Finite Group Databasebeta

← #7689372

Subgroups — #7689372

Order 512.

5241 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59952C213yesmaximal, complemented
2#59767C213yesmaximal, complemented
3#59640C213yesmaximal, complemented
4#59236C213yesmaximal, complemented
5#59232C213yesmaximal, complemented
6#45408C213yesmaximal, complemented
7#45133C213yesmaximal, complemented
8#45009C213yesmaximal, complemented
9#44909C213yesmaximal, complemented
10#39500C213yesmaximal, complemented
11#38936C213yesmaximal, complemented
12#38290C213yesmaximal, complemented
13#38286C213yesmaximal, complemented
14#36474C211yesmaximal, characteristic, complemented
15#36467C211yesmaximal, characteristic, complemented
16#36457C211yesmaximal, characteristic, complemented
17#36430C211yesmaximal, characteristic, complemented
18#36430C211yesmaximal, characteristic, complemented
19#36373C213yesmaximal, complemented
20#36195C213yesmaximal, complemented
21#36049C211yesmaximal, characteristic, complemented
22#36029C211yesmaximal, characteristic, complemented
23#36018C211yesmaximal, characteristic, complemented
24#35948C211yesmaximal, characteristic, complemented
25#34800C213yesmaximal, complemented
26#34312C211yesmaximal, characteristic, complemented
27#34263C211yesmaximal, characteristic, complemented
28#34262C211yesmaximal, characteristic, complemented
29#34197C211yesmaximal, characteristic, complemented
30C4×#550C211yesmaximal, characteristic, complemented
31#34125C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44#2862C2213yes—
45#2861C2213yes—
46#2858C2213yes—
47#2850C2213yes—
48#2850C2213yes—
49#2808C2216yes—
50#2808C2216yes—
51#2803C2216yes—
52#2803C2216yes—
53#2785C2216yes—
54#2781C2216yes—
55#2775C2216yes—
56#2756C2216yes—
57#2756C2216yes—
58#2737C2216yes—
59#2733C2216yes—
60#2733C2216yes—
61#2699C2216yes—
62#2686C2216yes—
63#2641C2213yes—
64#2640C2213yes—
65#2619C2213yes—
66#2619C2213yes—
67#2610C2216yes—
68#2610C2216yes—
69#2593C2216yes—
70#2592C2213yes—
71#2592C2213yes—
72#2572C2216yes—
73#2572C2216yes—
74#2567C2213yes—
75#2563C2213yes—
76#2562C2213yes—
77#2562C2213yes—
78#2555C2216yes—
79#2550C2213yes—
80#2550C2213yes—
81#2550C2213yes—
82#2550C2213yes—
83#2548C2213yes—
84#2548C2213yes—
85#2548C2213yes—
86#2547C2213yes—
87#2546C2213yes—
88#2544C2213yes—
89#2544C2213yes—
90#2541C2213yes—
91#2536C2213yes—
92#2535C2213yes—
93#2535C2213yes—
94#2535C2213yes—
95#2532C2216yes—
96#2532C2213yes—
97#2532C2211yescharacteristic
98#2531C2216yes—
99#2529C2216yes—
100#2526C2213yes—
101#2526C2213yes—
102#2518C2213yes—
103#2518C2213yes—
104#2513C2213yes—
105#2508C2213yes—
106#2500C2213yes—
107#2500C2216yes—
108#2497C2213yes—
109#2492C2213yes—
110#2492C2213yes—
111#2492C2213yes—
112#2491C2213yes—
113#2491C2213yes—
114#2491C2213yes—
115#2491C2213yes—
116#2491C2213yes—
117#2491C2213yes—
118#2491C2213yes—
119#2491C2213yes—
120#2491C2216yes—
121#2491C2213yes—
122#2491C2213yes—
123#2490C2213yes—
124#2490C2213yes—
125#2490C2213yes—
126#2489C2213yes—
127#2485C2213yes—
128#2476C2216yes—
129#2474C2216yes—
130#2459C2216yes—
131#2459C2213yes—
132#2459C2216yes—
133#2459C2216yes—
134#2459C2216yes—
135#2459C2213yes—
136#2439C2213yes—
137#2428C2213yes—
138#2428C2213yes—
139#2428C2213yes—
140#2428C2213yes—
141#2427C2213yes—
142#2427C2213yes—
143#2426C2213yes—
144#2426C2213yes—
145#2420C2216yes—
146#2416C2213yes—
147#2416C2213yes—
148#2415C2213yes—
149#2415C2213yes—
150#2414C2213yes—
151#2414C2213yes—
152#2414C2213yes—
153#2414C2213yes—
154#2414C2213yes—
155#2398C2213yes—
156#2398C2213yes—
157#2392C2213yes—
158#2392C2213yes—
159#2372C2216yes—
160#2372C2216yes—
161#2367C2213yes—
162#2366C2213yes—
163#2363C2213yes—
164#2363C2216yes—
165#2363C2213yes—
166#2363C2213yes—
167#2360C2213yes—
168#2357C2213yes—
169#2357C2213yes—
170#2357C2213yes—
171#2357C2213yes—
172#2357C2213yes—
173#2356C2213yes—
174#2355C2213yes—
175#2354C2213yes—
