Finite Group Databasebeta

← #8957969

Subgroups — #8957969

Order 512.

4752 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58024C214yesmaximal, complemented
2#57917C214yesmaximal, complemented
3#56086C214yesmaximal, complemented
4#52014C214yesmaximal, complemented
5#51992C212yesmaximal, complemented
6#51978C212yesmaximal, complemented
7#51837C214yesmaximal, complemented
8#51041C212yesmaximal, complemented
9#50183C212yesmaximal, complemented
10#48778C212yesmaximal, complemented
11#47167C214yesmaximal, complemented
12#43474C214yesmaximal, complemented
13#43385C214yesmaximal, complemented
14#41437C212yesmaximal, complemented
15#41273C214yesmaximal, complemented
16#40713C214yesmaximal, complemented
17#37933C212yesmaximal, complemented
18#37753C212yesmaximal, complemented
19#36718C211yesmaximal, characteristic, complemented
20#36075C212yesmaximal, complemented
21#35846C212yesmaximal, complemented
22#35563C211yesmaximal, characteristic
23#35351C211yesmaximal, characteristic, complemented
24C2×#563C2212yescomplemented
25C2×#556C2212yes—
26C2×#544C2212yescomplemented
27C2×#543C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#518C2211yescharacteristic
33#2848C2212yes—
34#2837C2214yescomplemented
35#2837C2214yescomplemented
36#2830C2214yescomplemented
37#2827C2214yescomplemented
38#2826C2214yescomplemented
39#2802C2214yescomplemented
40#2800C2214yescomplemented
41#2797C2214yescomplemented
42#2786C2214yescomplemented
43#2780C2214yescomplemented
44#2777C2214yescomplemented
45#2775C2214yescomplemented
46#2770C2214yescomplemented
47#2768C2214yescomplemented
48#2761C2214yescomplemented
49#2761C2214yescomplemented
50#2761C2214yescomplemented
51#2755C2214yescomplemented
52#2752C2214yescomplemented
53#2751C2214yescomplemented
54#2749C2214yescomplemented
55#2748C2212yescomplemented
56#2744C2214yes—
57#2738C2214yes—
58#2738C2214yes—
59#2735C2214yes—
60#2735C2214yes—
61#2732C2214yescomplemented
62#2732C2214yescomplemented
63#2731C2214yescomplemented
64#2729C2214yescomplemented
65#2729C2214yescomplemented
66#2726C2214yescomplemented
67#2724C2212yescomplemented
68#2723C2214yescomplemented
69#2719C2214yescomplemented
70#2716C2214yescomplemented
71#2711C2214yescomplemented
72#2710C2214yescomplemented
73#2709C2212yescomplemented
74#2709C2212yescomplemented
75#2708C2214yescomplemented
76#2707C2214yes—
77#2706C2214yescomplemented
78#2704C2214yescomplemented
79#2702C2214yescomplemented
80#2702C2214yescomplemented
81#2701C2214yescomplemented
82#2701C2214yescomplemented
83#2698C2214yes—
84#2694C2214yescomplemented
85#2685C2214yes—
86#2685C2214yes—
87#2681C2214yes—
88#2681C2214yes—
89#2681C2214yescomplemented
90#2681C2214yescomplemented
91#2677C2214yescomplemented
92#2674C2214yes—
93#2672C2214yes—
94#2672C2214yes—
95#2667C2212yes—
96#2664C2214yescomplemented
97#2664C2214yescomplemented
98#2651C2214yescomplemented
99#2651C2214yescomplemented
100#2649C2214yescomplemented
101#2646C2212yescomplemented
102#2641C2214yescomplemented
103#2639C2212yescomplemented
104#2638C2212yes—
105#2638C2212yescomplemented
106#2636C2214yescomplemented
107#2627C2212yescomplemented
108#2626C2212yes—
109#2625C2212yes—
110#2621C2212yescomplemented
111#2618C2212yescomplemented
112#2612C2214yescomplemented
113#2611C2214yes—
114#2608C2214yescomplemented
115#2606C2214yescomplemented
116#2603C2214yescomplemented
117#2601C2214yescomplemented
118#2601C2214yescomplemented
119#2595C2214yescomplemented
120#2583C2212yes—
121#2583C2212yescomplemented
122#2581C2212yescomplemented
123#2575C2214yescomplemented
124#2572C2214yescomplemented
125#2559C2214yescomplemented
126#2559C2214yescomplemented
127#2558C2214yescomplemented
128#2556C2214yescomplemented
129#2546C2212yescomplemented
130#2536C2214yescomplemented
131#2534C2212yes—
132#2534C2212yes—
