Finite Group Databasebeta

← #8934701

Subgroups — #8934701

Order 512.

4894 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60029C212yesmaximal, complemented
2#59841C212yesmaximal, complemented
3#59743C212yesmaximal, complemented
4#59606C214yesmaximal, complemented
5#59135C212yesmaximal, complemented
6#52083C211yesmaximal, characteristic, complemented
7#51999C212yesmaximal, complemented
8#51783C212yesmaximal, complemented
9#51749C211yesmaximal, characteristic, complemented
10#51418C212yesmaximal, complemented
11#51142C214yesmaximal, complemented
12#50313C214yesmaximal, complemented
13#49859C214yesmaximal, complemented
14#49573C214yesmaximal, complemented
15#49252C214yesmaximal, complemented
16#48410C214yesmaximal, complemented
17#48044C214yesmaximal, complemented
18#47664C212yesmaximal, complemented
19#47625C214yesmaximal, complemented
20#35678C212yesmaximal, complemented
21#35667C211yesmaximal, characteristic, complemented
22#35475C214yesmaximal, complemented
23#35422C212yesmaximal, complemented
24C2×H(3,𝔽4)C2211yescharacteristic
25C2×#560C2212yescomplemented
26C2×#555C2212yes—
27C2×#555C2211yescharacteristic, complemented
28C2×#540C2212yes—
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic, complemented
32C2×#519C2211yescharacteristic, complemented
33#2832C2212yescomplemented
34#2803C2214yescomplemented
35#2800C2214yescomplemented
36#2799C2212yescomplemented
37#2791C2214yescomplemented
38#2790C2214yescomplemented
39#2786C2214yes—
40#2783C2214yescomplemented
41#2772C2214yescomplemented
42#2772C2214yescomplemented
43#2764C2214yescomplemented
44#2761C2214yescomplemented
45#2756C2214yescomplemented
46#2753C2214yes—
47#2751C2214yescomplemented
48#2742C2212yescomplemented
49#2740C2214yescomplemented
50#2733C2212yes—
51#2733C2212yes—
52#2731C2212yes—
53#2731C2212yes—
54#2731C2214yescomplemented
55#2731C2212yescomplemented
56#2731C2212yescomplemented
57#2725C2214yescomplemented
58#2716C2214yescomplemented
59#2712C2214yes—
60#2709C2212yescomplemented
61#2708C2214yescomplemented
62#2705C2214yes—
63#2703C2214yes—
64#2703C2214yes—
65#2702C2214yescomplemented
66#2700C2214yes—
67#2699C2214yescomplemented
68#2699C2214yescomplemented
69#2697C2212yescomplemented
70#2695C2214yescomplemented
71#2691C2214yescomplemented
72#2688C2214yes—
73#2687C2214yescomplemented
74#2684C2212yes—
75#2682C2214yes—
76#2678C2214yes—
77#2678C2214yes—
78#2678C2214yescomplemented
79#2676C2214yes—
80#2676C2214yes—
81#2676C2214yescomplemented
82#2675C2212yes—
83#2673C2214yescomplemented
84#2670C2214yes—
85#2669C2214yes—
86#2661C2214yes—
87#2661C2214yes—
88#2651C2214yes—
89#2640C2212yes—
90#2631C2212yes—
91#2620C2214yes—
92#2618C2214yes—
93#2610C2214yes—
94#2610C2212yes—
95#2609C2214yescomplemented
96#2608C2212yescomplemented
97#2602C2214yes—
98#2602C2214yescomplemented
99#2598C2212yescomplemented
100#2596C2214yescomplemented
101#2589C2214yescomplemented
102#2587C2214yescomplemented
103#2583C2214yescomplemented
104#2577C2214yescomplemented
105#2574C2214yescomplemented
106#2572C2212yes—
107#2572C2214yescomplemented
108#2565C2212yescomplemented
109#2565C2212yescomplemented
110#2563C2214yescomplemented
111#2560C2214yes—
112#2559C2214yes—
113#2559C2214yescomplemented
114#2558C2214yescomplemented
115#2557C2214yes—
116#2557C2214yes—
117#2554C2214yes—
118#2554C2214yes—
119#2554C2214yescomplemented
120#2548C2212yes—
121#2548C2212yes—
122#2546C2212yescomplemented
123#2546C2212yescomplemented
124#2545C2212yes—
125#2545C2212yes—
126#2539C2212yescomplemented
127#2534C2214yescomplemented
128#2533C2214yescomplemented
129#2532C2214yescomplemented
130#2525C2214yescomplemented
131#2520C2214yescomplemented
132#2518C2214yes—
133#2518C2214yescomplemented
134#2518C2214yescomplemented
135#2516C2214yescomplemented
136#2515C2214yescomplemented
137#2512C2214yescomplemented
