Finite Group Databasebeta

← #8943659

Subgroups — #8943659

Order 512.

5686 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58257C212yesmaximal, complemented
2#57207C214yesmaximal, complemented
3#56584C212yesmaximal, complemented
4#56403C214yesmaximal, complemented
5#51937C214yesmaximal, complemented
6#50878C212yesmaximal, complemented
7#49548C212yesmaximal, complemented
8#49205C214yesmaximal, complemented
9#48628C214yesmaximal, complemented
10#47883C212yesmaximal, complemented
11#46413C214yesmaximal, complemented
12#43174C214yesmaximal, complemented
13#43020C214yesmaximal, complemented
14#41044C214yesmaximal, complemented
15#40521C214yesmaximal, complemented
16#40500C212yesmaximal, complemented
17#37940C212yesmaximal, complemented
18#37932C212yesmaximal, complemented
19#36706C211yesmaximal, characteristic, complemented
20#35925C212yesmaximal, complemented
21#35750C212yesmaximal, complemented
22#35584C211yesmaximal, characteristic, complemented
23#35347C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic
25C2×#547C2212yes—
26C2×#546C2214yescomplemented
27C2×#544C2211yescharacteristic, complemented
28C2×#538C2214yescomplemented
29C2×#538C2211yescharacteristic, complemented
30C2×#534C2212yes—
31C22×#121C2211yescharacteristic
32#2848C2211yescharacteristic, complemented
33#2847C2211yescharacteristic, complemented
34#2835C2212yescomplemented
35#2834C2212yescomplemented
36#2826C2214yescomplemented
37#2821C2212yescomplemented
38#2814C2212yescomplemented
39#2814C2214yescomplemented
40#2812C2214yescomplemented
41#2797C2214yescomplemented
42#2796C2214yescomplemented
43#2790C2214yescomplemented
44#2788C2214yescomplemented
45#2786C2214yescomplemented
46#2781C2214yescomplemented
47#2780C2214yescomplemented
48#2779C2214yescomplemented
49#2778C2214yescomplemented
50#2763C2212yescomplemented
51#2757C2214yescomplemented
52#2757C2214yescomplemented
53#2753C2214yescomplemented
54#2750C2214yescomplemented
55#2749C2214yescomplemented
56#2746C2214yescomplemented
57#2746C2214yescomplemented
58#2745C2214yescomplemented
59#2743C2214yescomplemented
60#2736C2212yescomplemented
61#2735C2214yescomplemented
62#2734C2214yescomplemented
63#2720C2214yescomplemented
64#2718C2214yescomplemented
65#2718C2214yescomplemented
66#2717C2214yescomplemented
67#2715C2214yescomplemented
68#2708C2214yescomplemented
69#2708C2214yescomplemented
70#2707C2214yescomplemented
71#2706C2214yescomplemented
72#2706C2214yescomplemented
73#2701C2214yescomplemented
74#2697C2214yescomplemented
75#2695C2214yescomplemented
76#2693C2212yescomplemented
77#2691C2214yescomplemented
78#2691C2214yescomplemented
79#2691C2214yescomplemented
80#2688C2214yescomplemented
81#2687C2214yescomplemented
82#2687C2214yescomplemented
83#2686C2214yescomplemented
84#2682C2214yescomplemented
85#2680C2214yescomplemented
86#2678C2214yescomplemented
87#2678C2214yescomplemented
88#2676C2214yescomplemented
89#2675C2214yescomplemented
90#2674C2214yescomplemented
91#2672C2214yescomplemented
92#2672C2214yescomplemented
93#2671C2214yescomplemented
94#2671C2214yescomplemented
95#2670C2212yescomplemented
96#2668C2214yescomplemented
97#2667C2212yescomplemented
98#2666C2214yescomplemented
99#2661C2214yescomplemented
100#2653C2214yescomplemented
101#2648C2214yescomplemented
102#2646C2212yescomplemented
103#2646C2212yescomplemented
104#2640C2212yescomplemented
105#2639C2212yescomplemented
106#2638C2212yescomplemented
107#2635C2214yescomplemented
108#2631C2212yescomplemented
109#2626C2212yescomplemented
110#2626C2211yescharacteristic, complemented
111#2617C2211yescharacteristic, complemented
112#2617C2212yescomplemented
113#2616C2212yes—
114#2615C2212yescomplemented
115#2613C2214yescomplemented
