Finite Group Databasebeta

← #7687232

Subgroups — #7687232

Order 512.

4804 conjugacy classes of subgroups.

The subgroup lattice has 1265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59764C213yesmaximal, complemented
2#59507C213yesmaximal, complemented
3#59298C213yesmaximal, complemented
4#59295C213yesmaximal, complemented
5#59227C213yesmaximal, complemented
6#45132C213yesmaximal, complemented
7#45027C213yesmaximal, complemented
8#45007C213yesmaximal, complemented
9#44968C213yesmaximal, complemented
10#38274C213yesmaximal, complemented
11#38226C213yesmaximal, complemented
12#38074C213yesmaximal, complemented
13#37889C213yesmaximal, complemented
14#36585C211yesmaximal, characteristic, complemented
15#36584C211yesmaximal, characteristic, complemented
16#36433C211yesmaximal, characteristic
17#36433C211yesmaximal, characteristic
18#36431C211yesmaximal, characteristic, complemented
19#36391C213yesmaximal, complemented
20#36200C213yesmaximal, complemented
21#35971C211yesmaximal, characteristic, complemented
22#35898C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35816C211yesmaximal, characteristic, complemented
25#34808C213yesmaximal, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34295C211yesmaximal, characteristic
28#34263C211yesmaximal, characteristic, complemented
29#34197C211yesmaximal, characteristic, complemented
30#34129C211yesmaximal, characteristic, complemented
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2860C2213yes—
39#2859C2213yes—
40#2854C2213yes—
41#2854C2213yes—
42#2851C2213yes—
43#2787C2216yes—
44#2787C2216yes—
45#2781C2216yes—
46#2781C2216yes—
47#2779C2216yes—
48#2779C2216yes—
49#2765C2216yes—
50#2751C2216yes—
51#2750C2216yes—
52#2745C2216yes—
53#2743C2216yes—
54#2707C2216yes—
55#2695C2216yes—
56#2687C2216yes—
57#2647C2213yes—
58#2647C2213yes—
59#2644C2213yes—
60#2629C2213yes—
61#2609C2216yes—
62#2580C2213yes—
63#2575C2216yes—
64#2571C2213yes—
65#2571C2213yes—
66#2571C2213yes—
67#2570C2213yes—
68#2570C2213yes—
69#2566C2213yes—
70#2566C2213yes—
71#2562C2216yes—
72#2558C2216yes—
73#2553C2216yes—
74#2552C2213yes—
75#2538C2213yes—
76#2533C2213yes—
77#2532C2213yes—
78#2529C2216yes—
79#2529C2216yes—
80#2529C2213yes—
81#2528C2213yes—
82#2528C2216yes—
83#2525C2213yes—
84#2524C2211yescharacteristic
85#2520C2213yes—
86#2519C2213yes—
87#2515C2216yes—
88#2513C2213yes—
89#2513C2213yes—
90#2513C2213yes—
91#2513C2213yes—
92#2512C2213yes—
93#2512C2213yes—
94#2509C2213yes—
95#2509C2213yes—
96#2509C2213yes—
97#2509C2213yes—
98#2509C2213yes—
99#2509C2213yes—
100#2508C2213yes—
101#2508C2213yes—
102#2507C2213yes—
103#2507C2213yes—
104#2506C2213yes—
105#2506C2213yes—
106#2500C2213yes—
107#2500C2213yes—
108#2498C2213yes—
109#2497C2213yes—
110#2496C2213yes—
111#2494C2213yes—
112#2494C2213yes—
113#2494C2213yes—
114#2494C2213yes—
115#2493C2213yes—
116#2489C2216yes—
117#2488C2213yes—
118#2485C2213yes—
119#2485C2213yes—
120#2484C2213yes—
121#2481C2216yes—
122#2481C2213yes—
123#2479C2216yes—
124#2477C2216yes—
125#2475C2216yes—
126#2473C2213yes—
127#2470C2216yes—
128#2454C2213yes—
129#2454C2213yes—
130#2452C2213yes—
131#2452C2213yes—
132#2445C2213yes—
133#2445C2213yes—
134#2445C2213yes—
135#2445C2213yes—
136#2442C2213yes—
137#2441C2213yes—
138#2440C2213yes—
139#2439C2213yes—
140#2438C2213yes—
141#2422C2213yes—
142#2422C2213yes—
143#2420C2213yes—
144#2420C2213yes—
145#2419C2216yes—
146#2415C2216yes—
147#2413C2216yes—
148#2413C2213yes—
149#2402C2213yes—
150#2402C2213yes—
151#2401C2213yes—
152#2396C2213yes—
153#2373C2216yes—
154#2370C2213yes—
155#2370C2213yes—
156#2369C2213yes—
157#2366C2213yes—
158#2363C2213yes—
159#2361C2213yes—
160#2359C2216yes—
161#2357C2213yes—
162#2357C2213yes—
163#2357C2213yes—
164#2355C2213yes—
165#2354C2213yes—
166#2354C2213yes—
167#2354C2213yes—
168#2352C2213yes—
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185#2349C2213yes—
186#2349C2213yes—
187D4×C4⋊C4C2213yes—
188D4×C4⋊C4C2213yes—
189#2346C2213yes—
190#2346C2213yes—
191#2346C2216yes—
192#2346C2213yes—
193#2346C2213yes—
194#2345C2213yes—
195#2344C2213yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2331C2213yes—
205#2330C2213yes—
206#2328C2213yes—
207#2324C2213yes—
