Finite Group Databasebeta

← #7674067

Subgroups — #7674067

Order 512.

4897 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45379C212yesmaximal, complemented
2#45376C212yesmaximal, complemented
3#45256C212yesmaximal, complemented
4#45206C212yesmaximal, complemented
5#45164C211yesmaximal, characteristic, complemented
6#45034C212yesmaximal, complemented
7#44965C211yesmaximal, characteristic, complemented
8#44948C211yesmaximal, characteristic, complemented
9#44931C211yesmaximal, characteristic, complemented
10#44880C212yesmaximal, complemented
11#40477C214yesmaximal, complemented
12#40452C214yesmaximal, complemented
13#40092C214yesmaximal, complemented
14#40088C214yesmaximal, complemented
15#38802C214yesmaximal, complemented
16#38796C214yesmaximal, complemented
17#38608C214yesmaximal, complemented
18#38601C214yesmaximal, complemented
19#35549C212yesmaximal, complemented
20#35546C212yesmaximal, complemented
21#35197C212yesmaximal, complemented
22#35175C212yesmaximal, complemented
23#34644C211yesmaximal, characteristic, complemented
24#34333C212yesmaximal, complemented
25#34330C212yesmaximal, complemented
26C4×#540C211yesmaximal, characteristic, complemented
27C4×#540C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#550C2212yes—
30C2×#540C2211yescharacteristic
31C2×#540C2211yescharacteristic
32#2855C2214yes—
33#2854C2214yes—
34#2851C2214yes—
35#2850C2214yes—
36#2808C2214yes—
37#2805C2214yes—
38#2787C2214yes—
39#2786C2214yes—
40#2786C2214yes—
41#2781C2214yes—
42#2774C2214yes—
43#2765C2214yes—
44#2761C2214yes—
45#2761C2214yes—
46#2759C2214yes—
47#2750C2214yes—
48#2750C2214yes—
49#2743C2214yes—
50#2741C2214yes—
51#2741C2214yes—
52#2715C2214yes—
53#2708C2214yes—
54#2701C2214yes—
55#2696C2214yes—
56#2694C2214yes—
57#2692C2214yes—
58#2690C2214yes—
59#2687C2214yes—
60#2683C2214yes—
61#2682C2214yes—
62#2681C2214yes—
63#2676C2214yes—
64#2676C2214yes—
65#2671C2214yes—
66#2671C2214yes—
67#2671C2214yes—
68#2667C2212yes—
69#2667C2212yes—
70#2667C2214yes—
71#2666C2212yes—
72#2666C2212yes—
73#2666C2212yes—
74#2666C2212yes—
75#2665C2212yes—
76#2665C2212yes—
77#2665C2214yes—
78#2648C2214yes—
79#2648C2214yes—
80#2601C2214yes—
81#2599C2214yes—
82#2596C2214yes—
83#2590C2214yes—
84#2589C2214yes—
85#2587C2214yes—
86#2584C2212yes—
87#2580C2212yes—
88#2578C2214yes—
89#2576C2214yes—
90#2574C2214yes—
91#2572C2214yes—
92#2571C2212yes—
93#2566C2212yes—
94#2558C2214yes—
95#2558C2214yes—
96#2556C2214yes—
97#2553C2214yes—
98#2550C2212yes—
99#2548C2212yes—
100#2541C2212yes—
101#2540C2214yes—
102#2538C2212yes—
103#2536C2214yes—
104#2518C2214yes—
105#2518C2214yes—
106#2515C2214yes—
107#2513C2212yes—
108#2513C2212yes—
109#2513C2212yes—
110#2512C2212yes—
111#2510C2214yes—
112#2509C2212yes—
113#2508C2214yes—
114#2508C2212yes—
115#2508C2212yes—
116#2506C2212yes—
117#2495C2212yes—
118#2494C2212yes—
119#2493C2214yes—
120#2491C2212yes—
121#2490C2212yes—
122#2488C2214yes—
123#2488C2214yes—
124#2488C2214yes—
125#2486C2214yes—
126#2481C2214yes—
127#2474C2214yes—
128#2474C2214yes—
129#2468C2214yes—
130#2467C2214yes—
131#2461C2214yes—
132#2459C2214yes—
133#2458C2214yes—
134#2457C2214yes—
135#2457C2214yes—
136#2457C2214yes—
137#2457C2214yes—
138#2454C2212yes—
139#2454C2212yes—
140#2452C2212yes—
141#2452C2212yes—
142#2449C2214yes—
143#2448C2214yes—
144#2445C2212yes—
145#2445C2212yes—
146#2445C2212yes—
147#2445C2212yes—
148#2444C2214yes—
149#2443C2214yes—
150#2430C2214yes—
151#2430C2214yes—
152#2430C2214yes—
153#2428C2212yes—
154#2428C2212yes—
155#2427C2214yes—
156#2427C2214yes—
157#2425C2214yes—
158#2425C2214yes—
159#2422C2212yes—
160#2420C2212yes—
161#2420C2214yes—
162#2420C2214yes—
163#2419C2214yes—
164#2417C2214yes—
165#2416C2214yes—
166#2416C2214yes—
167#2406C2214yes—
168#2402C2211yescharacteristic
169#2402C2211yescharacteristic
170#2399C2211yescharacteristic
171#2399C2211yescharacteristic