133#2533C2214yescomplemented
134#2530C2214yescomplemented
135#2529C2214yescomplemented
136#2526C2214yescomplemented
137#2525C2214yescomplemented
138#2519C2214yescomplemented
139#2518C2214yescomplemented
140#2518C2214yescomplemented
141#2509C2214yescomplemented
142#2484C2212yes—
143#2484C2212yescomplemented
144#2483C2212yes—
145#2482C2212yes—
146#2482C2214yes—
147#2480C2214yes—
148#2480C2214yes—
149#2480C2214yes—
150#2479C2214yescomplemented
151#2478C2214yes—
152#2478C2214yescomplemented
153#2477C2214yescomplemented
154#2477C2214yescomplemented
155#2476C2214yescomplemented
156#2476C2214yescomplemented
157#2475C2214yes—
158#2474C2214yescomplemented
159#2473C2214yescomplemented
160#2472C2214yes—
161#2472C2214yes—
162#2472C2214yes—
163#2470C2214yescomplemented
164#2466C2214yes—
165#2466C2214yescomplemented
166#2465C2214yescomplemented
167#2460C2214yescomplemented
168#2452C2214yescomplemented
169#2452C2214yescomplemented
170#2449C2214yescomplemented
171#2447C2214yes—
172#2444C2214yes—
173#2444C2214yes—
174#2443C2214yes—
175#2443C2214yes—
176#2435C2212yes—
177#2432C2214yes—
178#2429C2214yescomplemented
179#2428C2214yes—
180#2427C2214yescomplemented
181#2426C2214yes—
182#2421C2214yescomplemented
183#2416C2214yes—
184#2414C2214yes—
185#2411C2214yes—
186#2408C2212yes—
187#2408C2212yes—
188#2405C2212yes—
189#2405C2212yes—
190#2405C2212yes—
191#2398C2214yescomplemented
192#2396C2212yescomplemented
193#2395C2212yes—
194#2395C2212yescomplemented
195#2378C2212yes—
196#2376C2212yescomplemented
197#2374C2212yescomplemented
198#2372C2212yescomplemented
199#2367C2214yescomplemented
200#2365C2214yescomplemented
201#2363C2214yescomplemented
202#2360C2214yescomplemented
203#2359C2214yescomplemented
204#2357C2212yes—
205#2346C2212yes—
206#2343C2214yescomplemented
207#2335C2214yescomplemented
208#2333C2214yescomplemented
209#2329C2212yescomplemented
210#2329C2212yescomplemented
211#2316C2211yescharacteristic
212#2316C2212yescomplemented
213#2312C2211yescharacteristic
214#2309C2211yescharacteristic
215#2308C2212yes—
216#2308C2211yescharacteristic
217C2×#385C2212yes—
218#2280C2211yescharacteristic
219C22×#41C2311yescharacteristic
220C23×D4C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224#563—48no—
225#556—48no—
226#544—48no—
227#543—44no—
228#535—44no—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2314yes—
232C2×#127C2312yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#125C2314yes—
240C2×#124C2312yes—
241C2×#124C2314yes—
242C2×#124C2314yes—
243#525—44no—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2312yes—
247C2×#123C2312yes—
248C2×#123C2312yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2312yes—
254C2×C22⋊Q8C2312yes—
255C2×C22⋊Q8C2312yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×#121—44no—
264C2×#121C2314yes—
265C2×#121C2312yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C2×#120C2312yes—
271C2×#120C2312yes—
272C2×#120C2312yes—
273#520—44no—
274#518—44no—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2312yes—
284C2×#117C2312yes—
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2314yes—
289C2×#117C2314yes—
290C2×#117C2312yes—
291C2×#117C2312yes—
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2312yes—
294C22×C4⋊C4C2312yes—
295C22×C4⋊C4C2312yes—
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2312yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2312yes—
314#400C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2312yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2312yes—
330#398C2312yes—
331#398C2312yes—
332#398C2312yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2312yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2312yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#395C2314yes—
384#395C2312yes—
385#395C2312yes—
