Finite Group Databasebeta

← #8899171

Subgroups — #8899171

Order 512.

5516 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58257C212yesmaximal, complemented
2#57963C212yesmaximal, complemented
3#57219C214yesmaximal, complemented
4#57195C214yesmaximal, complemented
5#51993C212yesmaximal, complemented
6#51945C212yesmaximal, complemented
7#51176C214yesmaximal, complemented
8#51111C214yesmaximal, complemented
9#47035C212yesmaximal, complemented
10#46814C214yesmaximal, complemented
11#46609C214yesmaximal, complemented
12#46426C212yesmaximal, complemented
13#46420C214yesmaximal, complemented
14#46357C212yesmaximal, complemented
15#38878C214yesmaximal, complemented
16#38390C214yesmaximal, complemented
17#37718C214yesmaximal, complemented
18#36816C212yesmaximal, complemented
19#36718C211yesmaximal, characteristic, complemented
20#35616C212yesmaximal, complemented
21#35584C211yesmaximal, characteristic, complemented
22#35435C212yesmaximal, complemented
23#35347C211yesmaximal, characteristic
24C22×H(5,𝔽2)C2211yescharacteristic
25C2×#544C2211yescharacteristic, complemented
26C2×#543C2211yescharacteristic, complemented
27C2×#542C2214yescomplemented
28C2×#536C2212yes—
29C2×#536C2212yescomplemented
30C2×#534C2212yes—
31C22×#124C2212yescomplemented
32C22×#121C2211yescharacteristic
33#2852C2214yescomplemented
34#2848C2212yescomplemented
35#2840C2212yescomplemented
36#2834C2212yescomplemented
37#2830C2214yescomplemented
38#2817C2212yescomplemented
39#2816C2214yescomplemented
40#2814C2214yescomplemented
41#2808C2214yescomplemented
42#2804C2212yescomplemented
43#2803C2214yescomplemented
44#2797C2214yescomplemented
45#2796C2214yescomplemented
46#2790C2214yescomplemented
47#2781C2214yescomplemented
48#2763C2212yescomplemented
49#2759C2214yescomplemented
50#2751C2214yescomplemented
51#2751C2214yescomplemented
52#2746C2214yescomplemented
53#2741C2214yescomplemented
54#2737C2214yescomplemented
55#2736C2212yescomplemented
56#2736C2214yescomplemented
57#2735C2214yescomplemented
58#2735C2212yescomplemented
59#2735C2214yescomplemented
60#2731C2214yescomplemented
61#2730C2214yescomplemented
62#2729C2214yescomplemented
63#2728C2214yescomplemented
64#2720C2214yescomplemented
65#2718C2214yescomplemented
66#2717C2214yescomplemented
67#2716C2214yescomplemented
68#2713C2214yescomplemented
69#2712C2214yescomplemented
70#2710C2214yescomplemented
71#2702C2214yescomplemented
72#2701C2214yescomplemented
73#2701C2214yescomplemented
74#2700C2214yescomplemented
75#2700C2214yescomplemented
76#2700C2214yescomplemented
77#2697C2212yescomplemented
78#2697C2212yescomplemented
79#2696C2214yescomplemented
80#2696C2214yescomplemented
81#2692C2214yescomplemented
82#2692C2214yescomplemented
83#2687C2214yescomplemented
84#2686C2214yescomplemented
85#2686C2214yescomplemented
86#2685C2214yescomplemented
87#2685C2214yescomplemented
88#2685C2214yescomplemented
89#2684C2214yescomplemented
90#2684C2214yescomplemented
91#2683C2212yescomplemented
92#2681C2214yescomplemented
93#2681C2214yescomplemented
94#2680C2214yescomplemented
95#2680C2214yescomplemented
96#2677C2214yescomplemented
97#2677C2212yescomplemented
98#2674C2214yescomplemented
99#2674C2214yescomplemented
100#2674C2214yescomplemented
101#2672C2214yescomplemented
102#2672C2214yescomplemented
103#2662C2214yescomplemented
104#2653C2214yescomplemented
105#2653C2214yescomplemented
106#2653C2214yescomplemented
107#2649C2214yescomplemented
108#2648C2214yescomplemented
109#2632C2214yescomplemented
110#2626C2212yescomplemented
111#2607C2212yescomplemented
112#2602C2214yescomplemented
113#2597C2214yescomplemented
114#2589C2214yescomplemented