172#2396C2212yes—
173#2396C2212yes—
174#2370C2212yes—
175#2370C2212yes—
176#2368C2214yes—
177#2368C2214yes—
178#2366C2212yes—
179#2366C2212yes—
180#2366C2212yes—
181#2365C2212yes—
182#2364C2214yes—
183#2364C2214yes—
184#2363C2214yes—
185#2360C2214yes—
186#2357C2212yes—
187#2357C2212yes—
188#2355C2212yes—
189#2355C2212yes—
190#2354C2212yes—
191#2349C2212yes—
192#2349C2212yes—
193D4×C4⋊C4C2212yes—
194#2345C2214yes—
195#2339C2214yes—
196#2335C2214yes—
197#2335C2214yes—
198#2333C2214yes—
199#2333C2214yes—
200#2333C2214yes—
201#2333C2214yes—
202#2331C2212yes—
203#2330C2212yes—
204#2330C2211yescharacteristic
205#2330C2211yescharacteristic
206#2329C2214yes—
207#2329C2214yes—
208#2328C2212yes—
209#2328C2212yes—
210#2328C2211yescharacteristic
211#2328C2211yescharacteristic
212#2324C2212yes—
213#2324C2212yes—
214#2319C2212yes—
215#2319C2212yes—
216#2319C2212yes—
217#2319C2212yes—
218#2314C2211yescharacteristic
219#2314C2211yescharacteristic
220C4×#127C2211yescharacteristic
221C4×#127C2211yescharacteristic
222C4×#125C2211yescharacteristic
223C4×#125C2211yescharacteristic
224C4×C22⋊Q8C2214yes—
225C4×#123C2214yes—
226C4×#123C2214yes—
227C4×#121C2214yes—
228C4×#121C2214yes—
229C4×#121C2214yes—
230C4×#121C2212yes—
231C4×#121C2212yes—
232#2297C2214yes—
233#2295C2212yes—
234#2295C2212yes—
235C2×#387C2214yes—
236#2283C2211yescharacteristic
237#2283C2211yescharacteristic
238#2275C2212yes—
239#2275C2212yes—
240C42×D4C2212yes—
241C42×D4C2212yes—
242C4×#117C2211yescharacteristic
243C22×#41C2314yes—
244#554—216no—
245#550—216no—
246#540—28no—
247#540—28no—
248C2×C4⋊Q8C2312yes—
249C2×#127C2311yescharacteristic
250C2×#127C2312yes—
251C2×#127C2312yes—
252C2×#127C2311yescharacteristic
253C2×#126C2314yes—
254C2×#125C2311yescharacteristic
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2311yescharacteristic
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2314yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2314yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2314yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2314yes—
309C22×C42C2311yescharacteristic
310C22×C42C2314yes—
311C22×C42C2314yes—
312#401C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2312yes—
321#400C2312yes—
322#400C2312yes—
323#400C2312yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2312yes—
330#399C2312yes—
331#399C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2312yes—
337#398C2314yes—
338#398C2312yes—
339#398C2312yes—
340#398C2312yes—
341#398C2312yes—
342#398C2312yes—
343#398C2312yes—
344#398C2312yes—
345#398C2312yes—
346#398C2312yes—
347#398C2312yes—
348#398C2312yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2312yes—
369#396C2312yes—
370#396C2312yes—
371#396C2312yes—
372#396C2314yes—
373#396C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2312yes—
377#395C2312yes—
378#395C2312yes—
379#395C2312yes—
380#395C2312yes—
381#395C2312yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#393C2314yes—
399#393C2314yes—
400#393C2314yes—
401#393C2314yes—
402#393C2312yes—
403#393C2312yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#391C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2314yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2312yes—
417#391C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2314yes—
421#390C2314yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2314yes—
429#390C2314yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2314yes—
438#390C2314yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2314yes—
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#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2312yes—
515#387C2312yes—
516#387C2312yes—
517#387C2314yes—
518#387C2314yes—
519#387C2312yes—
520#387C2314yes—
521#387C2314yes—
522#387C2312yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2312yes—
