Finite Group Databasebeta

← #9040193

Subgroups — #9040193

Order 512.

5782 conjugacy classes of subgroups.

The subgroup lattice has 1410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51993C212yesmaximal, complemented
2#51940C212yesmaximal, complemented
3#50952C214yesmaximal, complemented
4#50659C212yesmaximal, complemented
5#49597C212yesmaximal, complemented
6#49548C212yesmaximal, complemented
7#48937C214yesmaximal, complemented
8#48930C214yesmaximal, complemented
9#48773C212yesmaximal, complemented
10#48647C214yesmaximal, complemented
11#48351C214yesmaximal, complemented
12#47994C214yesmaximal, complemented
13#47933C214yesmaximal, complemented
14#47848C212yesmaximal, complemented
15#35913C212yesmaximal, complemented
16#35764C214yesmaximal, complemented
17#35750C212yesmaximal, complemented
18#35730C212yesmaximal, complemented
19#35716C214yesmaximal, complemented
20#35584C211yesmaximal, characteristic, complemented
21#35371C214yesmaximal, complemented
22#35355C211yesmaximal, characteristic, complemented
23#35347C211yesmaximal, characteristic, complemented
24C22×H(5,𝔽2)C2211yescharacteristic, complemented
25C2×H(3,𝔽4)C2212yescomplemented
26C2×#551C2212yescomplemented
27C2×#547C2212yes—
28C2×#546C2214yescomplemented
29C2×#544C2211yescharacteristic, complemented
30C2×#534C2212yes—
31C22×#121C2211yescharacteristic
32C2×#518C2211yescharacteristic, complemented
33#2804C2212yescomplemented
34#2797C2214yescomplemented
35#2797C2214yescomplemented
36#2796C2214yescomplemented
37#2775C2214yescomplemented
38#2763C2214yescomplemented
39#2759C2214yescomplemented
40#2757C2214yescomplemented
41#2749C2214yescomplemented
42#2748C2212yescomplemented
43#2746C2214yescomplemented
44#2741C2214yescomplemented
45#2737C2214yescomplemented
46#2736C2214yescomplemented
47#2734C2214yescomplemented
48#2724C2212yescomplemented
49#2723C2214yescomplemented
50#2720C2214yescomplemented
51#2718C2214yescomplemented
52#2717C2212yescomplemented
53#2717C2212yescomplemented
54#2714C2214yescomplemented
55#2712C2214yescomplemented
56#2710C2214yescomplemented
57#2710C2214yescomplemented
58#2710C2214yescomplemented
59#2708C2214yescomplemented
60#2707C2214yescomplemented
61#2700C2214yescomplemented
62#2697C2212yescomplemented
63#2697C2212yescomplemented
64#2697C2214yescomplemented
65#2696C2214yescomplemented
66#2686C2214yescomplemented
67#2686C2214yescomplemented
68#2685C2214yescomplemented
69#2684C2214yescomplemented
70#2684C2214yescomplemented
71#2680C2214yescomplemented
72#2679C2212yescomplemented
73#2678C2214yescomplemented
74#2676C2214yescomplemented
75#2674C2214yescomplemented
76#2672C2214yescomplemented
77#2672C2214yescomplemented
78#2668C2214yescomplemented
79#2665C2212yescomplemented
80#2663C2214yescomplemented
81#2661C2214yescomplemented
82#2653C2214yescomplemented
83#2650C2214yescomplemented
84#2648C2214yescomplemented
85#2638C2212yescomplemented
86#2638C2212yescomplemented
87#2628C2212yescomplemented
88#2622C2214yescomplemented
89#2617C2214yescomplemented
90#2616C2212yescomplemented
91#2613C2214yescomplemented
92#2602C2214yescomplemented
93#2602C2214yescomplemented
94#2597C2214yescomplemented
95#2586C2214yescomplemented
96#2579C2212yescomplemented
97#2578C2214yescomplemented
98#2578C2214yescomplemented
99#2576C2214yescomplemented
100#2576C2214yescomplemented
101#2575C2214yescomplemented
102#2572C2214yescomplemented