116#2609C2214yescomplemented
117#2603C2212yescomplemented
118#2602C2214yescomplemented
119#2600C2214yescomplemented
120#2598C2214yescomplemented
121#2579C2212yescomplemented
122#2578C2214yescomplemented
123#2574C2214yescomplemented
124#2573C2214yescomplemented
125#2561C2212yescomplemented
126#2561C2212yescomplemented
127#2557C2214yescomplemented
128#2557C2214yescomplemented
129#2555C2214yescomplemented
130#2553C2214yescomplemented
131#2553C2214yescomplemented
132#2537C2214yescomplemented
133#2534C2214yescomplemented
134#2531C2214yescomplemented
135#2510C2214yescomplemented
136#2505C2214yescomplemented
137#2491C2214yescomplemented
138#2491C2214yescomplemented
139#2490C2214yescomplemented
140#2490C2214yescomplemented
141#2483C2212yescomplemented
142#2481C2214yescomplemented
143#2480C2214yescomplemented
144#2480C2214yescomplemented
145#2477C2214yescomplemented
146#2476C2214yescomplemented
147#2473C2214yescomplemented
148#2470C2214yescomplemented
149#2468C2214yescomplemented
150#2468C2214yescomplemented
151#2464C2214yescomplemented
152#2464C2214yescomplemented
153#2460C2214yescomplemented
154#2457C2214yescomplemented
155#2456C2214yescomplemented
156#2456C2214yescomplemented
157#2455C2214yescomplemented
158#2450C2214yescomplemented
159#2443C2214yescomplemented
160#2440C2214yescomplemented
161#2437C2212yescomplemented
162#2435C2212yes—
163#2435C2212yescomplemented
164#2432C2214yescomplemented
165#2432C2214yescomplemented
166#2430C2214yes—
167#2430C2214yes—
168#2430C2212yescomplemented
169#2430C2214yescomplemented
170#2425C2214yescomplemented
171#2424C2214yescomplemented
172#2420C2214yescomplemented
173#2419C2214yescomplemented
174#2418C2214yescomplemented
175#2418C2214yescomplemented
176#2418C2214yescomplemented
177#2414C2214yescomplemented
178#2412C2214yescomplemented
179#2411C2214yescomplemented
180#2410C2214yes—
181#2410C2214yes—
182#2410C2214yes—
183#2410C2214yes—
184#2410C2212yescomplemented
185#2410C2212yescomplemented
186#2408C2212yes—
187#2407C2214yescomplemented
188#2406C2212yes—
189#2406C2214yescomplemented
190#2405C2212yes—
191#2405C2214yes—
192#2405C2214yes—
193#2404C2212yes—
194#2403C2212yes—
195#2392C2214yescomplemented
196#2388C2212yes—
197C2×#394C2214yescomplemented
198#2378C2212yescomplemented
199#2377C2214yescomplemented
200#2358C2214yescomplemented
201#2358C2214yescomplemented
202#2353C2212yescomplemented
203#2349C2214yescomplemented
204#2343C2214yescomplemented
205#2342C2214yescomplemented
206#2339C2212yes—
207D4×C22⋊C4C2214yescomplemented
208#2329C2212yescomplemented
209#2325C2212yescomplemented
210#2321C2214yescomplemented
211#2315C2211yescharacteristic, complemented
212#2315C2212yescomplemented
213#2315C2212yescomplemented
214#2309C2212yescomplemented
215#2308C2211yescharacteristic
216C2×#386C2212yes—
217#2280C2212yescomplemented
218#2274C2211yescharacteristic, complemented
219C2×H(5,𝔽2)—48no—
220C2×H(5,𝔽2)—44no—
221C22×#41C2312yes—
222C22×#41C2314yes—
223C22×#41C2312yes—
224C23×D4C2311yescharacteristic
225C23×D4C2314yes—
226C23×D4C2312yes—
227C23×D4C2311yescharacteristic
228C23×D4C2312yes—
229C23×D4C2311yescharacteristic
230C24×C4C2311yescharacteristic
231#547—48no—
232#546—416no—
233#544—44no—
234#538—44no—
235#538—416no—
236#534—48no—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239C2×#126C2312yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2314yes—
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2312yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2314yes—
265C2×#121—44no—
266C2×#121C2312yes—
267C2×#121C2311yescharacteristic
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284C2×#120C2314yes—
285C2×#120C2314yes—
286C2×#120C2312yes—