527#387C2314yes—
528#387C2312yes—
529#387C2312yes—
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#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#384C2311yescharacteristic
577#384C2311yescharacteristic
578#384C2312yes—
579#383C2311yescharacteristic
580#383C2314yes—
581#383C2311yescharacteristic
582#383C2311yescharacteristic
583#383C2311yescharacteristic
584#382C2311yescharacteristic
585#382C2311yescharacteristic
586#382C2312yes—
587#382C2312yes—
588#382C2312yes—
589#382C2314yes—
590#382C2314yes—
591#382C2312yes—
592#382C2312yes—
593#382C2314yes—
594#381C2314yes—
595#381C2314yes—
596#381C2314yes—
597#381C2314yes—
598#381C2314yes—
599#381C2314yes—
600#381C2314yes—
601#381C2311yescharacteristic
602#381C2311yescharacteristic
603#381C2311yescharacteristic
604#381C2311yescharacteristic
605#380C2312yes—
606#380C2312yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611#380C2314yes—
612#380C2314yes—
613#380C2314yes—
614#380C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2312yes—
618#380C2312yes—
619#380C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2314yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2311yescharacteristic
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668#376C2311yescharacteristic
669#376C2312yes—
670#376C2312yes—
671#376C2311yescharacteristic
672C2×#95C2314yes—
673C2×#95C2314yes—
674C2×#95C2314yes—
675C2×#95C2314yes—
676C43C2311yescharacteristic
677C43C2311yescharacteristic
678C2×#41—216no—
679C2×#41—84no—
680C2×#41—84no—
681C22×Q8C2412yes—
682C22×Q8C2414yes—
683C22×Q8C2412yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2414yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2414yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C23×C4C2411yescharacteristic
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2414yes—
705C23×C4C2414yes—
706C23×C4C2414yes—
707C4⋊Q8—28no—
708#127—28no—
709#127—28no—
710#127—24no—
711#127#4118yes—
712#126—84no—
713#125—28no—
714#125—24no—
715#125—84no—
716#125#4118yescomplemented
717#124—84no—
718#124—84no—
719#123—216no—
720#123—216no—
721#123—84no—
722#123—84no—
723#123—84no—
724#123—84no—
725#123—84no—
726C22⋊Q8—216no—
727C22⋊Q8—216no—
728C22⋊Q8—216no—
729C22⋊Q8—84no—
730C22⋊Q8—84no—
731C22⋊Q8—84no—
732#121—216no—
733#121—28no—
734#121—216no—
735#121—216no—
736#121—216no—
737#121—216no—
738#121—28no—
739#121—84no—
740#121—84no—
741#121—84no—
742#121—84no—
743C4×Q8—28no—
744C4×Q8—28no—
745C4×Q8—84no—
746C4×D4—28no—
747C4×D4—28no—
748C4×D4—28no—
749C4×D4—28no—
750C4×D4—28no—
751C4×D4—28no—
752C4×D4—28no—
753C4×D4—28no—
754C4×D4—28no—
755C4×D4—28no—
756C4×D4—84no—
757C4×D4—84no—
758C4×D4—84no—
759C4×D4—84no—
760C4×D4—84no—
761C4×D4—84no—
762C4×D4—84no—
763#117—24no—
764#117—24no—
765#117—84no—
766C2×C4⋊C4—216no—
767C2×C4⋊C4—84no—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
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⋊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⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C42—24no—
864C2×C42—84no—
865C2×C42—84no—
866C2×C42C2411yescharacteristic
867C2×C42C2411yescharacteristic
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2411yescharacteristic
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892#95C2412yes—
893#95C2412yes—
894#95C2414yes—
895#95C2412yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2411yescharacteristic
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2411yescharacteristic
943#95C2414yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2411yescharacteristic
949#95C2411yescharacteristic
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960C24C2511yescharacteristic
961C24C2514yes—
962C24C2514yes—
963#41—832no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—28no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—28no—