103#2563C2212yescomplemented
104#2561C2212yescomplemented
105#2561C2212yescomplemented
106#2561C2212yescomplemented
107#2560C2214yescomplemented
108#2559C2214yescomplemented
109#2559C2214yescomplemented
110#2557C2214yescomplemented
111#2557C2214yescomplemented
112#2555C2214yescomplemented
113#2553C2214yescomplemented
114#2539C2214yescomplemented
115#2535C2212yescomplemented
116#2521C2214yescomplemented
117#2518C2214yescomplemented
118#2510C2214yescomplemented
119#2510C2214yescomplemented
120#2505C2214yescomplemented
121#2500C2214yescomplemented
122#2491C2214yescomplemented
123#2491C2214yescomplemented
124#2490C2214yescomplemented
125#2490C2214yescomplemented
126#2488C2214yescomplemented
127#2480C2214yescomplemented
128#2480C2214yescomplemented
129#2477C2214yescomplemented
130#2476C2214yescomplemented
131#2476C2214yescomplemented
132#2476C2214yescomplemented
133#2473C2214yescomplemented
134#2472C2214yescomplemented
135#2472C2214yescomplemented
136#2472C2214yescomplemented
137#2471C2214yescomplemented
138#2470C2214yescomplemented
139#2470C2214yescomplemented
140#2467C2214yescomplemented
141#2464C2214yescomplemented
142#2461C2214yescomplemented
143#2460C2214yescomplemented
144#2459C2214yescomplemented
145#2457C2214yescomplemented
146#2457C2214yescomplemented
147#2457C2214yescomplemented
148#2456C2214yescomplemented
149#2447C2214yescomplemented
150#2440C2214yescomplemented
151#2437C2214yescomplemented
152#2435C2212yescomplemented
153#2435C2212yescomplemented
154#2432C2214yescomplemented
155#2432C2214yescomplemented
156#2430C2214yes—
157#2430C2214yescomplemented
158#2430C2214yescomplemented
159#2427C2214yescomplemented
160#2427C2214yescomplemented
161#2424C2214yescomplemented
162#2422C2214yescomplemented
163#2420C2214yescomplemented
164#2418C2214yescomplemented
165#2418C2214yescomplemented
166#2412C2214yescomplemented
167#2410C2214yes—
168#2410C2214yes—
169#2410C2214yes—
170#2410C2214yescomplemented
171#2408C2212yes—
172#2408C2214yescomplemented
173#2407C2214yescomplemented
174#2406C2214yescomplemented
175#2406C2212yescomplemented
176#2405C2212yescomplemented
177#2405C2214yescomplemented
178#2405C2211yescharacteristic, complemented
179#2405C2211yescharacteristic, complemented
180#2405C2214yescomplemented
181#2404C2212yes—
182#2404C2212yescomplemented
183#2403C2212yes—
184#2403C2211yescharacteristic, complemented
185#2403C2211yescharacteristic, complemented
186#2395C2214yescomplemented
187#2392C2212yescomplemented
188#2388C2212yes—
189#2388C2212yescomplemented
190C2×#394C2214yescomplemented
191#2383C2214yescomplemented
192#2378C2212yescomplemented
193#2376C2212yescomplemented
194#2375C2212yescomplemented
195#2375C2212yescomplemented
196#2368C2214yescomplemented
197#2361C2214yescomplemented
198#2359C2214yescomplemented
199#2358C2212yescomplemented
200#2358C2212yescomplemented
201#2358C2212yescomplemented
202#2357C2212yescomplemented
203#2352C2214yescomplemented
204#2342C2214yescomplemented
205#2339C2212yescomplemented
206D4×C22⋊C4C2214yescomplemented
207#2329C2214yescomplemented
208#2321C2212yescomplemented
209#2321C2214yescomplemented
210#2318C2214yescomplemented
211#2312C2211yescharacteristic, complemented
212#2309C2212yescomplemented
213#2308C2211yescharacteristic, complemented
214C4×#120C2212yescomplemented
215C2×#386C2212yescomplemented
216#2280C2212yescomplemented
217#2274C2211yescharacteristic, complemented
