Finite Group Databasebeta

← #7658687

Subgroups — #7658687

Order 512.

4041 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42748C213yesmaximal
2#42744C213yesmaximal, complemented
3#42738C213yesmaximal
4#42733C213yesmaximal, complemented
5#42703C213yesmaximal, complemented
6#42689C213yesmaximal, complemented
7#42670C213yesmaximal
8#42663C213yesmaximal
9#42600C213yesmaximal, complemented
10#42597C213yesmaximal
11#42562C213yesmaximal
12#42553C213yesmaximal, complemented
13#37630C213yesmaximal, complemented
14#37592C213yesmaximal
15#37580C213yesmaximal, complemented
16#36700C213yesmaximal
17#35971C211yesmaximal, characteristic, complemented
18#35971C211yesmaximal, characteristic, complemented
19#35971C211yesmaximal, characteristic, complemented
20#35937C211yesmaximal, characteristic, complemented
21#35920C211yesmaximal, characteristic
22#35883C211yesmaximal, characteristic
23#35883C211yesmaximal, characteristic
24#35883C211yesmaximal, characteristic
25#35868C211yesmaximal, characteristic, complemented
26#35868C211yesmaximal, characteristic, complemented
27#35786C211yesmaximal, characteristic
28#35711C211yesmaximal, characteristic
29#34336C211yesmaximal, characteristic, complemented
30#34335C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2839C2213yes—
36#2839C2213yes—
37#2839C2213yes—
38#2839C2213yes—
39#2839C2216yes—
40#2836C2213yes—
41#2836C2213yes—
42#2836C2213yes—
43#2836C2213yes—
44#2833C2213yes—
45#2833C2213yes—
46#2833C2213yes—
47#2833C2213yes—
48#2831C2211yescharacteristic
49#2831C2213yes—
50#2831C2213yes—
51#2831C2213yes—
52#2798C2216yes—
53#2789C2216yes—
54#2783C2216yes—
55#2776C2216yes—
56#2769C2216yes—
57#2766C2216yes—
58#2762C2216yes—
59#2762C2216yes—
60#2762C2216yes—
61#2762C2216yes—
62#2758C2216yes—
63#2755C2216yes—
64#2725C2216yes—
65#2719C2216yes—
66#2716C2216yes—
67#2713C2216yes—
68#2666C2216yes—
69#2666C2216yes—
70#2660C2213yes—
71#2655C2216yes—
72#2655C2216yes—
73#2655C2216yes—
74#2655C2216yes—
75#2655C2216yes—
76#2650C2216yes—
77#2647C2213yes—
78#2647C2213yes—
79#2647C2213yes—
80#2647C2213yes—
81#2647C2213yes—
82#2645C2213yes—
83#2645C2213yes—
84#2645C2213yes—
85#2645C2213yes—
86#2645C2216yes—
87#2642C2216yes—
88#2637C2216yes—
89#2634C2216yes—
90#2629C2213yes—
91#2628C2213yes—
92#2584C2213yes—
93#2582C2213yes—
94#2581C2213yes—
95#2571C2213yes—
96#2571C2213yes—
97#2571C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2570C2213yes—
102#2570C2213yes—
103#2568C2213yes—
104#2565C2213yes—
105#2552C2213yes—
106#2552C2213yes—
107#2551C2213yes—
108#2551C2213yes—
109#2550C2213yes—
110#2550C2213yes—
111#2546C2213yes—
112#2533C2216yes—
113#2528C2216yes—
114#2524C2216yes—
115#2519C2216yes—
116#2514C2213yes—
117#2514C2213yes—
118#2514C2213yes—
119#2514C2213yes—
120#2514C2213yes—
121#2514C2213yes—
122#2511C2213yes—
123#2511C2213yes—
124#2511C2213yes—
125#2511C2213yes—
126#2511C2213yes—
127#2511C2213yes—
128#2509C2213yes—
129#2509C2213yes—
130#2509C2213yes—
131#2509C2213yes—
132#2509C2213yes—
133#2508C2213yes—
134#2508C2213yes—
135#2508C2213yes—
136#2508C2213yes—
137#2508C2213yes—
138#2508C2213yes—
139#2507C2213yes—
140#2507C2213yes—
141#2507C2213yes—
142#2507C2213yes—
143#2507C2213yes—
144#2506C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2506C2213yes—
148#2497C2213yes—
149#2497C2213yes—
150#2497C2213yes—
151#2496C2213yes—
152#2496C2213yes—
153#2496C2213yes—
154#2495C2213yes—
155#2495C2213yes—
156#2495C2213yes—
157#2494C2213yes—
158#2494C2213yes—
159#2494C2213yes—
160#2453C2216yes—
161#2453C2213yes—
162#2451C2213yes—
163#2451C2213yes—
164#2451C2213yes—
165#2446C2216yes—
166#2441C2213yes—
167#2439C2213yes—
168#2439C2213yes—
169#2439C2213yes—
170#2402C2213yes—
171#2402C2213yes—
172#2402C2213yes—
173#2402C2213yes—
174#2402C2213yes—