208#2319C2213yes—
209#2319C2213yes—
210#2319C2213yes—
211#2314C2213yes—
212C4×#125C2213yes—
213C4×#125C2213yes—
214C4×#126C2213yes—
215C4×C22⋊Q8C2213yes—
216C4×#123C2213yes—
217C4×#123C2213yes—
218C4×#121C2213yes—
219#2298C2213yes—
220#2296C2213yes—
221#2296C2213yes—
222#2295C2213yes—
223#2293C2213yes—
224#2293C2213yes—
225#2293C2213yes—
226#2290C2213yes—
227#2285C2213yes—
228#2285C2213yes—
229#2283C2213yes—
230#2283C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C4×#117C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#557—28no—
241#550—28no—
242C2×C4⋊Q8C2313yes—
243C2×#127C2313yes—
244C2×#126C2313yes—
245C2×#126C2316yes—
246C2×#125C2313yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2316yes—
250C2×#123C2316yes—
251C2×#123C2313yes—
252C2×#123C2313yes—
253C2×#123C2316yes—
254C2×C22⋊Q8C2313yes—
255C2×C22⋊Q8C2316yes—
256C2×#121C2313yes—
257C2×#121C2313yes—
258#520—28no—
259C4×#41—28no—
260C4×#41—28no—
261C4×#41—28no—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×C4×D4C2313yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2316yes—
286C2×#117C2313yes—
287C2×#117C2313yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C2×#117C2316yes—
291C2×#117C2313yes—
292C2×#117C2313yes—
293C2×#117C2316yes—
294C22×C4⋊C4C2313yes—
295C22×C4⋊C4C2313yes—
296C22×C4⋊C4C2313yes—
297C22×C42C2313yes—
298C22×C42C2313yes—
299C22×C42C2313yes—
300#401C2313yes—
301#401C2316yes—
302#400C2313yes—
303#400C2316yes—
304#400C2313yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2313yes—
310#400C2313yes—
311#400C2316yes—
312#400C2316yes—
313#400C2311yescharacteristic
314#400C2313yes—
315#400C2313yes—
316#400C2311yescharacteristic
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#399C2316yes—
322#399C2313yes—
323#398C2313yes—
324#398C2316yes—
325#398C2313yes—
326#398C2313yes—
327#398C2316yes—
328#398C2313yes—
329#398C2316yes—
330#398C2316yes—
331#398C2311yescharacteristic
332#398C2311yescharacteristic
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#397C2316yes—
338#397C2313yes—
339#397C2316yes—
340#397C2316yes—
341#397C2313yes—
342#397C2313yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#396C2313yes—
348#396C2316yes—
349#396C2316yes—
350#396C2316yes—
351#396C2313yes—
352#396C2316yes—
353#396C2316yes—
354#396C2313yes—
355#395C2313yes—
356#394C2316yes—
357#394C2316yes—
358#394C2316yes—
359#394C2316yes—
360#394C2316yes—
361#394C2316yes—
362#393C2316yes—
363#393C2313yes—
364#391C2313yes—
365#391C2316yes—
366#391C2313yes—
367#391C2313yes—
368#390C2313yes—
369#390C2313yes—
370#390C2313yes—
371#390C2313yes—
372#390C2313yes—
373#390C2313yes—
374#390C2313yes—
375#390C2313yes—
376#390C2313yes—
377#390C2316yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2316yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2316yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2313yes—
419#389C2316yes—
420#389C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#388C2313yes—
428#388C2313yes—
429#388C2313yes—
430#388C2316yes—
431#388C2316yes—
432#388C2316yes—
433#388C2316yes—
434#388C2316yes—
435#388C2313yes—
436#388C2316yes—
437#388C2316yes—
438#388C2316yes—
439#388C2316yes—
440#388C2313yes—
441#388C2313yes—
442#388C2316yes—
443#388C2316yes—
444#388C2313yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2316yes—
449#388C2316yes—
450#388C2316yes—
451#388C2316yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#387C2313yes—
459#387C2313yes—
460#387C2313yes—
461#387C2313yes—
462#387C2316yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2316yes—
469#387C2316yes—
470#387C2316yes—
471#387C2316yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2313yes—
477#387C2316yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2311yescharacteristic
484#387C2311yescharacteristic
485#387C2313yes—
486#387C2313yes—
487#387C2311yescharacteristic
488#387C2311yescharacteristic
489#387C2311yescharacteristic
490#387C2311yescharacteristic
491#386C2316yes—
492#386C2313yes—
493#386C2316yes—
494#386C2316yes—
495#386C2316yes—
496#386C2316yes—
497#386C2313yes—
498#386C2313yes—
499#386C2313yes—
500#385C2313yes—
501#385C2316yes—
502#385C2316yes—
503#385C2316yes—
504#385C2316yes—