176#2354C2213yes—
177#2352C2213yes—
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184#2347C2213yes—
185#2347C2213yes—
186#2347C2213yes—
187#2346C2213yes—
188#2346C2213yes—
189#2346C2213yes—
190#2345C2213yes—
191#2344C2213yes—
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2324C2213yes—
205#2323C2213yes—
206#2320C2213yes—
207#2319C2213yes—
208#2319C2213yes—
209#2319C2213yes—
210#2314C2213yes—
211#2314C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#127C2213yes—
214C4×#124C2213yes—
215C4×#124C2213yes—
216C4×#124C2213yes—
217C4×#121C2213yes—
218C4×#121C2213yes—
219C4×#121C2213yes—
220C4×#121C2213yes—
221#2298C2213yes—
222#2298C2213yes—
223#2295C2213yes—
224#2293C2213yes—
225#2293C2213yes—
226#2293C2213yes—
227#2293C2213yes—
228#2283C2213yes—
229#2283C2213yes—
230#2283C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242Q82—44no—
243#557—44no—
244#550—28no—
245#550—44no—
246#550—44no—
247#548—28no—
248#548—44no—
249#548—44no—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×#127C2313yes—
256C2×#127C2313yes—
257C2×#127C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2316yes—
264C2×#124C2316yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#124C2316yes—
268C2×#124C2316yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2313yes—
276C2×#121C2313yes—
277C2×#121C2316yes—
278C2×#121C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2316yes—
285#520—28no—
286#519—28no—
287C4×#41—28no—
288C4×#41—28no—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
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×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
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×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2316yes—
319C2×#117C2313yes—
320C2×#117C2313yes—
321C2×#117C2313yes—
322C2×#117C2313yes—
323C2×#117C2313yes—
324C2×#117C2313yes—
325C2×#117C2313yes—
326C2×#117C2316yes—
327C22×C4⋊C4C2313yes—
328C22×C42C2313yes—
329C22×C42C2313yes—
330#400C2313yes—
331#400C2316yes—
332#400C2313yes—
333#400C2313yes—
334#400C2311yescharacteristic
335#398C2316yes—
336#398C2311yescharacteristic
337#398C2313yes—
338#398C2316yes—
339#397C2316yes—
340#397C2316yes—
341#397C2313yes—
342#397C2311yescharacteristic
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#396C2313yes—
350#396C2313yes—
351#396C2313yes—
352#396C2313yes—
353#395C2316yes—
354#395C2316yes—
355#394C2316yes—
356#394C2316yes—
357#394C2316yes—
358#394C2316yes—
359#394C2313yes—
360#394C2316yes—
361#394C2313yes—
362#394C2316yes—
363#394C2313yes—
364#394C2316yes—
365#394C2316yes—
366#394C2316yes—
367#394C2313yes—
368#394C2316yes—
369#394C2313yes—
370#394C2313yes—
371#394C2313yes—
372#394C2313yes—
373#394C2313yes—
374#394C2313yes—
375#394C2316yes—
376#394C2316yes—
377#394C2316yes—
378#393C2316yes—
379#393C2316yes—
380#393C2313yes—
381#393C2316yes—
382#393C2316yes—
383#393C2313yes—
384#393C2316yes—
385#393C2311yescharacteristic
386#393C2313yes—
387#392C2316yes—
388#392C2316yes—
389#392C2313yes—
390#392C2316yes—
391#392C2316yes—
392#392C2313yes—
393#392C2316yes—
394#391C2311yescharacteristic
395#391C2313yes—
396#391C2316yes—
397#391C2316yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2316yes—
405#391C2313yes—
406#391C2316yes—
407#391C2311yescharacteristic
408#390C2313yes—
409#390C2313yes—
410#390C2316yes—
411#390C2316yes—
412#390C2316yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2316yes—
432#390C2313yes—
433#390C2316yes—
434#390C2313yes—
435#390C2313yes—
436#390C2316yes—
437#390C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#388C2313yes—
459#388C2316yes—
460#388C2316yes—
461#388C2316yes—
462#388C2313yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2313yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2313yes—
471#388C2316yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2313yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2316yes—