218#2273C2214yescomplemented
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
230C23×D4C2311yescharacteristic
231C24×C4C2311yescharacteristic
232H(3,𝔽4)—48no—
233#551—48no—
234#547—48no—
235#546—416no—
236#544—44no—
237#534—48no—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#125C2314yes—
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248C2×#124C2314yes—
249C2×#124C2312yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2312yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2312yes—
259C2×#123C2312yes—
260C2×#123C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121—44no—
269C2×#121C2314yes—
270C2×#121C2314yes—
271C2×#121C2314yes—
272C2×#121C2314yes—
273C2×#121C2314yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#120C2314yes—
279C2×#120C2312yes—
280C2×#120C2312yes—
281C2×#120C2312yes—
282C2×#120C2314yes—
283C2×#120C2312yes—
284C2×#120C2312yes—
285C2×#120C2312yes—
286C2×#120C2314yes—
287C2×#120C2312yes—
288C2×#120C2312yes—
289C2×#120C2314yes—
290#518—44no—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2314yes—
304C2×#117C2312yes—
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊C4C2314yes—
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2314yes—
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2312yes—
311C22×C22⋊C4C2312yes—
312C22×C22⋊C4C2314yes—
313C22×C22⋊C4C2314yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2314yes—
316C22×C22⋊C4C2311yescharacteristic
317#401C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#398C2312yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#397C2314yes—
334#397C2312yes—
335#397C2312yes—
336#397C2312yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
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#395C2312yes—
362#395C2314yes—
363#395C2314yes—
364#395C2314yes—
365#395C2312yes—
366#395C2314yes—
367#395C2314yes—
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#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2312yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2312yes—
403#393C2312yes—
404#393C2312yes—
405#393C2312yes—
406#393C2314yes—
407#393C2312yes—
408#393C2312yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#392C2312yes—
414#392C2314yes—
415#392C2312yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2312yes—
423#392C2314yes—
424#392C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2312yes—
435#390C2312yes—
436#390C2314yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2314yes—
444#390C2314yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#388C2314yes—
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#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2312yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2312yes—
522#386C2314yes—
523#386C2314yes—
524#386C2312yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2312yes—
531#386C2312yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2312yes—
536#386C2312yes—
537#386C2314yes—
538#386C2314yes—
539#386C2312yes—
540#386C2314yes—
541#386C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2312yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
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#384C2314yes—
566#383C2314yes—
567#383C2314yes—
568#382C2314yes—
569#382C2314yes—
570#382C2312yes—
571#381C2314yes—
572#381C2314yes—
573#381C2312yes—
574#381C2314yes—
575#381C2314yes—
576#381C2312yes—
