
#433492
#397022
#392142
#387882
#386472
#385412
#384722
#363942
#363382
#360722
#359462
#343222
#342962