505#385C2313yes—
506#385C2313yes—
507#385C2316yes—
508#385C2316yes—
509#385C2316yes—
510#385C2316yes—
511#385C2313yes—
512#385C2313yes—
513#385C2313yes—
514#384C2313yes—
515#384C2313yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#383C2311yescharacteristic
522#383C2313yes—
523#383C2311yescharacteristic
524#382C2311yescharacteristic
525#382C2313yes—
526#382C2313yes—
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2316yes—
532#382C2316yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2316yes—
538#382C2313yes—
539#381C2316yes—
540#381C2316yes—
541#381C2313yes—
542#381C2313yes—
543#381C2313yes—
544#381C2313yes—
545#380C2313yes—
546#380C2316yes—
547#380C2316yes—
548#380C2316yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2316yes—
560#380C2316yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2316yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2311yescharacteristic
599C4×C4⋊C4C2311yescharacteristic
600C4×C4⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2316yes—
619#376C2313yes—
620C2×#95C2313yes—
621C2×#95C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41#4118yes—
630C22×Q8C2413yes—
631C22×Q8C2411yescharacteristic
632C22×D4C2413yes—
633C22×D4C2413yes—
634C22×D4C2416yes—
635C22×D4C2413yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2416yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C23×C4C2413yes—
645C4⋊Q8—212no—
646#127—212no—
647#126—46no—
648#126—412no—
649#125—212no—
650#125—212no—
651#125—46no—
652#125—86no—
653#123—46no—
654#123—412no—
655#123—46no—
656#123—86no—
657C22⋊Q8—46no—
658C22⋊Q8—86no—
659#121—212no—
660#121—212no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—212no—
674C4×Q8#4118yes—
675C4×D4—212no—
676C4×D4—212no—
677C4×D4—212no—
678C4×D4—212no—
679C4×D4—212no—
680C4×D4—212no—
681C4×D4—212no—
682C4×D4—212no—
683C4×D4—212no—
684C4×D4—86no—
685#117—212no—
686#117—212no—
687#117—212no—
688#117—212no—
689#117—412no—
690#117—46no—
691#117—46no—
692#117—86no—
693C2×C4⋊C4—212no—
694C2×C4⋊C4—46no—
695C2×C4⋊C4—46no—
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2416yes—
757C2×C22⋊C4C2416yes—
758C2×C22⋊C4C2416yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2416yes—
767C2×C22⋊C4C2416yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2416yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2416yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2413yes—
786C2×C42—212no—
787C2×C42—212no—
788C2×C42—212no—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2416yes—
816C2×C42C2416yes—
817C2×C42C2416yes—
818C2×C42C2413yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2416yes—
849#95C2416yes—
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2416yes—
864#95C2416yes—
865#95C2411yescharacteristic
866#95C2416yes—
867#95C2416yes—
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2413yes—
871#95C2411yescharacteristic
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2416yes—
876#95C2416yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2416yes—
885#95C2416yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2416yes—
890C24C2513yes—
891C24C2513yes—
892#41—232no—
893#41—416no—
894C2×Q8—26no—
895C2×Q8—43no—
896C2×Q8—43no—
897C2×Q8C2×#4114yes—
898C2×Q8C2×#4114yes—
899C2×Q82−1+414yes—
900C2×D4—26no—
901C2×D4—212no—
902C2×D4—26no—
903C2×D4—26no—
904C2×D4—26no—
905C2×D4—26no—
906C2×D4—26no—
907C2×D4—46no—
908C2×D4—46no—
909C2×D4—43no—
910C2×D4—43no—
911C2×D4C2×#41112yes—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—26no—
924C22×C4—26no—
925C22×C4—212no—
926C22×C4—43no—
927C22×C4—43no—
928C22×C4—43no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4—43no—
932C22×C4—46no—
933C22×C4—43no—
934C22×C4—46no—
935C22×C4—43no—
936C22×C4—43no—
937C22×C4—43no—
938C22×C4C2×#41112yes—
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2513yes—
946C22×C4C2511yescharacteristic
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2513yes—
951C22×C4C2511yescharacteristic
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2513yes—
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2513yes—
960C22×C4C2513yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2513yes—