175#2401C2213yes—
176#2401C2213yes—
177#2401C2213yes—
178#2401C2213yes—
179#2399C2213yes—
180#2396C2213yes—
181#2396C2213yes—
182#2370C2213yes—
183#2370C2213yes—
184#2369C2213yes—
185#2369C2213yes—
186#2365C2213yes—
187#2365C2213yes—
188#2356C2213yes—
189#2355C2213yes—
190#2355C2213yes—
191#2355C2213yes—
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212#2347C2213yes—
213#2346C2213yes—
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220#2331C2213yes—
221#2331C2213yes—
222#2331C2213yes—
223#2330C2213yes—
224#2320C2213yes—
225#2314C2213yes—
226C4×C4⋊Q8C2213yes—
227C4×#125C2213yes—
228#2298C2213yes—
229#2295C2213yes—
230#2295C2213yes—
231#2295C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239Q82—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2316yes—
246C2×#126C2316yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2316yes—
250C2×#125C2316yes—
251#519—28no—
252C2×C4×Q8C2313yes—
253C2×C4×Q8C2313yes—
254C2×C4×Q8C2313yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2316yes—
270C2×C4×Q8C2311yescharacteristic
271C2×#117C2313yes—
272C2×#117C2313yes—
273#401C2313yes—
274#401C2313yes—
275#401C2313yes—
276#401C2313yes—
277#401C2316yes—
278#401C2316yes—
279#401C2316yes—
280#400C2313yes—
281#400C2316yes—
282#400C2313yes—
283#400C2313yes—
284#400C2316yes—
285#400C2316yes—
286#400C2316yes—
287#400C2313yes—
288#400C2313yes—
289#400C2313yes—
290#400C2311yescharacteristic
291#400C2311yescharacteristic
292#400C2313yes—
293#400C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2311yescharacteristic
298#400C2313yes—
299#400C2313yes—
300#400C2313yes—
301#400C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2316yes—
330#400C2316yes—
331#400C2316yes—
332#399C2313yes—
333#399C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2316yes—
340#398C2316yes—
341#398C2311yescharacteristic
342#398C2311yescharacteristic
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2313yes—
360#398C2313yes—
361#398C2313yes—
362#398C2313yes—
363#398C2313yes—
364#398C2313yes—
365#398C2316yes—
366#398C2316yes—
367#398C2316yes—
368#398C2316yes—
369#398C2316yes—
370#398C2316yes—
371#398C2316yes—
372#397C2311yescharacteristic
373#397C2311yescharacteristic
374#397C2313yes—
375#397C2313yes—
376#397C2311yescharacteristic
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#397C2313yes—
382#397C2313yes—
383#397C2313yes—
384#396C2311yescharacteristic
385#396C2311yescharacteristic
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2316yes—
393#395C2311yescharacteristic
394#395C2313yes—
395#395C2313yes—
396#395C2313yes—
397#395C2313yes—
398#395C2313yes—
399#395C2316yes—
400#395C2316yes—
401#395C2316yes—
402#393C2311yescharacteristic
403#393C2313yes—
404#393C2316yes—
405#391C2316yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2316yes—
411#391C2316yes—
412#391C2311yescharacteristic
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2316yes—
423#391C2316yes—
424#391C2316yes—
425#391C2316yes—
426#391C2313yes—
427#391C2313yes—
428#391C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2316yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2316yes—
462#389C2316yes—
463#389C2313yes—
464#389C2316yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2316yes—
481#389C2316yes—
482#388C2313yes—
483#388C2316yes—
484#388C2311yescharacteristic
485#388C2313yes—
486#388C2313yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#387C2313yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2311yescharacteristic
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2316yes—
531#387C2316yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#384C2313yes—
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#383C2316yes—
542#383C2316yes—
543#383C2316yes—