577#380C2314yes—
578#380C2314yes—
579#380C2312yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2314yes—
586#380C2314yes—
587#379C2314yes—
588#379C2314yes—
589#379C2314yes—
590#379C2312yes—
591#379C2311yescharacteristic
592#379C2311yescharacteristic
593#379C2314yes—
594#379C2312yes—
595#379C2314yes—
596#379C2314yes—
597#379C2312yes—
598#379C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2312yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C2×#95C2314yes—
623C2×#95C2314yes—
624C25C2411yescharacteristic
625C25C2412yes—
626C25C2411yescharacteristic
627C25C2411yescharacteristic
628C25C2411yescharacteristic
629C25C2412yes—
630H(5,𝔽2)—464no—
631C2×#41—28no—
632C2×#41—48no—
633C2×#41—48no—
634C2×#41—48no—
635C2×#41—48no—
636C2×#41—48no—
637C2×#41—44no—
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×Q8C2412yes—
641C22×Q8C2414yes—
642C22×D4—28no—
643C22×D4—216no—
644C22×D4—24no—
645C22×D4—44no—
646C22×D4—48no—
647C22×D4—44no—
648C22×D4—42no—
649C22×D4—42no—
650C22×D4—42no—
651C22×D4—48no—
652C22×D4—48no—
653C22×D4—44no—
654C22×D4—44no—
655C22×D4—44no—
656C22×D4—44no—
657C22×D4—44no—
658C22×D4C2412yes—
659C22×D4C2412yes—
660C22×D4C2414yes—
661C22×D4C2414yes—
662C22×D4C2414yes—
663C22×D4C2412yes—
664C22×D4C2414yes—
665C22×D4C2414yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C22×D4C2414yes—
669C22×D4C2412yes—
670C22×D4C2412yes—
671C22×D4C2412yes—
672C22×D4C2412yes—
673C22×D4C2414yes—
674C22×D4C2414yes—
675C23×C4—44no—
676C23×C4—42no—
677C23×C4C2411yescharacteristic
678C23×C4C2414yes—
679C23×C4C2411yescharacteristic
680C23×C4C2414yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2411yescharacteristic
684C23×C4C2411yescharacteristic
685C23×C4C2412yes—
686C23×C4C2414yes—
687C23×C4C2412yes—
688C23×C4C2414yes—
689C23×C4C2414yes—
690C23×C4C2411yescharacteristic
691C23×C4C2412yes—
692C23×C4C2411yescharacteristic
693C23×C4C2412yes—
694C23×C4C2411yescharacteristic
695C4⋊Q8—44no—
696C4⋊Q8—48no—
697#126—48no—
698#126—48no—
699#125—48no—
700#124—48no—
701#124—44no—
702#124—48no—
703#124—48no—
704#124—48no—
705#124—48no—
706#124—44no—
707#123—48no—
708#123—48no—
709#123—48no—
710#123—48no—
711#123—44no—
712#123—48no—
713#123—44no—
714#123—44no—
715#123—48no—
716#123—48no—
717#123—44no—
718C22⋊Q8—28no—
719C22⋊Q8—44no—
720C22⋊Q8—48no—
721C22⋊Q8—48no—
722C22⋊Q8—48no—
723C22⋊Q8—48no—
724C22⋊Q8—44no—
725#121—48no—
726#121—48no—
727#121—48no—
728#121—48no—
729#121—48no—
730#121—48no—
731#121—48no—
732#121—48no—
733#121—48no—
734#120—28no—
735#120—28no—
736#120—216no—
737#120—44no—
738#120—44no—
739#120—44no—
740#120—44no—
741#120—44no—
742#120—48no—
743#120—48no—
744#120—48no—
745#120—44no—
746C4×D4—28no—
747C4×D4—44no—
748C4×D4—44no—
749C4×D4—48no—
750C4×D4—48no—
751C4×D4—44no—
752C4×D4—44no—
753C4×D4—48no—
754C4×D4—48no—
755C4×D4—48no—
756#117—44no—
757#117—44no—
758#117—48no—
759#117—44no—
760C2×C4⋊C4—24no—
761C2×C4⋊C4—48no—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C22⋊C4—216no—
793C2×C22⋊C4—24no—
794C2×C22⋊C4—48no—
795C2×C22⋊C4—48no—
796C2×C22⋊C4—48no—
797C2×C22⋊C4—44no—
798C2×C22⋊C4—42no—
799C2×C22⋊C4—44no—
800C2×C22⋊C4—48no—
801C2×C22⋊C4—42no—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
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×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⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