115#2583C2212yescomplemented
116#2561C2212yescomplemented
117#2561C2212yescomplemented
118#2561C2214yescomplemented
119#2561C2214yescomplemented
120#2560C2214yescomplemented
121#2560C2214yescomplemented
122#2558C2214yescomplemented
123#2554C2214yescomplemented
124#2553C2214yescomplemented
125#2553C2214yescomplemented
126#2551C2214yescomplemented
127#2549C2214yescomplemented
128#2523C2212yescomplemented
129#2521C2214yescomplemented
130#2520C2214yescomplemented
131#2516C2214yescomplemented
132#2516C2214yescomplemented
133#2500C2214yescomplemented
134#2493C2214yescomplemented
135#2492C2214yescomplemented
136#2491C2214yescomplemented
137#2491C2214yescomplemented
138#2490C2214yescomplemented
139#2490C2214yescomplemented
140#2482C2214yescomplemented
141#2480C2214yescomplemented
142#2480C2214yescomplemented
143#2479C2214yescomplemented
144#2478C2214yescomplemented
145#2477C2214yescomplemented
146#2477C2214yescomplemented
147#2475C2214yescomplemented
148#2474C2214yescomplemented
149#2474C2214yescomplemented
150#2474C2214yescomplemented
151#2474C2214yescomplemented
152#2472C2214yescomplemented
153#2472C2214yescomplemented
154#2472C2214yescomplemented
155#2470C2214yescomplemented
156#2465C2214yescomplemented
157#2461C2214yescomplemented
158#2458C2214yescomplemented
159#2458C2214yescomplemented
160#2451C2214yescomplemented
161#2438C2214yescomplemented
162#2437C2212yescomplemented
163#2437C2214yescomplemented
164#2435C2212yes—
165#2435C2214yes—
166#2435C2212yes—
167#2435C2214yes—
168#2435C2212yescomplemented
169#2435C2212yescomplemented
170#2435C2212yescomplemented
171#2434C2214yescomplemented
172#2432C2212yes—
173#2432C2212yes—
174#2432C2214yescomplemented
175#2432C2212yescomplemented
176#2432C2214yescomplemented
177#2432C2212yescomplemented
178#2430C2214yes—
179#2430C2214yes—
180#2418C2214yescomplemented
181#2418C2214yescomplemented
182#2410C2214yes—
183#2410C2214yes—
184#2409C2214yescomplemented
185#2406C2212yes—
186#2405C2211yescharacteristic
187#2405C2211yescharacteristic
188#2405C2214yes—
189#2405C2214yes—
190#2405C2214yescomplemented
191#2405C2212yescomplemented
192#2405C2214yescomplemented
193#2405C2212yescomplemented
194#2404C2212yes—
195#2403C2211yescharacteristic
196#2403C2211yescharacteristic
197#2376C2212yescomplemented
198#2375C2212yescomplemented
199#2374C2212yescomplemented
200#2368C2214yescomplemented
201#2358C2212yescomplemented
202#2342C2214yescomplemented
203#2337C2214yescomplemented
204#2335C2214yescomplemented
205#2334C2214yescomplemented
206#2333C2214yescomplemented
207#2332C2212yescomplemented
208#2332C2212yescomplemented
209#2312C2211yescharacteristic, complemented
210#2309C2212yescomplemented
211#2309C2212yescomplemented
212#2308C2211yescharacteristic
213C4×C22⋊Q8C2214yescomplemented
214#2297C2212yes—
215#2297C2212yescomplemented
216C2×#386C2212yes—
217#2280C2212yescomplemented
218#2274C2211yescharacteristic, complemented
219C2×H(5,𝔽2)—48no—
220C2×H(5,𝔽2)—44no—
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C23×Q8C2312yes—
225C23×D4C2311yescharacteristic
226C23×D4C2312yes—
227C23×D4C2312yes—
228C23×D4C2311yescharacteristic
229C23×D4C2311yescharacteristic
230C23×D4C2311yescharacteristic
231C23×D4C2312yes—
232C23×D4C2311yescharacteristic
233C24×C4C2311yescharacteristic
234#544—44no—
235#543—44no—
236#542—416no—
237#536—48no—
238#536—48no—
239#534—48no—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2312yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#125C2314yes—
249C2×#124—48no—
250C2×#124C2314yes—
251C2×#124C2314yes—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2314yes—
258C2×#124C2314yes—
259C2×#124C2312yes—