386#395C2312yes—
387#395C2314yes—
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#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2312yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#392C2314yes—
421#392C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#390C2314yes—
429#390C2312yes—
430#390C2312yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
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#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
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#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2312yes—
539#386C2314yes—
540#386C2312yes—
541#386C2312yes—
542#386C2312yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
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#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#383C2314yes—
570#383C2314yes—
571#382C2314yes—
572#382C2312yes—
573#382C2314yes—
574#382C2314yes—
575#381C2312yes—
576#381C2314yes—
577#381C2314yes—
578#381C2314yes—
579#381C2314yes—
580#381C2312yes—
581#381C2312yes—
582#380C2312yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2314yes—
588#380C2312yes—
589#380C2314yes—
590#380C2312yes—
591#380C2314yes—
592#379C2312yes—
593#379C2314yes—
594#379C2312yes—
595#379C2312yes—
596#379C2312yes—
597#379C2314yes—
598#379C2314yes—
599#379C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2312yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619#376C2314yes—
620#376C2314yes—
621C2×#95C2312yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C25C2411yescharacteristic
625C25C2411yescharacteristic
626C2×#41—24no—
627C2×#41—42no—
628C2×#41—42no—
629C22×Q8C2412yes—
630C22×Q8C2414yes—
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C22×D4—24no—
634C22×D4—42no—
635C22×D4—42no—
636C22×D4—42no—
637C22×D4—42no—
638C22×D4—44no—
639C22×D4—44no—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2411yescharacteristic
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2414yes—
649C23×C4—42no—
650C23×C4—42no—
651C23×C4—42no—
652C23×C4C2411yescharacteristic
653C23×C4C2412yes—
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C23×C4C2412yes—
657C23×C4C2411yescharacteristic
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2412yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2411yescharacteristic
669C4⋊Q8—216no—
670C4⋊Q8—44no—
671C4⋊Q8—48no—
672#127—44no—
673#126—48no—
674#126—48no—
675#126—48no—
676#126—48no—
677#125—48no—
678#125—48no—
679#125—48no—
680#124—28no—
681#124—48no—
682#124—48no—
683#123—48no—
684#123—48no—
685#123—44no—
686#123—44no—
687#123—44no—
688#123—44no—
689#123—44no—
690C22⋊Q8—28no—
691C22⋊Q8—28no—
692C22⋊Q8—44no—
693C22⋊Q8—48no—
694C22⋊Q8—48no—
695C22⋊Q8—48no—
696C22⋊Q8—48no—
697C22⋊Q8—48no—
698C22⋊Q8—48no—
699C22⋊Q8—44no—
700C22⋊Q8—44no—
701C22⋊Q8—44no—
702#121—48no—
703#121—48no—
704#121—48no—
705#121—48no—
706#121—48no—
707#121—44no—
708#120—44no—
709#120—44no—
710#120—44no—
711C4×Q8—44no—
712C4×Q8—48no—
713C4×Q8—44no—
714C4×D4—28no—
715C4×D4—48no—
716C4×D4—48no—
717C4×D4—44no—
718C4×D4—48no—
719C4×D4—44no—
720#117—28no—
721#117—42no—
722#117—44no—
723#117—48no—
724#117—48no—
725#117—42no—
726#117—42no—
727#117—44no—
728C2×C4⋊C4—24no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—44no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C22⋊C4—24no—
781C2×C22⋊C4—44no—
782C2×C22⋊C4—44no—
783C2×C22⋊C4—44no—
784C2×C22⋊C4—44no—
785C2×C22⋊C4—42no—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C42C2414yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2412yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2412yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2412yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
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—
900C24—22no—