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2513yes—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—22no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—212no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—26no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—46no—
1005C4⋊C4—46no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—46no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—46no—
1014C4⋊C4—43no—
1015C4⋊C4—46no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—46no—
1026C4⋊C4C2×#41112yes—
1027C22⋊C4—212no—
1028C22⋊C4—212no—
1029C22⋊C4—26no—
1030C22⋊C4—26no—
1031C22⋊C4—212no—
1032C22⋊C4—26no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—26no—
1037C22⋊C4—26no—
1038C22⋊C4—43no—
1039C22⋊C4—46no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—46no—
1043C22⋊C4—46no—
1044C22⋊C4—43no—
1045C22⋊C4—43no—
1046C22⋊C4—43no—
1047C22⋊C4—46no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4—46no—
1052C22⋊C4—46no—
1053C22⋊C4—43no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—46no—
1057C22⋊C4—46no—
1058C42—22no—
1059C42—22no—
1060C42—22no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42—26no—
1074C42—26no—
1075C42—26no—
1076C42—26no—
1077C42—22no—
1078C42—22no—
1079C42—46no—
1080C42—43no—
1081C42—43no—
1082C42—43no—
1083C42—43no—
1084C42—43no—
1085C42—46no—
1086C42—46no—
1087C42C2×#41112yes—
1088C23—23no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23—23no—
1096C23—23no—
1097C23—23no—
1098C23—23no—
1099C23—23no—
1100C23—23no—
1101C23C22×#4116yes—
1102C23C2611yescharacteristic
1103Q8—86no—
1104Q8#552116yes—
1105D4—224no—
1106D4—412no—
1107D4—812no—
1108D4—86no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—224no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—412no—
1189C2×C4—412no—
1190C2×C4—412no—
1191C2×C4—412no—
1192C2×C4—812no—
1193C2×C4—86no—
1194C2×C4—86no—
1195C2×C4—86no—
1196C2×C4C22×#4112yes—
1197C2×C4C22×#4112yes—
1198C2×C4C22×#4116yes—
1199C2×C4C22×#4116yes—
1200C2×C4C22×#4116yes—
1201C2×C4C2×2−1+416yes—
1202C2×C4#58512yes—
1203C2×C4#58512yes—
1204C2×C4#58512yes—
1205C22—26no—
1206C22—26no—
1207C22—26no—
1208C22—43no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22—43no—
1213C22—43no—
1214C22—43no—
1215C22—43no—
1216C22—43no—
1217C22—43no—
1218C22—43no—
1219C22C23×#4111yescharacteristic
1220C22C23×#4111yescharacteristic
1221C22C22×2−1+411yescharacteristic
1222C22C2×#58511yescharacteristic
1223C22C2×#58511yescharacteristic
1224C22C2×#58511yescharacteristic
1225C22H(7,𝔽2)11yescharacteristic
1226C4—26no—
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—43no—
1233C4—41no—
1234C4—43no—
1235C4—41no—
1236C4—43no—
1237C4—43no—
1238C4—41no—
1239C4—43no—
1240C4—41no—
1241C4—43no—
1242C4—41no—
1243C4—41no—
1244C4—43no—
1245C4—43no—
1246C4—43no—
1247C4—43no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—43no—
1252C4—43no—
1253C4—41no—
1254C4C2×#552112yes—
1255C2—46no—
1256C2—83no—
1257C2C22×#55211yescharacteristic
1258C2#6279311yescharacteristic
1259C2#6281611yescharacteristic
1260C2#6295211yescharacteristic
1261C2#6299411yescharacteristic
1262C2#6300811yescharacteristic
1263C2#6303311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59764C2semidirect
2. #59507C2semidirect
3. #59298C2semidirect
4. #59295C2semidirect
5. #59227C2semidirect
6. #45132C2semidirect
7. #45027C2semidirect
8. #45007C2semidirect
9. #44968C2semidirect
10. #38274C2semidirect
11. #38226C2semidirect
12. #38074C2semidirect
13. #37889C2semidirect
14. #36585C2semidirect
15. #36584C2semidirect
18. #36431C2semidirect
19. #36391C2semidirect
20. #36200C2semidirect
21. #35971C2semidirect
22. #35898C2semidirect
23. #35868C2semidirect
24. #35816C2semidirect
25. #34808C2semidirect
26. #34336C2semidirect
28. #34263C2semidirect
29. #34197C2semidirect
30. #34129C2semidirect
31. C4⋊C4×#41C2semidirect

Maximal subgroups

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

subgroupindex
#597642
#595072
#592982
#592952
#592272
#451322
#450272
#450072
#449682
#382742
#382262
#380742
#378892
#365852
#365842
#364332
#364312
#363912
#362002
#359712
#358982
#358682
#358162
#348082
#343362
#342952
#342632
#341972
#341292
C4⋊C4×#412