260C2×#124C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2312yes—
264C2×#123C2312yes—
265C2×#123C2314yes—
266C2×#123C2312yes—
267C2×#123C2312yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×#121—44no—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#120C2312yes—
292C2×#120C2312yes—
293C2×#120C2312yes—
294C2×#120C2312yes—
295C2×#120C2314yes—
296C2×C4×Q8C2314yes—
297C2×C4×D4C2314yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2314yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2314yes—
308C22×C22⋊C4C2314yes—
309C22×C22⋊C4C2314yes—
310C22×C22⋊C4C2312yes—
311C22×C42C2312yes—
312#401C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2312yes—
322#399C2314yes—
323#399C2314yes—
324#399C2312yes—
325#399C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2312yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2312yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#395C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2312yes—
408#393C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2312yes—
414#393C2314yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2312yes—
420#393C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#390C2312yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2312yes—
452#390C2314yes—
453#390C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
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#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#386C2312yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2312yes—
536#386C2312yes—
537#386C2314yes—
538#386C2312yes—
539#386C2314yes—
540#386C2314yes—
541#386C2312yes—
542#386C2312yes—
543#386C2312yes—
544#386C2312yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#385C2312yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2312yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#384C2314yes—
573#383C2314yes—
574#382C2314yes—
575#381C2314yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2312yes—
580#380C2312yes—
581#380C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#379C2314yes—
588#379C2314yes—
589#379C2314yes—
590#379C2314yes—
591#379C2314yes—
592#379C2314yes—
593#379C2311yescharacteristic
594#379C2311yescharacteristic
595#379C2314yes—
596#379C2312yes—
597#379C2312yes—
598#379C2314yes—
599#379C2314yes—
600#379C2314yes—
601#379C2314yes—
602#379C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2314yes—
623C2×#95C2314yes—
624C25C2411yescharacteristic
625C25C2411yescharacteristic
626C25C2412yes—
627C25C2411yescharacteristic
628C25C2411yescharacteristic
629C25C2411yescharacteristic
630H(5,𝔽2)—464no—
631C2×#41—28no—
632C2×#41—28no—
633C2×#41—44no—
634C2×#41—44no—
635C2×#41—44no—
636C2×#41—44no—
637C2×#41—44no—
638C2×#41—44no—
639C2×#41—44no—
640C22×Q8—44no—
641C22×Q8—44no—
642C22×Q8—44no—
643C22×Q8C2412yes—
644C22×Q8C2412yes—
645C22×Q8C2414yes—
646C22×Q8C2412yes—
647C22×Q8C2414yes—
648C22×Q8C2412yes—
649C22×Q8C2412yes—
650C22×D4—28no—
651C22×D4—28no—
652C22×D4—24no—
653C22×D4—44no—
654C22×D4—44no—
655C22×D4—44no—
656C22×D4—44no—
657C22×D4—44no—
658C22×D4—44no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—44no—
662C22×D4—44no—
663C22×D4—42no—
664C22×D4—44no—
665C22×D4—44no—
666C22×D4—44no—
667C22×D4—42no—
668C22×D4—44no—
669C22×D4C2412yes—
670C22×D4C2412yes—
671C22×D4C2412yes—
672C22×D4C2412yes—
673C22×D4C2412yes—
674C22×D4C2414yes—
675C22×D4C2414yes—
676C22×D4C2412yes—
677C22×D4C2412yes—
678C22×D4C2412yes—
679C22×D4C2412yes—
680C22×D4C2412yes—
681C22×D4C2414yes—
682C22×D4C2412yes—
683C23×C4—44no—
684C23×C4—42no—
685C23×C4C2411yescharacteristic
686C23×C4C2412yes—
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2414yes—