901C24—24no—
902C24—22no—
903C24—22no—
904C24—42no—
905C24—42no—
906C24—41no—
907C24—41no—
908C24—42no—
909C24—41no—
910C24—41no—
911C24—42no—
912C24—41no—
913C24—41no—
914C24—42no—
915C24C2512yes—
916C24C2512yes—
917C24C2512yes—
918C24C2511yescharacteristic
919C24C2512yes—
920#41—416no—
921C2×Q8—24no—
922C2×Q8—28no—
923C2×Q8—41no—
924C2×Q8—41no—
925C2×Q8—44no—
926C2×Q8—44no—
927C2×Q8—44no—
928C2×Q8—42no—
929C2×Q8—42no—
930C2×Q8—42no—
931C2×Q8H(5,𝔽2)14yes—
932C2×D4—24no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—28no—
937C2×D4—24no—
938C2×D4—22no—
939C2×D4—24no—
940C2×D4—24no—
941C2×D4—41no—
942C2×D4—44no—
943C2×D4—42no—
944C2×D4—41no—
945C2×D4—44no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—44no—
950C2×D4—42no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—416no—
960C2×D4—88no—
961C2×D4—88no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—41no—
985C22×C4—42no—
986C22×C4—41no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—44no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—44no—
1005C22×C4—42no—
1006C22×C4—88no—
1007C22×C4H(5,𝔽2)14yes—
1008C22×C4C2514yes—
1009C22×C4C2514yes—
1010C22×C4C2512yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2514yes—
1021C22×C4C2514yes—
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C22×C4C2511yescharacteristic
1026C4⋊C4—24no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—41no—
1042C4⋊C4—44no—
1043C4⋊C4—42no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—24no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—24no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—42no—
1118C22⋊C4—44no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C42—28no—
1126C42—24no—
1127C42—24no—
1128C42—28no—
1129C42—44no—
1130C42—44no—
1131C42—44no—
1132C42—44no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—44no—
1140C23—28no—
1141C23—22no—
1142C23—21no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—21no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—22no—
1152C23—22no—
1153C23—22no—
1154C23—22no—
1155C23—22no—
1156C23—22no—
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—44no—
1167C23—44no—
1168C23—82no—
1169C23—82no—
1170C23—84no—
1171C23—84no—
1172C23—82no—
1173C23—82no—
1174C23—82no—
1175C23—82no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23C2×H(5,𝔽2)12yes—
1181C23#58514yes—
1182C23C2611yescharacteristic
1183Q8—44no—
1184Q8—88no—
1185Q8—84no—
1186Q8—162no—
1187D4—416no—
1188D4—48no—
1189D4—44no—
1190D4—84no—
1191D4—84no—
1192D4—88no—
1193D4—88no—
1194D4—164no—
1195D4—164no—
1196C2×C4—28no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—44no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—48no—
1247C2×C4—84no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4—82no—
1251C2×C4—82no—
1252C2×C4—162no—
1253C2×C4—162no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4C2×H(5,𝔽2)14yes—
1260C2×C4C2×H(5,𝔽2)14yes—
1261C2×C4C2×H(5,𝔽2)12yes—
1262C2×C4#58512yes—
1263C22—22no—
1264C22—22no—
1265C22—24no—
1266C22—22no—
1267C22—24no—
1268C22—24no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—88no—
1291C22—164no—
1292C22—164no—
1293C22C22×H(5,𝔽2)11yescharacteristic
1294C22C22×H(5,𝔽2)11yescharacteristic
1295C22C2×#58511yescharacteristic
1296C22C2×#58512yes—
1297C222−1+612yes—
1298C4—22no—
1299C4—22no—
1300C4—24no—
1301C4—24no—
1302C4—42no—
1303C4—44no—
1304C4—44no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C4—42no—
1309C4—44no—
1310C4—44no—
1311C4—44no—
1312C4—44no—
1313C4—44no—
1314C4—44no—
1315C4—44no—
1316C2—44no—
1317C2—42no—
1318C2—82no—
1319C2—82no—
1320C2—82no—
1321C2#6281811yescharacteristic
1322C2#6282011yescharacteristic
1323C2#6288711yescharacteristic
1324C2#6291912yes—