484#388C2313yes—
485#388C2313yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2313yes—
491#388C2316yes—
492#388C2313yes—
493#388C2313yes—
494#388C2316yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2311yescharacteristic
500#388C2311yescharacteristic
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2311yescharacteristic
506#388C2311yescharacteristic
507#388C2311yescharacteristic
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2311yescharacteristic
520#386C2316yes—
521#386C2316yes—
522#386C2316yes—
523#386C2316yes—
524#386C2316yes—
525#386C2316yes—
526#386C2316yes—
527#386C2316yes—
528#386C2313yes—
529#386C2316yes—
530#386C2313yes—
531#386C2313yes—
532#386C2313yes—
533#385C2316yes—
534#384C2313yes—
535#384C2313yes—
536#383C2316yes—
537#383C2313yes—
538#383C2316yes—
539#383C2311yescharacteristic
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2316yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#381C2316yes—
551#381C2316yes—
552#381C2316yes—
553#381C2313yes—
554#381C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2316yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2316yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2311yescharacteristic
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2316yes—
601C4×C22⋊C4C2316yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2316yes—
621#376C2313yes—
622#376C2313yes—
623#376C2316yes—
624#376C2316yes—
625#376C2313yes—
626#376C2311yescharacteristic
627C43C2313yes—
628C43C2313yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2411yescharacteristic
644C22×Q8C2413yes—
645C22×Q8C2416yes—
646C22×Q8C2411yescharacteristic
647C22×D4C2413yes—
648C22×D4C2413yes—
649C22×D4C2413yes—
650C22×D4C2413yes—
651C22×D4C2416yes—
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2413yes—
656C22×D4C2413yes—
657C22×D4C2416yes—
658C22×D4C2416yes—
659C23×C4C2413yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2413yes—
664C23×C4C2416yes—
665C23×C4C2413yes—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C4⋊Q8—46no—
669C4⋊Q8—46no—
670C4⋊Q8—46no—
671C4⋊Q8—46no—
672C4⋊Q8—46no—
673#127—212no—
674#127—46no—
675#127—46no—
676#125—46no—
677#125—46no—
678#124—212no—
679#124—412no—
680#124—46no—
681#124—46no—
682#124—46no—
683#124—46no—
684#124—412no—
685#124—86no—
686#124—86no—
687C22⋊Q8—212no—
688C22⋊Q8—46no—
689C22⋊Q8—46no—
690#121—212no—
691#121—212no—
692#121—212no—
693#121—46no—
694#121—412no—
695#121—46no—
696#121—46no—
697#121—46no—
698#121—46no—
699#121—46no—
700#121—46no—
701#121—46no—
702#121—86no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—24no—
712C4×Q8—212no—
713C4×Q8—212no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8#4118yes—
717C4×Q8#4118yes—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—212no—
721C4×D4—212no—
722C4×D4—212no—
723C4×D4—212no—
724C4×D4—212no—
725C4×D4—212no—
726C4×D4—46no—
727C4×D4—46no—
728C4×D4—46no—
729C4×D4—46no—
730C4×D4—46no—
731C4×D4—46no—
732C4×D4—86no—
733#117—212no—
734#117—212no—
735#117—212no—
736#117—212no—
737#117—212no—
738#117—46no—
739#117—46no—
740#117—86no—
741C2×C4⋊C4—212no—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2416yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2416yes—
821C2×C22⋊C4C2416yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2416yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2416yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2416yes—
837C2×C42—212no—
838C2×C42—212no—
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2416yes—
846C2×C42C2413yes—
847C2×C42C2411yescharacteristic
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857C2×C42C2413yes—
858C2×C42C2416yes—
859C2×C42C2413yes—
860C2×C42C2413yes—
861C2×C42C2413yes—
862C2×C42C2413yes—
863C2×C42C2413yes—
864C2×C42C2413yes—
865C2×C42C2416yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2416yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2416yes—