138#2500C2212yes—
139#2500C2212yescomplemented
140#2491C2214yes—
141#2491C2214yescomplemented
142#2491C2214yescomplemented
143#2481C2214yescomplemented
144#2480C2214yescomplemented
145#2477C2214yescomplemented
146#2476C2214yes—
147#2476C2214yescomplemented
148#2476C2214yescomplemented
149#2476C2214yescomplemented
150#2476C2214yescomplemented
151#2476C2214yescomplemented
152#2474C2214yes—
153#2472C2214yes—
154#2472C2214yescomplemented
155#2471C2214yescomplemented
156#2467C2214yes—
157#2466C2214yes—
158#2463C2212yescomplemented
159#2461C2214yes—
160#2459C2214yescomplemented
161#2459C2214yescomplemented
162#2458C2214yescomplemented
163#2458C2214yescomplemented
164#2458C2214yescomplemented
165#2458C2214yescomplemented
166#2457C2214yes—
167#2457C2214yescomplemented
168#2455C2212yes—
169#2439C2214yescomplemented
170#2439C2214yescomplemented
171#2436C2212yes—
172#2436C2214yescomplemented
173#2436C2212yescomplemented
174#2431C2212yes—
175#2429C2214yescomplemented
176#2429C2214yescomplemented
177#2428C2214yes—
178#2428C2214yes—
179#2424C2214yes—
180#2424C2214yes—
181#2424C2214yescomplemented
182#2416C2214yes—
183#2416C2214yescomplemented
184#2416C2214yescomplemented
185#2413C2214yescomplemented
186#2413C2214yescomplemented
187#2411C2214yes—
188#2404C2212yes—
189#2381C2211yescharacteristic, complemented
190#2378C2214yescomplemented
191#2375C2214yescomplemented
192#2374C2214yescomplemented
193#2374C2212yescomplemented
194#2373C2214yescomplemented
195#2372C2211yescharacteristic
196#2369C2212yescomplemented
197#2361C2214yescomplemented
198#2361C2214yescomplemented
199#2352C2214yescomplemented
200#2352C2214yescomplemented
201#2344C2214yescomplemented
202#2337C2214yescomplemented
203#2335C2214yes—
204#2333C2214yes—
205#2333C2214yes—
206#2333C2212yescomplemented
207#2326C2212yes—
208#2326C2212yescomplemented
209#2310C2211yescharacteristic, complemented
210C4×#126C2214yescomplemented
211C4×#124C2212yes—
212C4×#124C2212yescomplemented
213C4×#121C2214yescomplemented
214#2298C2212yescomplemented
215#2297C2211yescharacteristic
216#2296C2211yescharacteristic, complemented
217#2293C2214yescomplemented
218#2273C2212yescomplemented
219C22×#41C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222H(3,𝔽4)—44no—
223#560—48no—
224#555—48no—
225#555—44no—
226#540—48no—
227#536—44no—
228#536—44no—
229C2×C4⋊Q8—44no—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2312yes—
236C2×#127C2312yes—
237C2×#127C2312yes—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#125C2312yes—
242C2×#124C2312yes—
243C2×#124C2311yescharacteristic
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248C2×#124C2312yes—
249C2×#124C2311yescharacteristic
250C2×#124C2312yes—
251C2×#124C2314yes—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2312yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#120C2314yes—
280C2×#120C2312yes—
281C2×#120C2312yes—
282C2×#120C2314yes—
283C2×#120C2314yes—
284#519—44no—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×#117C2312yes—
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2314yes—
301C2×#117C2314yes—
302C2×#117C2314yes—
303C2×#117C2312yes—
304C22×C4⋊C4C2314yes—
305C22×C4⋊C4C2314yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2314yes—
308C22×C42C2311yescharacteristic
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#399C2314yes—
317#399C2312yes—
318#398C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#396C2314yes—
344#396C2314yes—
345#396C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#395C2314yes—
356#395C2312yes—
357#394C2314yes—
358#394C2312yes—
359#394C2314yes—
360#394C2312yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
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#393C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2312yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#392C2312yes—