287C2×#120C2312yes—
288C2×#120C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C2×#117C2314yes—
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2314yes—
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2312yes—
308C22×C22⋊C4C2312yes—
309C22×C22⋊C4C2314yes—
310C22×C22⋊C4C2314yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313#401C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2312yes—
326#399C2314yes—
327#399C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#397C2312yes—
341#397C2312yes—
342#397C2312yes—
343#397C2312yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2312yes—
351#397C2314yes—
352#397C2312yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#395C2312yes—
374#395C2312yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2312yes—
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#393C2312yes—
413#393C2312yes—
414#393C2312yes—
415#393C2312yes—
416#393C2312yes—
417#393C2312yes—
418#393C2312yes—
419#393C2314yes—
420#393C2312yes—
421#393C2312yes—
422#392C2314yes—
423#392C2314yes—
424#392C2312yes—
425#392C2314yes—
426#392C2312yes—
427#392C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2312yes—
431#392C2312yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
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#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2312yes—
509#386C2312yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2312yes—
548#385C2312yes—
549#385C2314yes—
550#385C2312yes—
551#385C2312yes—
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#384C2314yes—
567#383C2312yes—
568#383C2314yes—
569#382C2314yes—
570#382C2314yes—
571#381C2314yes—
572#381C2312yes—
573#381C2314yes—
574#381C2314yes—
575#381C2314yes—
576#381C2314yes—
577#380C2312yes—
578#380C2312yes—
579#380C2312yes—
580#380C2312yes—
581#380C2311yescharacteristic
582#380C2311yescharacteristic
583#380C2312yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#379C2314yes—
597#379C2314yes—
598#379C2312yes—
599#379C2314yes—
600#379C2312yes—
601#379C2314yes—
602#379C2312yes—
603#379C2312yes—
604#379C2312yes—
605#379C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618#376C2312yes—
619C2×#95C2312yes—
620C2×#95C2312yes—
621C2×#95C2314yes—
622C2×#95C2312yes—
623C25C2411yescharacteristic
624C25C2412yes—
625C25C2411yescharacteristic
626C25C2411yescharacteristic
627C25C2412yes—
628H(5,𝔽2)—464no—
629C2×#41—28no—
630C2×#41—48no—
631C2×#41—48no—
632C2×#41—48no—
633C2×#41—48no—
634C2×#41—48no—
635C2×#41—44no—
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×Q8C2412yes—
639C22×Q8C2411yescharacteristic
640C22×D4—28no—
641C22×D4—216no—
642C22×D4—24no—
643C22×D4—48no—
644C22×D4—44no—
645C22×D4—42no—
646C22×D4—42no—
647C22×D4—48no—
648C22×D4—48no—
649C22×D4—44no—
650C22×D4—44no—
651C22×D4—44no—
652C22×D4—44no—
653C22×D4—44no—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2414yes—
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2412yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C22×D4C2414yes—
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2414yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C22×D4C2412yes—
669C22×D4C2412yes—
670C22×D4C2411yescharacteristic
671C23×C4—44no—
672C23×C4—42no—
673C23×C4C2411yescharacteristic
674C23×C4C2414yes—
675C23×C4C2414yes—
676C23×C4C2414yes—
677C23×C4C2411yescharacteristic
678C23×C4C2411yescharacteristic
679C23×C4C2412yes—
680C23×C4C2412yes—
681C23×C4C2412yes—
682C23×C4C2412yes—
683C23×C4C2414yes—
684C23×C4C2414yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2414yes—
688C23×C4C2414yes—
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C4⋊Q8—44no—
692C4⋊Q8—48no—
693#126—44no—
694#126—48no—
695#126—48no—
696#125—48no—