690C23×C4C2414yes—
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2414yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2412yes—
697C23×C4C2412yes—
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C4⋊Q8—44no—
701C4⋊Q8—48no—
702C4⋊Q8—44no—
703C4⋊Q8—48no—
704C4⋊Q8—48no—
705#126—48no—
706#126—48no—
707#126—48no—
708#125—48no—
709#124—216no—
710#124—48no—
711#124—44no—
712#124—44no—
713#124—44no—
714#124—44no—
715#124—48no—
716#124—44no—
717#124—44no—
718#124—48no—
719#124—48no—
720#123—216no—
721#123—44no—
722#123—48no—
723#123—48no—
724#123—48no—
725#123—48no—
726#123—44no—
727#123—44no—
728#123—44no—
729#123—48no—
730C22⋊Q8—28no—
731C22⋊Q8—28no—
732C22⋊Q8—48no—
733C22⋊Q8—48no—
734C22⋊Q8—48no—
735C22⋊Q8—44no—
736C22⋊Q8—44no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739C22⋊Q8—48no—
740C22⋊Q8—48no—
741C22⋊Q8—48no—
742C22⋊Q8—48no—
743C22⋊Q8—44no—
744C22⋊Q8—44no—
745#121—216no—
746#121—48no—
747#121—48no—
748#121—48no—
749#120—44no—
750#120—44no—
751#120—44no—
752#120—48no—
753#120—44no—
754C4×Q8—48no—
755C4×D4—48no—
756#117—44no—
757#117—48no—
758#117—44no—
759#117—44no—
760#117—44no—
761C2×C4⋊C4—24no—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C22⋊C4—24no—
798C2×C22⋊C4—48no—
799C2×C22⋊C4—48no—
800C2×C22⋊C4—48no—
801C2×C22⋊C4—44no—
802C2×C22⋊C4—42no—
803C2×C22⋊C4—44no—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C42—44no—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2414yes—
886#95C2412yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2412yes—
913#95C2412yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923C24—24no—
924C24—22no—
925C24—22no—
926C24—24no—
927C24—24no—
928C24—22no—
929C24—24no—
930C24—41no—
931C24—42no—
932C24—42no—
933C24—41no—
934C24—42no—
935C24—42no—
936C24—42no—
937C24—42no—
938C24—44no—
939C24—42no—
940C24—44no—
941C24—42no—
942C24—42no—
943C24—42no—
944C24—42no—
945C24—42no—
946C24—42no—
947C24—42no—
948C24C2511yescharacteristic
949C24C2512yes—
950C24C2511yescharacteristic
951C24C2512yes—
952C24C2511yescharacteristic
953C24C2512yes—
954C24C2512yes—
955#41—432no—
956#41—432no—
957#41—432no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—28no—
963C2×Q8—42no—
964C2×Q8—44no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—44no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—42no—
974C2×Q8—44no—
975C2×Q8—42no—
976C2×Q8—44no—
977C2×Q8—816no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—28no—
987C2×D4—28no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—24no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—42no—
1000C2×D4—42no—
1001C2×D4—42no—
1002C2×D4—42no—
1003C2×D4—42no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—432no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—42no—
1012C2×D4—42no—
1013C2×D4—44no—
1014C2×D4—42no—
1015C2×D4—42no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—416no—
1021C2×D4—432no—
1022C2×D4—416no—
1023C2×D4—432no—
1024C2×D4—416no—
1025C2×D4—88no—
1026C2×D4—88no—
1027C2×D4H(5,𝔽2)18yes—
1028C22×C4—22no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—41no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—41no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—42no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—88no—
1066C22×C4H(5,𝔽2)14yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—42no—
1135C22⋊C4—44no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—42no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C42—28no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—42no—
1183C42—42no—
1184C42—44no—
1185C42—42no—
1186C42—42no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—44no—