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#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922C24—24no—
923C24—22no—
924C24—22no—
925C24—28no—
926C24—22no—
927C24—41no—
928C24—44no—
929C24—44no—
930C24—42no—
931C24—42no—
932C24—42no—
933C24—42no—
934C24—42no—
935C24—42no—
936C24—42no—
937C24—42no—
938C24—44no—
939C24—42no—
940C24—42no—
941C24—42no—
942C24—42no—
943C24—42no—
944C24—42no—
945C24—42no—
946C24—42no—
947C24H(5,𝔽2)18yes—
948C24C2511yescharacteristic
949C24C2512yes—
950C24C2511yescharacteristic
951C24C2512yes—
952C24C2511yescharacteristic
953C24C2514yes—
954C24C2512yes—
955#41—432no—
956#41—464no—
957#41—816no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—44no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—42no—
968C2×D4—28no—
969C2×D4—24no—
970C2×D4—28no—
971C2×D4—28no—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—28no—
978C2×D4—28no—
979C2×D4—28no—
980C2×D4—28no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—28no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—42no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—42no—
1004C2×D4—42no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—464no—
1019C2×D4—416no—
1020C2×D4—432no—
1021C2×D4—416no—
1022C2×D4—432no—
1023C2×D4—88no—
1024C2×D4—88no—
1025C22×C4—22no—
1026C22×C4—24no—
1027C22×C4—28no—
1028C22×C4—24no—
1029C22×C4—22no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—22no—
1033C22×C4—28no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—41no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—42no—
1056C22×C4—41no—
1057C22×C4—42no—
1058C22×C4—41no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—42no—
1068C22×C4—88no—
1069C22×C4H(5,𝔽2)14yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—28no—
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—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—42no—
1139C22⋊C4—44no—
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—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—42no—
1161C22⋊C4—42no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C42—24no—
1182C42—42no—
1183C42—42no—
1184C42—42no—
1185C42—42no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—42no—
1192C42—44no—
1193C42—44no—
1194C23—28no—
1195C23—22no—
1196C23—24no—
1197C23—24no—
1198C23—22no—
1199C23—22no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—22no—
1205C23—22no—
1206C23—24no—
1207C23—24no—
1208C23—21no—
1209C23—21no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—24no—
1214C23—24no—
1215C23—22no—
1216C23—24no—
1217C23—24no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—48no—
1227C23—416no—
1228C23—48no—
1229C23—44no—
1230C23—44no—
1231C23—44no—
1232C23—82no—
1233C23—82no—
1234C23—88no—
1235C23—82no—
1236C23—82no—
1237C23—82no—
1238C23—82no—
1239C23—88no—
1240C23—88no—
1241C23—162no—
1242C23—162no—
1243C23—164no—
1244C23—164no—
1245C23—164no—
1246C23—162no—
1247C23—162no—
1248C23—161no—
1249C23—164no—
1250C23—161no—
1251C23C2×H(5,𝔽2)14yes—
1252C23C2×H(5,𝔽2)12yes—
1253C23C2×H(5,𝔽2)18yes—
1254C23C2611yescharacteristic
1255Q8—48no—
1256Q8—84no—
1257Q8—162no—
1258Q8—164no—
1259D4—216no—
1260D4—48no—
1261D4—416no—
1262D4—48no—
1263D4—416no—
1264D4—416no—
1265D4—416no—
1266D4—84no—
1267D4—84no—
1268D4—88no—
1269D4—88no—
1270D4—88no—
1271D4—88no—
1272D4—84no—
1273D4—84no—
1274D4—88no—
1275D4—164no—
1276C2×C4—28no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