397#392C2314yes—
398#392C2314yes—
399#392C2314yes—
400#392C2312yes—
401#392C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#390C2314yes—
424#390C2314yes—
425#390C2314yes—
426#390C2312yes—
427#390C2312yes—
428#390C2314yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2314yes—
443#390C2312yes—
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#388C2314yes—
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#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#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2312yes—
553#386C2312yes—
554#386C2314yes—
555#386C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2312yes—
568#385C2312yes—
569#384C2312yes—
570#384C2312yes—
571#383C2314yes—
572#383C2314yes—
573#383C2312yes—
574#382C2314yes—
575#382C2314yes—
576#382C2312yes—
577#382C2312yes—
578#381C2314yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2312yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#379C2314yes—
590#379C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2312yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2312yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2312yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620#376C2312yes—
621#376C2312yes—
622C43C2312yes—
623C25C2412yes—
624C2×#41—42no—
625C2×#41—42no—
626C2×#41—42no—
627C22×Q8—24no—
628C22×Q8—42no—
629C22×Q8—42no—
630C22×Q8—42no—
631C22×Q8—42no—
632C22×Q8—42no—
633C22×Q8C2412yes—
634C22×Q8C2411yescharacteristic
635C22×Q8C2412yes—
636C22×Q8C2412yes—
637C22×Q8C2411yescharacteristic
638C22×Q8C2412yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2414yes—
646C22×D4C2411yescharacteristic
647C22×D4C2412yes—
648C22×D4C2412yes—
649C22×D4C2414yes—
650C22×D4C2412yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2412yes—
656C23×C4C2411yescharacteristic
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2414yes—
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2414yes—
665C23×C4C2412yes—
666C23×C4C2414yes—
667C4⋊Q8—28no—
668C4⋊Q8—24no—
669C4⋊Q8—44no—
670C4⋊Q8—44no—
671C4⋊Q8—42no—
672C4⋊Q8—48no—
673#127—44no—
674#127—44no—
675#126—48no—
676#126—48no—
677#126—48no—
678#125—44no—
679#124—24no—
680#124—28no—
681#124—28no—
682#124—44no—
683#124—48no—
684#124—44no—
685#124—42no—
686#124—44no—
687#124—48no—
688#124—44no—
689#124—44no—
690#124—48no—
691#123—28no—
692#123—48no—
693#123—48no—
694#123—48no—
695#123—48no—
696#123—48no—
697#123—44no—
698#123—48no—
699C22⋊Q8—48no—
700C22⋊Q8—48no—
701C22⋊Q8—48no—
702#121—216no—
703#121—48no—
704#121—48no—
705#121—44no—
706#121—48no—
707#121—48no—
708#121—48no—
709#121—48no—
710#121—48no—
711#121—48no—
712#121—48no—
713#121—44no—
714#121—44no—
715#121—48no—
716#120—48no—
717#120—48no—
718#120—48no—
719#120—44no—
720#120—44no—
721C4×Q8—44no—
722C4×Q8—44no—
723C4×Q8—44no—
724C4×Q8—44no—
725C4×D4—44no—
726C4×D4—48no—
727C4×D4—44no—
728C4×D4—44no—
729C4×D4—48no—
730C4×D4—48no—
731C4×D4—48no—
732#117—24no—
733#117—28no—
734#117—42no—
735#117—48no—
736#117—48no—
737#117—48no—
738#117—42no—
739#117—44no—
740C2×C4⋊C4—48no—
741C2×C4⋊C4—48no—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C22⋊C4—48no—
780C2×C22⋊C4—44no—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
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⋊C4C2411yescharacteristic
836C2×C42—42no—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2412yes—
840C2×C42C2411yescharacteristic
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2411yescharacteristic
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2414yes—
847C2×C42C2411yescharacteristic
848C2×C42C2411yescharacteristic
849C2×C42C2412yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2412yes—
861#95C2412yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2412yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