697#124—44no—
698#124—48no—
699#124—48no—
700#124—48no—
701#123—48no—
702#123—48no—
703#123—48no—
704#123—48no—
705#123—48no—
706#123—44no—
707#123—48no—
708#123—48no—
709#123—48no—
710#123—84no—
711#123—84no—
712C22⋊Q8—28no—
713C22⋊Q8—48no—
714C22⋊Q8—42no—
715C22⋊Q8—44no—
716C22⋊Q8—48no—
717C22⋊Q8—44no—
718C22⋊Q8—44no—
719#121—44no—
720#121—44no—
721#121—48no—
722#121—48no—
723#121—48no—
724#121—48no—
725#121—48no—
726#121—48no—
727#121—48no—
728#121—48no—
729#121—48no—
730#121—48no—
731#121—42no—
732#121—48no—
733#121—48no—
734#120—216no—
735#120—216no—
736#120—48no—
737#120—44no—
738#120—48no—
739#120—48no—
740#120—82no—
741#120—82no—
742C4×D4—28no—
743C4×D4—48no—
744C4×D4—44no—
745C4×D4—48no—
746C4×D4—48no—
747C4×D4—48no—
748C4×D4—48no—
749C4×D4—84no—
750C4×D4—84no—
751#117—44no—
752#117—48no—
753#117—44no—
754C2×C4⋊C4—24no—
755C2×C4⋊C4—48no—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C22⋊C4—216no—
794C2×C22⋊C4—24no—
795C2×C22⋊C4—44no—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—44no—
798C2×C22⋊C4—48no—
799C2×C22⋊C4—42no—
800C2×C22⋊C4—84no—
801C2×C22⋊C4—84no—
802C2×C22⋊C4—82no—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C42C2414yes—
866C2×C42C2412yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873#95C2412yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2412yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
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#95C2412yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917C24—24no—
918C24—22no—
919C24—22no—
920C24—28no—
921C24—22no—
922C24—42no—
923C24—42no—
924C24—42no—
925C24—41no—
926C24—42no—
927C24—42no—
928C24—42no—
929C24—42no—
930C24—42no—
931C24—41no—
932C24—41no—
933C24—42no—
934C24—41no—
935C24—42no—
936C24—44no—
937C24—42no—
938C24—42no—
939C24—41no—
940C24—42no—
941C24—42no—
942C24—41no—
943C24H(5,𝔽2)18yes—
944C24C2512yes—
945C24C2512yes—
946C24C2512yes—
947C24C2511yescharacteristic
948C24C2514yes—
949C24C2512yes—
950#41—432no—
951#41—464no—
952#41—816no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—44no—
956C2×Q8—44no—
957C2×Q8—41no—
958C2×Q8—44no—
959C2×Q8—42no—
960C2×Q8—42no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—28no—
968C2×D4—28no—
969C2×D4—24no—
970C2×D4—28no—
971C2×D4—28no—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—24no—
976C2×D4—28no—
977C2×D4—28no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—42no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—42no—
1001C2×D4—42no—
1002C2×D4—44no—
1003C2×D4—41no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—42no—
1007C2×D4—44no—
1008C2×D4—464no—
1009C2×D4—416no—
1010C2×D4—432no—
1011C2×D4—432no—
1012C2×D4—88no—
1013C2×D4—88no—
1014C22×C4—22no—
1015C22×C4—24no—
1016C22×C4—28no—
1017C22×C4—24no—
1018C22×C4—22no—
1019C22×C4—28no—
1020C22×C4—28no—
1021C22×C4—22no—
1022C22×C4—28no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—24no—
1026C22×C4—42no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—42no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—42no—
1061C22×C4—88no—
1062C22×C4H(5,𝔽2)14yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—41no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—41no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—24no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—42no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
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—42no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C42—24no—
1180C42—28no—
1181C42—44no—
1182C42—44no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C23—28no—
1188C23—22no—
1189C23—24no—
1190C23—24no—
1191C23—22no—
1192C23—22no—
1193C23—24no—