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—24no—
1317C2×C4—24no—
1318C2×C4—44no—
1319C2×C4—44no—
1320C2×C4—416no—
1321C2×C4—48no—
1322C2×C4—48no—
1323C2×C4—88no—
1324C2×C4—88no—
1325C2×C4—84no—
1326C2×C4—88no—
1327C2×C4—82no—
1328C2×C4—82no—
1329C2×C4—88no—
1330C2×C4—161no—
1331C2×C4—164no—
1332C2×C4—164no—
1333C2×C4—162no—
1334C2×C4—161no—
1335C2×C4C2×H(5,𝔽2)14yes—
1336C2×C4#58514yes—
1337C2×C4#58514yes—
1338C22—28no—
1339C22—22no—
1340C22—24no—
1341C22—22no—
1342C22—28no—
1343C22—28no—
1344C22—28no—
1345C22—22no—
1346C22—44no—
1347C22—42no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—42no—
1353C22—44no—
1354C22—42no—
1355C22—42no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—42no—
1360C22—41no—
1361C22—42no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—41no—
1369C22—42no—
1370C22—41no—
1371C22—42no—
1372C22—88no—
1373C22—168no—
1374C22—168no—
1375C22—164no—
1376C22—164no—
1377C22—164no—
1378C22C22×H(5,𝔽2)11yescharacteristic
1379C22C22×H(5,𝔽2)12yes—
1380C22C2×#58512yes—
1381C22C2×#58512yes—
1382C4—24no—
1383C4—24no—
1384C4—24no—
1385C4—44no—
1386C4—42no—
1387C4—42no—
1388C4—44no—
1389C4—44no—
1390C4—44no—
1391C4—44no—
1392C4—44no—
1393C4—44no—
1394C4—44no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C2—44no—
1399C2—42no—
1400C2—48no—
1401C2—82no—
1402C2—81no—
1403C2—82no—
1404C2—81no—
1405C2#6281711yescharacteristic
1406C2#6282111yescharacteristic
1407C2#6282214yes—
1408C2#6282411yescharacteristic
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. #51993C2semidirect
2. #51940C2semidirect
3. #50952C2semidirect
4. #50659C2semidirect
5. #49597C2semidirect
6. #49548C2semidirect
7. #48937C2semidirect
8. #48930C2semidirect
9. #48773C2semidirect
10. #48647C2semidirect
11. #48351C2semidirect
12. #47994C2semidirect
13. #47933C2semidirect
14. #47848C2semidirect
15. #35913C2semidirect
16. #35764C2semidirect
17. #35750C2semidirect
18. #35730C2semidirect
19. #35716C2semidirect
20. #35584C2semidirect
21. #35371C2semidirect
22. #35355C2semidirect
23. #35347C2semidirect
24. C22×H(5,𝔽2)C22semidirect
25. C2×H(3,𝔽4)C22semidirect
26. C2×#551C22semidirect
28. C2×#546C22semidirect
29. C2×#544C22semidirect
32. C2×#518C22semidirect
33. #2804C22semidirect
34. #2797C22semidirect
35. #2797C22semidirect
36. #2796C22semidirect
37. #2775C22semidirect
38. #2763C22semidirect
39. #2759C22semidirect
40. #2757C22semidirect
41. #2749C22semidirect
42. #2748C22semidirect
43. #2746C22semidirect
44. #2741C22semidirect
45. #2737C22semidirect
46. #2736C22semidirect
47. #2734C22semidirect
48. #2724C22semidirect
49. #2723C22semidirect
50. #2720C22semidirect
51. #2718C22semidirect
52. #2717C22semidirect
53. #2717C22semidirect
54. #2714C22semidirect
55. #2712C22semidirect
56. #2710C22semidirect
57. #2710C22semidirect
58. #2710C22semidirect
59. #2708C22semidirect
60. #2707C22semidirect
61. #2700C22semidirect
62. #2697C22semidirect
63. #2697C22semidirect
64. #2697C22semidirect
65. #2696C22semidirect
66. #2686C22semidirect
67. #2686C22semidirect
68. #2685C22semidirect
69. #2684C22semidirect
70. #2684C22semidirect
71. #2680C22semidirect
72. #2679C22semidirect
73. #2678C22semidirect
74. #2676C22semidirect
75. #2674C22semidirect
76. #2672C22semidirect
77. #2672C22semidirect
78. #2668C22semidirect
79. #2665C22semidirect
80. #2663C22semidirect
81. #2661C22semidirect