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#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2414yes—
905C24—42no—
906C24—44no—
907C24—42no—
908C24—42no—
909C24—44no—
910C24C2512yes—
911C24C2514yes—
912C24C2514yes—
913C24C2511yescharacteristic
914#41—88no—
915C2×Q8—24no—
916C2×Q8—22no—
917C2×Q8—24no—
918C2×Q8—22no—
919C2×Q8—24no—
920C2×Q8—24no—
921C2×Q8—41no—
922C2×Q8—42no—
923C2×Q8—41no—
924C2×Q8—41no—
925C2×Q8—41no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—42no—
929C2×Q8—41no—
930C2×Q8—42no—
931C2×Q8—41no—
932C2×Q8—44no—
933C2×Q8—42no—
934C2×Q8—416no—
935C2×Q8—88no—
936C2×Q8H(5,𝔽2)14yes—
937C2×D4—28no—
938C2×D4—24no—
939C2×D4—28no—
940C2×D4—24no—
941C2×D4—22no—
942C2×D4—28no—
943C2×D4—24no—
944C2×D4—28no—
945C2×D4—44no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—42no—
958C2×D4—41no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—41no—
962C2×D4—42no—
963C2×D4—44no—
964C2×D4—42no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—44no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—42no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—28no—
990C22×C4—28no—
991C22×C4—28no—
992C22×C4—24no—
993C22×C4—28no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—42no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2514yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2514yes—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C22⋊C4—24no—
1071C22⋊C4—22no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—42no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
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—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4H(5,𝔽2)14yes—
1125C42—24no—
1126C42—24no—
1127C42—24no—
1128C42—24no—
1129C42—24no—
1130C42—24no—
1131C42—22no—
1132C42—22no—
1133C42—42no—
1134C42—42no—
1135C42—44no—
1136C42—41no—
1137C42—41no—
1138C42—42no—
1139C42—42no—
1140C42—44no—
1141C42—44no—
1142C42—44no—
1143C42—42no—
1144C42—42no—
1145C42—44no—
1146C42—44no—
1147C42—44no—
1148C42—42no—
1149C23—21no—
1150C23—24no—
1151C23—21no—
1152C23—22no—
1153C23—22no—
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—24no—
1168C23—24no—
1169C23—24no—
1170C23—22no—
1171C23—48no—
1172C23—164no—
1173C23—164no—
1174C23—162no—
1175C23—162no—
1176C23C2×H(5,𝔽2)12yes—
1177C23C2611yescharacteristic
1178Q8—44no—
1179Q8—48no—
1180Q8—44no—
1181Q8—84no—
1182Q8—84no—
1183Q8—82no—
1184Q8—162no—
1185D4—88no—
1186D4—88no—
1187D4—84no—
1188D4—84no—
1189D4—82no—
1190D4—88no—
1191D4—88no—
1192D4—84no—
1193D4—84no—
1194D4—164no—
1195D4—162no—
1196D4—164no—
1197D4—164no—
1198D4—162no—
1199D4—164no—
1200D4—164no—
1201C2×C4—28no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—24no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—21no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
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—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—48no—
1249C2×C4—48no—
1250C2×C4—88no—
1251C2×C4—88no—
1252C2×C4—88no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—88no—
1256C2×C4—164no—
1257C2×C4—162no—
1258C2×C4C2×H(5,𝔽2)12yes—
1259C2×C4C2×H(5,𝔽2)14yes—
1260C2×C4C2×H(5,𝔽2)14yes—
1261C2×C4#58512yes—
1262C2×C4#58518yes—
1263C22—24no—
1264C22—22no—
1265C22—42no—
1266C22—42no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—42no—
1278C22—44no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—44no—
1283C22—42no—
1284C22—44no—
1285C22—44no—
1286C22—168no—
1287C22C22×H(5,𝔽2)11yescharacteristic
1288C22C22×H(5,𝔽2)11yescharacteristic
1289C22C2×#58514yes—
1290C22C2×#58511yescharacteristic
1291C4—28no—
1292C4—24no—
1293C4—22no—
1294C4—22no—
1295C4—24no—
1296C4—44no—
1297C4—42no—
1298C4—44no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—42no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C4—44no—
1309C4—44no—
1310C2—42no—