1194C23—24no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—21no—
1200C23—24no—
1201C23—22no—
1202C23—24no—
1203C23—21no—
1204C23—22no—
1205C23—22no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—22no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—48no—
1220C23—48no—
1221C23—48no—
1222C23—48no—
1223C23—44no—
1224C23—44no—
1225C23—82no—
1226C23—82no—
1227C23—84no—
1228C23—84no—
1229C23—82no—
1230C23—82no—
1231C23—82no—
1232C23—82no—
1233C23—88no—
1234C23—88no—
1235C23—162no—
1236C23—162no—
1237C23—162no—
1238C23—162no—
1239C23—162no—
1240C23—162no—
1241C23—162no—
1242C23—162no—
1243C23—162no—
1244C23—162no—
1245C23C2×H(5,𝔽2)14yes—
1246C23C2×H(5,𝔽2)12yes—
1247C23C2×H(5,𝔽2)18yes—
1248C23C2611yescharacteristic
1249Q8—48no—
1250Q8—84no—
1251Q8—162no—
1252Q8—161no—
1253D4—216no—
1254D4—416no—
1255D4—416no—
1256D4—416no—
1257D4—416no—
1258D4—416no—
1259D4—88no—
1260D4—84no—
1261D4—88no—
1262D4—88no—
1263D4—88no—
1264D4—88no—
1265D4—88no—
1266D4—162no—
1267D4—161no—
1268D4—162no—
1269D4—164no—
1270C2×C4—28no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—21no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—21no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—44no—
1315C2×C4—416no—
1316C2×C4—48no—
1317C2×C4—48no—
1318C2×C4—84no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—88no—
1322C2×C4—82no—
1323C2×C4—82no—
1324C2×C4—88no—
1325C2×C4—88no—
1326C2×C4—162no—
1327C2×C4—164no—
1328C2×C4—164no—
1329C2×C4—164no—
1330C2×C4—162no—
1331C2×C4C2×H(5,𝔽2)14yes—
1332C2×C4#58514yes—
1333C22—28no—
1334C22—22no—
1335C22—24no—
1336C22—22no—
1337C22—22no—
1338C22—28no—
1339C22—24no—
1340C22—28no—
1341C22—24no—
1342C22—42no—
1343C22—44no—
1344C22—44no—
1345C22—42no—
1346C22—42no—
1347C22—44no—
1348C22—42no—
1349C22—42no—
1350C22—44no—
1351C22—42no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—44no—
1367C22—88no—
1368C22—168no—
1369C22—168no—
1370C22—164no—
1371C22—164no—
1372C22C22×H(5,𝔽2)11yescharacteristic
1373C22C22×H(5,𝔽2)12yes—
1374C22C2×#58512yes—
1375C22H(7,𝔽2)11yescharacteristic
1376C222−1+611yescharacteristic
1377C4—24no—
1378C4—24no—
1379C4—44no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C4—41no—
1384C4—41no—
1385C4—42no—
1386C4—44no—
1387C4—42no—
1388C4—44no—
1389C4—44no—
1390C4—44no—
1391C4—44no—
1392C4—44no—
1393C4—44no—
1394C2—44no—
1395C2—42no—
1396C2—48no—
1397C2—82no—
1398C2—82no—
1399C2—82no—
1400C2#6281711yescharacteristic
1401C2#6282411yescharacteristic
1402C2#6287511yescharacteristic
1403C2#6290112yes—
1404C2#6290512yes—
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. #58257C2semidirect
2. #57207C2semidirect
3. #56584C2semidirect
4. #56403C2semidirect
5. #51937C2semidirect
6. #50878C2semidirect
7. #49548C2semidirect
8. #49205C2semidirect
9. #48628C2semidirect
10. #47883C2semidirect
11. #46413C2semidirect
12. #43174C2semidirect
13. #43020C2semidirect
14. #41044C2semidirect
15. #40521C2semidirect
16. #40500C2semidirect
17. #37940C2semidirect
18. #37932C2semidirect
19. #36706C2semidirect
20. #35925C2semidirect
21. #35750C2semidirect
22. #35584C2semidirect
23. #35347C2semidirect
26. C2×#546C22semidirect
27. C2×#544C22semidirect
28. C2×#538C22semidirect
29. C2×#538C22semidirect
32. #2848C22semidirect
33. #2847C22semidirect
34. #2835C22semidirect
35. #2834C22semidirect
36. #2826C22semidirect
37. #2821C22semidirect
38. #2814C22semidirect
39. #2814C22semidirect
40. #2812C22semidirect
41. #2797C22semidirect
42. #2796C22semidirect
43. #2790C22semidirect
44. #2788C22semidirect
45. #2786C22semidirect
46. #2781C22semidirect
47. #2780C22semidirect
48. #2779C22semidirect
49. #2778C22semidirect
50. #2763C22semidirect
51. #2757C22semidirect
52. #2757C22semidirect