82. #2653C22semidirect
83. #2650C22semidirect
84. #2648C22semidirect
85. #2638C22semidirect
86. #2638C22semidirect
87. #2628C22semidirect
88. #2622C22semidirect
89. #2617C22semidirect
90. #2616C22semidirect
91. #2613C22semidirect
92. #2602C22semidirect
93. #2602C22semidirect
94. #2597C22semidirect
95. #2586C22semidirect
96. #2579C22semidirect
97. #2578C22semidirect
98. #2578C22semidirect
99. #2576C22semidirect
100. #2576C22semidirect
101. #2575C22semidirect
102. #2572C22semidirect
103. #2563C22semidirect
104. #2561C22semidirect
105. #2561C22semidirect
106. #2561C22semidirect
107. #2560C22semidirect
108. #2559C22semidirect
109. #2559C22semidirect
110. #2557C22semidirect
111. #2557C22semidirect
112. #2555C22semidirect
113. #2553C22semidirect
114. #2539C22semidirect
115. #2535C22semidirect
116. #2521C22semidirect
117. #2518C22semidirect
118. #2510C22semidirect
119. #2510C22semidirect
120. #2505C22semidirect
121. #2500C22semidirect
122. #2491C22semidirect
123. #2491C22semidirect
124. #2490C22semidirect
125. #2490C22semidirect
126. #2488C22semidirect
127. #2480C22semidirect
128. #2480C22semidirect
129. #2477C22semidirect
130. #2476C22semidirect
131. #2476C22semidirect
132. #2476C22semidirect
133. #2473C22semidirect
134. #2472C22semidirect
135. #2472C22semidirect
136. #2472C22semidirect
137. #2471C22semidirect
138. #2470C22semidirect
139. #2470C22semidirect
140. #2467C22semidirect
141. #2464C22semidirect
142. #2461C22semidirect
143. #2460C22semidirect
144. #2459C22semidirect
145. #2457C22semidirect
146. #2457C22semidirect
147. #2457C22semidirect
148. #2456C22semidirect
149. #2447C22semidirect
150. #2440C22semidirect
151. #2437C22semidirect
152. #2435C22semidirect
153. #2435C22semidirect
154. #2432C22semidirect
155. #2432C22semidirect
157. #2430C22semidirect
158. #2430C22semidirect
159. #2427C22semidirect
160. #2427C22semidirect
161. #2424C22semidirect
162. #2422C22semidirect
163. #2420C22semidirect
164. #2418C22semidirect
165. #2418C22semidirect
166. #2412C22semidirect
170. #2410C22semidirect
172. #2408C22semidirect
173. #2407C22semidirect
174. #2406C22semidirect
175. #2406C22semidirect
176. #2405C22semidirect
177. #2405C22semidirect
178. #2405C22semidirect
179. #2405C22semidirect
180. #2405C22semidirect
182. #2404C22semidirect
184. #2403C22semidirect
185. #2403C22semidirect
186. #2395C22semidirect
187. #2392C22semidirect
189. #2388C22semidirect
190. C2×#394C22semidirect
191. #2383C22semidirect
192. #2378C22semidirect
193. #2376C22semidirect
194. #2375C22semidirect
195. #2375C22semidirect
196. #2368C22semidirect
197. #2361C22semidirect
198. #2359C22semidirect
199. #2358C22semidirect
200. #2358C22semidirect
201. #2358C22semidirect
202. #2357C22semidirect
203. #2352C22semidirect
204. #2342C22semidirect
205. #2339C22semidirect
206. D4×C22⋊C4C22semidirect
207. #2329C22semidirect
208. #2321C22semidirect
209. #2321C22semidirect
210. #2318C22semidirect
211. #2312C22semidirect
212. #2309C22semidirect
213. #2308C22semidirect
214. C4×#120C22semidirect
215. C2×#386C22semidirect
216. #2280C22semidirect
217. #2274C22semidirect
218. #2273C22semidirect

Maximal subgroups

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

subgroupindex
#519932
#519402
#509522
#506592
#495972
#495482
#489372
#489302
#487732
#486472
#483512
#479942
#479332
#478482
#359132
#357642
#357502
#357302
#357162
#355842
#353712
#353552
#353472