1192C23—28no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—24no—
1199C23—24no—
1200C23—22no—
1201C23—24no—
1202C23—22no—
1203C23—24no—
1204C23—22no—
1205C23—24no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—21no—
1211C23—21no—
1212C23—22no—
1213C23—24no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—24no—
1221C23—24no—
1222C23—44no—
1223C23—48no—
1224C23—44no—
1225C23—44no—
1226C23—44no—
1227C23—82no—
1228C23—82no—
1229C23—88no—
1230C23—82no—
1231C23—82no—
1232C23—82no—
1233C23—82no—
1234C23—88no—
1235C23—88no—
1236C23—88no—
1237C23—162no—
1238C23—161no—
1239C23—162no—
1240C23—161no—
1241C23—164no—
1242C23—164no—
1243C23—161no—
1244C23—161no—
1245C23—164no—
1246C23C2×H(5,𝔽2)12yes—
1247C23C2×H(5,𝔽2)14yes—
1248C23C2×H(5,𝔽2)14yes—
1249C23C2611yescharacteristic
1250Q8—48no—
1251Q8—84no—
1252Q8—88no—
1253Q8—84no—
1254Q8—88no—
1255Q8—162no—
1256Q8—162no—
1257D4—48no—
1258D4—48no—
1259D4—48no—
1260D4—48no—
1261D4—48no—
1262D4—48no—
1263D4—48no—
1264D4—48no—
1265D4—48no—
1266D4—84no—
1267D4—84no—
1268D4—88no—
1269D4—88no—
1270D4—164no—
1271C2×C4—28no—
1272C2×C4—216no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—44no—
1317C2×C4—44no—
1318C2×C4—48no—
1319C2×C4—48no—
1320C2×C4—44no—
1321C2×C4—88no—
1322C2×C4—88no—
1323C2×C4—82no—
1324C2×C4—82no—
1325C2×C4—88no—
1326C2×C4—88no—
1327C2×C4—162no—
1328C2×C4—162no—
1329C2×C4C2×H(5,𝔽2)14yes—
1330C2×C4C2×H(5,𝔽2)14yes—
1331C2×C4#58514yes—
1332C22—24no—
1333C22—22no—
1334C22—24no—
1335C22—22no—
1336C22—22no—
1337C22—28no—
1338C22—28no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—41no—
1347C22—42no—
1348C22—41no—
1349C22—42no—
1350C22—42no—
1351C22—41no—
1352C22—41no—
1353C22—42no—
1354C22—42no—
1355C22—41no—
1356C22—41no—
1357C22—42no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—88no—
1365C22—168no—
1366C22—164no—
1367C22—164no—
1368C22—164no—
1369C22—164no—
1370C22C22×H(5,𝔽2)11yescharacteristic
1371C22C22×H(5,𝔽2)12yes—
1372C22C2×#58512yes—
1373C222−1+612yes—
1374C4—24no—
1375C4—24no—
1376C4—24no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—44no—
1381C4—42no—
1382C4—44no—
1383C4—44no—
1384C4—44no—
1385C4—44no—
1386C4—44no—
1387C4—44no—
1388C4—44no—
1389C4—44no—
1390C2—44no—
1391C2—42no—
1392C2—44no—
1393C2—82no—
1394C2—81no—
1395C2—81no—
1396C2—82no—
1397C2#6281711yescharacteristic
1398C2#6282411yescharacteristic
1399C2#6288711yescharacteristic
1400C2#6292114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35347C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58257C2semidirect
2. #57963C2semidirect
3. #57219C2semidirect
4. #57195C2semidirect
5. #51993C2semidirect
6. #51945C2semidirect
7. #51176C2semidirect
8. #51111C2semidirect
9. #47035C2semidirect
10. #46814C2semidirect
11. #46609C2semidirect
12. #46426C2semidirect
13. #46420C2semidirect
14. #46357C2semidirect
15. #38878C2semidirect
16. #38390C2semidirect
17. #37718C2semidirect
18. #36816C2semidirect
19. #36718C2semidirect
20. #35616C2semidirect
21. #35584C2semidirect
22. #35435C2semidirect
25. C2×#544C22semidirect
26. C2×#543C22semidirect
27. C2×#542C22semidirect
29. C2×#536C22semidirect
31. C22×#124C22semidirect
33. #2852C22semidirect
34. #2848C22semidirect
35. #2840C22semidirect
36. #2834C22semidirect
37. #2830C22semidirect
38. #2817C22semidirect
39. #2816C22semidirect
40. #2814C22semidirect
41. #2808C22semidirect
42. #2804C22semidirect
43. #2803C22semidirect
44. #2797C22semidirect
45. #2796C22semidirect
46. #2790C22semidirect
47. #2781C22semidirect
48. #2763C22semidirect
49. #2759C22semidirect
50. #2751C22semidirect
51. #2751C22semidirect
52. #2746C22semidirect
53. #2741C22semidirect
54. #2737C22semidirect