892#95C2416yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2411yescharacteristic
897#95C2411yescharacteristic
898#95C2411yescharacteristic
899#95C2411yescharacteristic
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2416yes—
911#95C2416yes—
912#95C2413yes—
913#95C2416yes—
914#95C2413yes—
915#95C2416yes—
916#95C2411yescharacteristic
917#95C2416yes—
918#95C2416yes—
919#95C2411yescharacteristic
920#95C2411yescharacteristic
921#95C2416yes—
922#95C2413yes—
923#95C2413yes—
924C24C2511yescharacteristic
925C24C2513yes—
926C24C2513yes—
927C24C2513yes—
928#41—416no—
929#41—416no—
930#41—416no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—22no—
935C2×Q8—22no—
936C2×Q8—26no—
937C2×Q8—41no—
938C2×Q8—43no—
939C2×Q8—43no—
940C2×Q8—46no—
941C2×Q8—46no—
942C2×Q8—46no—
943C2×Q8—416no—
944C2×Q8C2×#4114yes—
945C2×Q8C2×#4114yes—
946C2×Q8H(5,𝔽2)14yes—
947C2×D4—26no—
948C2×D4—26no—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—26no—
955C2×D4—212no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—43no—
961C2×D4—43no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—46no—
967C2×D4—43no—
968C2×D4—46no—
969C2×D4—43no—
970C2×D4—43no—
971C2×D4—43no—
972C2×D4—43no—
973C2×D4—43no—
974C2×D4—43no—
975C2×D4—43no—
976C2×D4—43no—
977C2×D4—46no—
978C2×D4—46no—
979C2×D4—46no—
980C2×D4—46no—
981C2×D4—46no—
982C2×D4—46no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—26no—
989C22×C4—26no—
990C22×C4—26no—
991C22×C4—26no—
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—212no—
1001C22×C4—43no—
1002C22×C4—46no—
1003C22×C4—43no—
1004C22×C4—43no—
1005C22×C4—43no—
1006C22×C4—43no—
1007C22×C4—43no—
1008C22×C4—43no—
1009C22×C4—46no—
1010C22×C4C2511yescharacteristic
1011C22×C4C2513yes—
1012C22×C4C2511yescharacteristic
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2513yes—
1020C22×C4C2513yes—
1021C22×C4C2513yes—
1022C22×C4C2513yes—
1023C22×C4C2513yes—
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2513yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2511yescharacteristic
1030C22×C4C2511yescharacteristic
1031C22×C4C2513yes—
1032C22×C4C2513yes—
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C22×C4C2513yes—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—22no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—22no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—22no—
1054C4⋊C4—26no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—46no—
1060C4⋊C4—43no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—41no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—43no—
1071C4⋊C4—43no—
1072C4⋊C4—43no—
1073C4⋊C4—46no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4C2×#41112yes—
1077C4⋊C4C2×#41112yes—
1078C22⋊C4—26no—
1079C22⋊C4—22no—
1080C22⋊C4—26no—
1081C22⋊C4—212no—
1082C22⋊C4—212no—
1083C22⋊C4—26no—
1084C22⋊C4—22no—
1085C22⋊C4—26no—
1086C22⋊C4—26no—
1087C22⋊C4—26no—
1088C22⋊C4—212no—
1089C22⋊C4—26no—
1090C22⋊C4—26no—
1091C22⋊C4—26no—
1092C22⋊C4—26no—
1093C22⋊C4—22no—
1094C22⋊C4—22no—
1095C22⋊C4—26no—
1096C22⋊C4—22no—
1097C22⋊C4—26no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—46no—
1103C22⋊C4—43no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—46no—
1113C22⋊C4—46no—
1114C22⋊C4—46no—
1115C22⋊C4—43no—
1116C22⋊C4—46no—
1117C22⋊C4—46no—
1118C22⋊C4—43no—
1119C22⋊C4—46no—
1120C22⋊C4—46no—
1121C22⋊C4—46no—
1122C22⋊C4—43no—
1123C22⋊C4—46no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—46no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C42—22no—
1133C42—22no—
1134C42—26no—
1135C42—26no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—26no—
1140C42—212no—
1141C42—26no—
1142C42—26no—
1143C42—26no—
1144C42—26no—
1145C42—26no—
1146C42—22no—
1147C42—22no—
1148C42—26no—
1149C42—22no—
1150C42—43no—
1151C42—43no—
1152C42—46no—
1153C42—43no—
1154C42—43no—
1155C42—43no—
1156C42—46no—
1157C42—43no—