53. #2753C22semidirect
54. #2750C22semidirect
55. #2749C22semidirect
56. #2746C22semidirect
57. #2746C22semidirect
58. #2745C22semidirect
59. #2743C22semidirect
60. #2736C22semidirect
61. #2735C22semidirect
62. #2734C22semidirect
63. #2720C22semidirect
64. #2718C22semidirect
65. #2718C22semidirect
66. #2717C22semidirect
67. #2715C22semidirect
68. #2708C22semidirect
69. #2708C22semidirect
70. #2707C22semidirect
71. #2706C22semidirect
72. #2706C22semidirect
73. #2701C22semidirect
74. #2697C22semidirect
75. #2695C22semidirect
76. #2693C22semidirect
77. #2691C22semidirect
78. #2691C22semidirect
79. #2691C22semidirect
80. #2688C22semidirect
81. #2687C22semidirect
82. #2687C22semidirect
83. #2686C22semidirect
84. #2682C22semidirect
85. #2680C22semidirect
86. #2678C22semidirect
87. #2678C22semidirect
88. #2676C22semidirect
89. #2675C22semidirect
90. #2674C22semidirect
91. #2672C22semidirect
92. #2672C22semidirect
93. #2671C22semidirect
94. #2671C22semidirect
95. #2670C22semidirect
96. #2668C22semidirect
97. #2667C22semidirect
98. #2666C22semidirect
99. #2661C22semidirect
100. #2653C22semidirect
101. #2648C22semidirect
102. #2646C22semidirect
103. #2646C22semidirect
104. #2640C22semidirect
105. #2639C22semidirect
106. #2638C22semidirect
107. #2635C22semidirect
108. #2631C22semidirect
109. #2626C22semidirect
110. #2626C22semidirect
111. #2617C22semidirect
112. #2617C22semidirect
114. #2615C22semidirect
115. #2613C22semidirect
116. #2609C22semidirect
117. #2603C22semidirect
118. #2602C22semidirect
119. #2600C22semidirect
120. #2598C22semidirect
121. #2579C22semidirect
122. #2578C22semidirect
123. #2574C22semidirect
124. #2573C22semidirect
125. #2561C22semidirect
126. #2561C22semidirect
127. #2557C22semidirect
128. #2557C22semidirect
129. #2555C22semidirect
130. #2553C22semidirect
131. #2553C22semidirect
132. #2537C22semidirect
133. #2534C22semidirect
134. #2531C22semidirect
135. #2510C22semidirect
136. #2505C22semidirect
137. #2491C22semidirect
138. #2491C22semidirect
139. #2490C22semidirect
140. #2490C22semidirect
141. #2483C22semidirect
142. #2481C22semidirect
143. #2480C22semidirect
144. #2480C22semidirect
145. #2477C22semidirect
146. #2476C22semidirect
147. #2473C22semidirect
148. #2470C22semidirect
149. #2468C22semidirect
150. #2468C22semidirect
151. #2464C22semidirect
152. #2464C22semidirect
153. #2460C22semidirect
154. #2457C22semidirect
155. #2456C22semidirect
156. #2456C22semidirect
157. #2455C22semidirect
158. #2450C22semidirect
159. #2443C22semidirect
160. #2440C22semidirect
161. #2437C22semidirect
163. #2435C22semidirect
164. #2432C22semidirect
165. #2432C22semidirect
168. #2430C22semidirect
169. #2430C22semidirect
170. #2425C22semidirect
171. #2424C22semidirect
172. #2420C22semidirect
173. #2419C22semidirect
174. #2418C22semidirect
175. #2418C22semidirect
176. #2418C22semidirect
177. #2414C22semidirect
178. #2412C22semidirect
179. #2411C22semidirect
184. #2410C22semidirect
185. #2410C22semidirect
187. #2407C22semidirect
189. #2406C22semidirect
195. #2392C22semidirect
197. C2×#394C22semidirect
198. #2378C22semidirect
199. #2377C22semidirect
200. #2358C22semidirect
201. #2358C22semidirect
202. #2353C22semidirect
203. #2349C22semidirect
204. #2343C22semidirect
205. #2342C22semidirect
207. D4×C22⋊C4C22semidirect
208. #2329C22semidirect
209. #2325C22semidirect
210. #2321C22semidirect
211. #2315C22semidirect
212. #2315C22semidirect
213. #2315C22semidirect
214. #2309C22semidirect
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
#572072
#565842
#564032
#519372
#508782
#495482
#492052
#486282
#478832
#464132
#431742
#430202
#410442
#405212
#405002
#379402
#379322
#367062
#359252
#357502
#355842
#353472