55. #2736C22semidirect
56. #2736C22semidirect
57. #2735C22semidirect
58. #2735C22semidirect
59. #2735C22semidirect
60. #2731C22semidirect
61. #2730C22semidirect
62. #2729C22semidirect
63. #2728C22semidirect
64. #2720C22semidirect
65. #2718C22semidirect
66. #2717C22semidirect
67. #2716C22semidirect
68. #2713C22semidirect
69. #2712C22semidirect
70. #2710C22semidirect
71. #2702C22semidirect
72. #2701C22semidirect
73. #2701C22semidirect
74. #2700C22semidirect
75. #2700C22semidirect
76. #2700C22semidirect
77. #2697C22semidirect
78. #2697C22semidirect
79. #2696C22semidirect
80. #2696C22semidirect
81. #2692C22semidirect
82. #2692C22semidirect
83. #2687C22semidirect
84. #2686C22semidirect
85. #2686C22semidirect
86. #2685C22semidirect
87. #2685C22semidirect
88. #2685C22semidirect
89. #2684C22semidirect
90. #2684C22semidirect
91. #2683C22semidirect
92. #2681C22semidirect
93. #2681C22semidirect
94. #2680C22semidirect
95. #2680C22semidirect
96. #2677C22semidirect
97. #2677C22semidirect
98. #2674C22semidirect
99. #2674C22semidirect
100. #2674C22semidirect
101. #2672C22semidirect
102. #2672C22semidirect
103. #2662C22semidirect
104. #2653C22semidirect
105. #2653C22semidirect
106. #2653C22semidirect
107. #2649C22semidirect
108. #2648C22semidirect
109. #2632C22semidirect
110. #2626C22semidirect
111. #2607C22semidirect
112. #2602C22semidirect
113. #2597C22semidirect
114. #2589C22semidirect
115. #2583C22semidirect
116. #2561C22semidirect
117. #2561C22semidirect
118. #2561C22semidirect
119. #2561C22semidirect
120. #2560C22semidirect
121. #2560C22semidirect
122. #2558C22semidirect
123. #2554C22semidirect
124. #2553C22semidirect
125. #2553C22semidirect
126. #2551C22semidirect
127. #2549C22semidirect
128. #2523C22semidirect
129. #2521C22semidirect
130. #2520C22semidirect
131. #2516C22semidirect
132. #2516C22semidirect
133. #2500C22semidirect
134. #2493C22semidirect
135. #2492C22semidirect
136. #2491C22semidirect
137. #2491C22semidirect
138. #2490C22semidirect
139. #2490C22semidirect
140. #2482C22semidirect
141. #2480C22semidirect
142. #2480C22semidirect
143. #2479C22semidirect
144. #2478C22semidirect
145. #2477C22semidirect
146. #2477C22semidirect
147. #2475C22semidirect
148. #2474C22semidirect
149. #2474C22semidirect
150. #2474C22semidirect
151. #2474C22semidirect
152. #2472C22semidirect
153. #2472C22semidirect
154. #2472C22semidirect
155. #2470C22semidirect
156. #2465C22semidirect
157. #2461C22semidirect
158. #2458C22semidirect
159. #2458C22semidirect
160. #2451C22semidirect
161. #2438C22semidirect
162. #2437C22semidirect
163. #2437C22semidirect
168. #2435C22semidirect
169. #2435C22semidirect
170. #2435C22semidirect
171. #2434C22semidirect
174. #2432C22semidirect
175. #2432C22semidirect
176. #2432C22semidirect
177. #2432C22semidirect
180. #2418C22semidirect
181. #2418C22semidirect
184. #2409C22semidirect
190. #2405C22semidirect
191. #2405C22semidirect
192. #2405C22semidirect
193. #2405C22semidirect
197. #2376C22semidirect
198. #2375C22semidirect
199. #2374C22semidirect
200. #2368C22semidirect
201. #2358C22semidirect
202. #2342C22semidirect
203. #2337C22semidirect
204. #2335C22semidirect
205. #2334C22semidirect
206. #2333C22semidirect
207. #2332C22semidirect
208. #2332C22semidirect
209. #2312C22semidirect
210. #2309C22semidirect
211. #2309C22semidirect
213. C4×C22⋊Q8C22semidirect
215. #2297C22semidirect
217. #2280C22semidirect
218. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#582572
#579632
#572192
#571952
#519932
#519452
#511762
#511112
#470352
#468142
#466092
#464262
#464202
#463572
#388782
#383902
#377182
#368162
#367182
#356162
#355842
#354352
#353472