1158C42—43no—
1159C42—43no—
1160C42C2×#41112yes—
1161C42C2×#41112yes—
1162C23—21no—
1163C23—23no—
1164C23—23no—
1165C23—23no—
1166C23—23no—
1167C23—21no—
1168C23—23no—
1169C23—23no—
1170C23—23no—
1171C23—23no—
1172C23—21no—
1173C23—23no—
1174C23—21no—
1175C23—23no—
1176C23—23no—
1177C23—23no—
1178C23—23no—
1179C23—23no—
1180C23—23no—
1181C23—21no—
1182C23—21no—
1183C23—23no—
1184C23—23no—
1185C23—23no—
1186C23—21no—
1187C23—23no—
1188C23—23no—
1189C23—23no—
1190C23C2611yescharacteristic
1191Q8—44no—
1192Q8—412no—
1193Q8—86no—
1194Q8—166no—
1195Q8#555116yes—
1196D4—412no—
1197D4—412no—
1198D4—412no—
1199D4—412no—
1200D4—812no—
1201D4—86no—
1202D4—86no—
1203D4—86no—
1204D4—86no—
1205D4—86no—
1206D4—166no—
1207D4—166no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—23no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—23no—
1254C2×C4—21no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—21no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—23no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—23no—
1274C2×C4—23no—
1275C2×C4—23no—
1276C2×C4—23no—
1277C2×C4—23no—
1278C2×C4—21no—
1279C2×C4—412no—
1280C2×C4—412no—
1281C2×C4—412no—
1282C2×C4—412no—
1283C2×C4—412no—
1284C2×C4—86no—
1285C2×C4—86no—
1286C2×C4—812no—
1287C2×C4—86no—
1288C2×C4C22×#4112yes—
1289C2×C4C22×#4116yes—
1290C2×C4C22×#4116yes—
1291C2×C4C22×#4112yes—
1292C2×C4C22×#4116yes—
1293C2×C4C22×#4116yes—
1294C2×C4C2×H(5,𝔽2)16yes—
1295C2×C4#58512yes—
1296C2×C4#58512yes—
1297C2×C4#58512yes—
1298C22—43no—
1299C22—43no—
1300C22—43no—
1301C22—41no—
1302C22—43no—
1303C22—43no—
1304C22—43no—
1305C22—41no—
1306C22—41no—
1307C22—43no—
1308C22—43no—
1309C22—43no—
1310C22—43no—
1311C22—43no—
1312C22—41no—
1313C22—43no—
1314C22—43no—
1315C22—43no—
1316C22—41no—
1317C22—43no—
1318C22—41no—
1319C22—43no—
1320C22—43no—
1321C22—43no—
1322C22—41no—
1323C22—43no—
1324C22—43no—
1325C22—43no—
1326C22C23×#4111yescharacteristic
1327C22C23×#4111yescharacteristic
1328C22C22×H(5,𝔽2)11yescharacteristic
1329C22C2×#58511yescharacteristic
1330C22C2×#58511yescharacteristic
1331C22C2×#58511yescharacteristic
1332C22H(7,𝔽2)11yescharacteristic
1333C4—22no—
1334C4—26no—
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—22no—
1339C4—26no—
1340C4—43no—
1341C4—43no—
1342C4—41no—
1343C4—43no—
1344C4—43no—
1345C4—43no—
1346C4—41no—
1347C4—41no—
1348C4—43no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—43no—
1353C4—43no—
1354C4—43no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—43no—
1359C4C2×#555112yes—
1360C2—83no—
1361C2—83no—
1362C2—83no—
1363C2—81no—
1364C2C22×#55511yescharacteristic
1365C2#6279311yescharacteristic
1366C2#6281611yescharacteristic
1367C2#6292311yescharacteristic
1368C2#6300611yescharacteristic
1369C2#6301011yescharacteristic
1370C2#6302011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59952C2semidirect
2. #59767C2semidirect
3. #59640C2semidirect
4. #59236C2semidirect
5. #59232C2semidirect
6. #45408C2semidirect
7. #45133C2semidirect
8. #45009C2semidirect
9. #44909C2semidirect
10. #39500C2semidirect
11. #38936C2semidirect
12. #38290C2semidirect
13. #38286C2semidirect
14. #36474C2semidirect
15. #36467C2semidirect
16. #36457C2semidirect
17. #36430C2semidirect
18. #36430C2semidirect
19. #36373C2semidirect
20. #36195C2semidirect
21. #36049C2semidirect
22. #36029C2semidirect
23. #36018C2semidirect
24. #35948C2semidirect
25. #34800C2semidirect
26. #34312C2semidirect
27. #34263C2semidirect
28. #34262C2semidirect
29. #34197C2semidirect
30. C4×#550C2semidirect
31. #34125C2semidirect

Maximal subgroups

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

subgroupindex
#599522
#597672
#596402
#592362
#592322
#454082
#451332
#450092
#449092
#395002
#389362
#382902
#382862
#364742
#364672
#364572
#364302
#363732
#361952
#360492
#360292
#360182
#359482
#348002
#343122
#342632
#342622
#341972
C4×#5502
#341252