982C2×D4—28no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4C2×#4118yes—
1002C2×D4C2×#41116yes—
1003C22×C4—28no—
1004C22×C4—28no—
1005C22×C4—28no—
1006C22×C4—22no—
1007C22×C4—22no—
1008C22×C4—28no—
1009C22×C4—22no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—28no—
1013C22×C4—28no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—28no—
1017C22×C4—28no—
1018C22×C4—44no—
1019C22×C4—44no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—42no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4C2511yescharacteristic
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4C2×#41116yes—
1114C4⋊C4C2×#4118yes—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
1144C22⋊C4—42no—
1145C22⋊C4—44no—
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—42no—
1156C22⋊C4—44no—
1157C22⋊C4—42no—
1158C22⋊C4—44no—
1159C42—22no—
1160C42—22no—
1161C42—24no—
1162C42—24no—
1163C42—24no—
1164C42—24no—
1165C42—22no—
1166C42—22no—
1167C42—22no—
1168C42—42no—
1169C42—42no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C42—44no—
1177C42—44no—
1178C42—42no—
1179C42—42no—
1180C42—44no—
1181C42—44no—
1182C42C2×#4114yes—
1183C42C2×#4114yes—
1184C422−1+414yes—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—24no—
1191C23—21no—
1192C23—24no—
1193C23—21no—
1194C23—24no—
1195C23—24no—
1196C23—21no—
1197C23—24no—
1198C23—24no—
1199C23—22no—
1200C23—24no—
1201C23—22no—
1202C23—24no—
1203C23C22×#4118yes—
1204C23C2611yescharacteristic
1205Q8—48no—
1206Q8—88no—
1207Q8—84no—
1208D4—216no—
1209D4—416no—
1210D4—48no—
1211D4—88no—
1212D4—88no—
1213D4—88no—
1214D4—88no—
1215D4—88no—
1216D4—88no—
1217D4—88no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—416no—
1279C2×C4—44no—
1280C2×C4—88no—
1281C2×C4—88no—
1282C2×C4—88no—
1283C2×C4—88no—
1284C2×C4—88no—
1285C2×C4—82no—
1286C2×C4—82no—
1287C2×C4—88no—
1288C2×C4—88no—
1289C2×C4—88no—
1290C2×C4—88no—
1291C2×C4C22×#4114yes—
1292C2×C4C22×#4114yes—
1293C2×C4C22×#4118yes—
1294C2×C4C22×#4112yes—
1295C2×C4C22×#4112yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4C2×2−1+412yes—
1298C2×C4C2×2−1+412yes—
1299C22—28no—
1300C22—28no—
1301C22—28no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—42no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—42no—
1312C22—44no—
1313C22—41no—
1314C22—41no—
1315C22—44no—
1316C22—41no—
1317C22—44no—
1318C22C23×#4111yescharacteristic
1319C22C23×#4111yescharacteristic
1320C22C22×2−1+411yescharacteristic
1321C22H(7,𝔽2)12yes—
1322C22H(7,𝔽2)12yes—
1323C4—24no—
1324C4—28no—
1325C4—24no—
1326C4—22no—
1327C4—22no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—42no—
1340C4—42no—
1341C4—41no—
1342C4—41no—
1343C4—44no—
1344C4—44no—
1345C4—41no—
1346C4#348214yes—
1347C2—48no—
1348C2—84no—
1349C2—81no—
1350C2C2×#348211yescharacteristic
1351C2#6284612yes—
1352C2#6285812yes—
1353C2#6288111yescharacteristic
1354C2#6288111yescharacteristic
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. #45379C2semidirect
2. #45376C2semidirect
3. #45256C2semidirect
4. #45206C2semidirect
5. #45164C2semidirect
6. #45034C2semidirect
7. #44965C2semidirect
8. #44948C2semidirect
9. #44931C2semidirect
10. #44880C2semidirect
11. #40477C2semidirect
12. #40452C2semidirect
13. #40092C2semidirect
14. #40088C2semidirect
15. #38802C2semidirect
16. #38796C2semidirect
17. #38608C2semidirect
18. #38601C2semidirect
19. #35549C2semidirect
20. #35546C2semidirect
21. #35197C2semidirect
22. #35175C2semidirect
23. #34644C2semidirect
24. #34333C2semidirect
25. #34330C2semidirect
26. C4×#540C2semidirect
27. C4×#540C2semidirect
716. #125#41semidirect

Maximal subgroups

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

subgroupindex
#453792
#453762
#452562
#452062
#451642
#450342
#449652
#449482
#449312
#448802
#404772
#404522
#400922
#400882
#388022
#387962
#386082
#386012
#355492
#355462
#351972
#351752
#346442
#343332
#343302
C4×#5402