1311C2—84no—
1312C2—84no—
1313C2—82no—
1314C2#6281811yescharacteristic
1315C2#6283912yes—
1316C2#6302012yes—
1317C2#6302412yes—
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. #60029C2semidirect
2. #59841C2semidirect
3. #59743C2semidirect
4. #59606C2semidirect
5. #59135C2semidirect
6. #52083C2semidirect
7. #51999C2semidirect
8. #51783C2semidirect
9. #51749C2semidirect
10. #51418C2semidirect
11. #51142C2semidirect
12. #50313C2semidirect
13. #49859C2semidirect
14. #49573C2semidirect
15. #49252C2semidirect
16. #48410C2semidirect
17. #48044C2semidirect
18. #47664C2semidirect
19. #47625C2semidirect
20. #35678C2semidirect
21. #35667C2semidirect
22. #35475C2semidirect
23. #35422C2semidirect
25. C2×#560C22semidirect
27. C2×#555C22semidirect
31. C22×C4⋊Q8C22semidirect
32. C2×#519C22semidirect
33. #2832C22semidirect
34. #2803C22semidirect
35. #2800C22semidirect
36. #2799C22semidirect
37. #2791C22semidirect
38. #2790C22semidirect
40. #2783C22semidirect
41. #2772C22semidirect
42. #2772C22semidirect
43. #2764C22semidirect
44. #2761C22semidirect
45. #2756C22semidirect
47. #2751C22semidirect
48. #2742C22semidirect
49. #2740C22semidirect
54. #2731C22semidirect
55. #2731C22semidirect
56. #2731C22semidirect
57. #2725C22semidirect
58. #2716C22semidirect
60. #2709C22semidirect
61. #2708C22semidirect
65. #2702C22semidirect
67. #2699C22semidirect
68. #2699C22semidirect
69. #2697C22semidirect
70. #2695C22semidirect
71. #2691C22semidirect
73. #2687C22semidirect
78. #2678C22semidirect
81. #2676C22semidirect
83. #2673C22semidirect
95. #2609C22semidirect
96. #2608C22semidirect
98. #2602C22semidirect
99. #2598C22semidirect
100. #2596C22semidirect
101. #2589C22semidirect
102. #2587C22semidirect
103. #2583C22semidirect
104. #2577C22semidirect
105. #2574C22semidirect
107. #2572C22semidirect
108. #2565C22semidirect
109. #2565C22semidirect
110. #2563C22semidirect
113. #2559C22semidirect
114. #2558C22semidirect
119. #2554C22semidirect
122. #2546C22semidirect
123. #2546C22semidirect
126. #2539C22semidirect
127. #2534C22semidirect
128. #2533C22semidirect
129. #2532C22semidirect
130. #2525C22semidirect
131. #2520C22semidirect
133. #2518C22semidirect
134. #2518C22semidirect
135. #2516C22semidirect
136. #2515C22semidirect
137. #2512C22semidirect
139. #2500C22semidirect
141. #2491C22semidirect
142. #2491C22semidirect
143. #2481C22semidirect
144. #2480C22semidirect
145. #2477C22semidirect
147. #2476C22semidirect
148. #2476C22semidirect
149. #2476C22semidirect
150. #2476C22semidirect
151. #2476C22semidirect
154. #2472C22semidirect
155. #2471C22semidirect
158. #2463C22semidirect
160. #2459C22semidirect
161. #2459C22semidirect
162. #2458C22semidirect
163. #2458C22semidirect
164. #2458C22semidirect
165. #2458C22semidirect
167. #2457C22semidirect
169. #2439C22semidirect
170. #2439C22semidirect
172. #2436C22semidirect
173. #2436C22semidirect
175. #2429C22semidirect
176. #2429C22semidirect
181. #2424C22semidirect
183. #2416C22semidirect
184. #2416C22semidirect
185. #2413C22semidirect
186. #2413C22semidirect
189. #2381C22semidirect
190. #2378C22semidirect
191. #2375C22semidirect
192. #2374C22semidirect
193. #2374C22semidirect
194. #2373C22semidirect
196. #2369C22semidirect
197. #2361C22semidirect
198. #2361C22semidirect
199. #2352C22semidirect
200. #2352C22semidirect
201. #2344C22semidirect
202. #2337C22semidirect
206. #2333C22semidirect
208. #2326C22semidirect
209. #2310C22semidirect
210. C4×#126C22semidirect
212. C4×#124C22semidirect
213. C4×#121C22semidirect
214. #2298C22semidirect
216. #2296C22semidirect
217. #2293C22semidirect
218. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#600292
#598412
#597432
#596062
#591352
#520832
#519992
#517832
#517492
#514182
#511422
#503132
#498592
#495732
#492522
#484102
#480442
#476642
#476252
#356782
#356672
#354752
#354222