1325C2#6293412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35563C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58024C2semidirect
2. #57917C2semidirect
3. #56086C2semidirect
4. #52014C2semidirect
5. #51992C2semidirect
6. #51978C2semidirect
7. #51837C2semidirect
8. #51041C2semidirect
9. #50183C2semidirect
10. #48778C2semidirect
11. #47167C2semidirect
12. #43474C2semidirect
13. #43385C2semidirect
14. #41437C2semidirect
15. #41273C2semidirect
16. #40713C2semidirect
17. #37933C2semidirect
18. #37753C2semidirect
19. #36718C2semidirect
20. #36075C2semidirect
21. #35846C2semidirect
23. #35351C2semidirect
24. C2×#563C22semidirect
26. C2×#544C22semidirect
34. #2837C22semidirect
35. #2837C22semidirect
36. #2830C22semidirect
37. #2827C22semidirect
38. #2826C22semidirect
39. #2802C22semidirect
40. #2800C22semidirect
41. #2797C22semidirect
42. #2786C22semidirect
43. #2780C22semidirect
44. #2777C22semidirect
45. #2775C22semidirect
46. #2770C22semidirect
47. #2768C22semidirect
48. #2761C22semidirect
49. #2761C22semidirect
50. #2761C22semidirect
51. #2755C22semidirect
52. #2752C22semidirect
53. #2751C22semidirect
54. #2749C22semidirect
55. #2748C22semidirect
61. #2732C22semidirect
62. #2732C22semidirect
63. #2731C22semidirect
64. #2729C22semidirect
65. #2729C22semidirect
66. #2726C22semidirect
67. #2724C22semidirect
68. #2723C22semidirect
69. #2719C22semidirect
70. #2716C22semidirect
71. #2711C22semidirect
72. #2710C22semidirect
73. #2709C22semidirect
74. #2709C22semidirect
75. #2708C22semidirect
77. #2706C22semidirect
78. #2704C22semidirect
79. #2702C22semidirect
80. #2702C22semidirect
81. #2701C22semidirect
82. #2701C22semidirect
84. #2694C22semidirect
89. #2681C22semidirect
90. #2681C22semidirect
91. #2677C22semidirect
96. #2664C22semidirect
97. #2664C22semidirect
98. #2651C22semidirect
99. #2651C22semidirect
100. #2649C22semidirect
101. #2646C22semidirect
102. #2641C22semidirect
103. #2639C22semidirect
105. #2638C22semidirect
106. #2636C22semidirect
107. #2627C22semidirect
110. #2621C22semidirect
111. #2618C22semidirect
112. #2612C22semidirect
114. #2608C22semidirect
115. #2606C22semidirect
116. #2603C22semidirect
117. #2601C22semidirect
118. #2601C22semidirect
119. #2595C22semidirect
121. #2583C22semidirect
122. #2581C22semidirect
123. #2575C22semidirect
124. #2572C22semidirect
125. #2559C22semidirect
126. #2559C22semidirect
127. #2558C22semidirect
128. #2556C22semidirect
129. #2546C22semidirect
130. #2536C22semidirect
133. #2533C22semidirect
134. #2530C22semidirect
135. #2529C22semidirect
136. #2526C22semidirect
137. #2525C22semidirect
138. #2519C22semidirect
139. #2518C22semidirect
140. #2518C22semidirect
141. #2509C22semidirect
143. #2484C22semidirect
150. #2479C22semidirect
152. #2478C22semidirect
153. #2477C22semidirect
154. #2477C22semidirect
155. #2476C22semidirect
156. #2476C22semidirect
158. #2474C22semidirect
159. #2473C22semidirect
163. #2470C22semidirect
165. #2466C22semidirect
166. #2465C22semidirect
167. #2460C22semidirect
168. #2452C22semidirect
169. #2452C22semidirect
170. #2449C22semidirect
178. #2429C22semidirect
180. #2427C22semidirect
182. #2421C22semidirect
191. #2398C22semidirect
192. #2396C22semidirect
194. #2395C22semidirect
196. #2376C22semidirect
197. #2374C22semidirect
198. #2372C22semidirect
199. #2367C22semidirect
200. #2365C22semidirect
201. #2363C22semidirect
202. #2360C22semidirect
203. #2359C22semidirect
206. #2343C22semidirect
207. #2335C22semidirect
208. #2333C22semidirect
209. #2329C22semidirect
210. #2329C22semidirect
212. #2316C22semidirect

Maximal subgroups

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

subgroupindex
#580242
#579172
#560862
#520142
#519922
#519782
#518372
#510412
#501832
#487782
#471672
#434742
#433852
#414372
#412732
#407132
#379332
#377532
#367182
#360752
#358462
#355632
#353512