544#383C2316yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2316yes—
557#382C2316yes—
558#382C2316yes—
559#382C2316yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2316yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2316yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2316yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2413yes—
625C22×Q8C2411yescharacteristic
626C22×Q8C2413yes—
627C22×Q8C2416yes—
628C22×Q8C2411yescharacteristic
629C23×C4C2413yes—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—212no—
634C4⋊Q8—86no—
635#126—86no—
636#125—212no—
637#125—212no—
638#125—86no—
639#125—86no—
640C4×Q8—24no—
641C4×Q8—24no—
642C4×Q8—24no—
643C4×Q8—24no—
644C4×Q8—24no—
645C4×Q8—24no—
646C4×Q8—24no—
647C4×Q8—24no—
648C4×Q8—24no—
649C4×Q8—24no—
650C4×Q8—24no—
651C4×Q8—24no—
652C4×Q8—24no—
653C4×Q8—212no—
654C4×Q8—212no—
655C4×Q8—212no—
656C4×Q8—212no—
657C4×Q8—86no—
658C4×Q8#4118yes—
659#117—212no—
660#117—212no—
661C2×C4⋊C4C2413yes—
662C2×C4⋊C4C2413yes—
663C2×C4⋊C4C2413yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2413yes—
666C2×C4⋊C4C2413yes—
667C2×C4⋊C4C2413yes—
668C2×C4⋊C4C2413yes—
669C2×C4⋊C4C2413yes—
670C2×C4⋊C4C2413yes—
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2413yes—
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2413yes—
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2416yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2416yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2416yes—
693C2×C4⋊C4C2416yes—
694C2×C4⋊C4C2416yes—
695C2×C4⋊C4C2416yes—
696C2×C4⋊C4C2416yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2416yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2413yes—
733C2×C22⋊C4C2413yes—
734C2×C22⋊C4C2411yescharacteristic
735C2×C22⋊C4C2413yes—
736C2×C22⋊C4C2413yes—
737C2×C22⋊C4C2413yes—
738C2×C22⋊C4C2411yescharacteristic
739C2×C22⋊C4C2411yescharacteristic
740C2×C22⋊C4C2411yescharacteristic
741C2×C22⋊C4C2411yescharacteristic
742C2×C22⋊C4C2411yescharacteristic
743C2×C22⋊C4C2411yescharacteristic
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2413yes—
747C2×C42C2416yes—
748C2×C42C2413yes—
749C2×C42C2413yes—
750C2×C42C2413yes—
751C2×C42C2413yes—
752C2×C42C2413yes—
753C2×C42C2413yes—
754C2×C42C2413yes—
755C2×C42C2413yes—
756C2×C42C2413yes—
757C2×C42C2413yes—
758C2×C42C2413yes—
759C2×C42C2413yes—
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2416yes—
763C2×C42C2416yes—
764C2×C42C2416yes—
765C2×C42C2411yescharacteristic
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2416yes—
769C2×C42C2416yes—
770C2×C42C2413yes—
771#95C2411yescharacteristic
772#95C2411yescharacteristic
773#95C2411yescharacteristic
774#95C2411yescharacteristic
775#95C2411yescharacteristic
776#95C2413yes—
777#95C2413yes—
778#95C2413yes—
779#95C2413yes—
780#95C2413yes—
781#95C2413yes—
782#95C2413yes—
783#95C2413yes—
784#95C2413yes—
785#95C2413yes—
786#95C2413yes—
787#95C2413yes—
788#95C2413yes—
789#95C2413yes—
790#95C2413yes—
791#95C2413yes—
792#95C2413yes—
793#95C2416yes—
794#95C2416yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2416yes—
808#95C2411yescharacteristic
809#95C2411yescharacteristic
810#95C2411yescharacteristic
811#95C2411yescharacteristic
812#95C2413yes—
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2416yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2416yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2416yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2416yes—
837#95C2416yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2416yes—
852#95C2416yes—
853#95C2416yes—
854#95C2416yes—
855#95C2416yes—
856#95C2416yes—
857#95C2416yes—
858#95C2416yes—
859#95C2416yes—
860#95C2416yes—
861C24C2511yescharacteristic
862C2×Q8—22no—
863C2×Q8—26no—
864C2×Q8—26no—
865C2×Q8—212no—
866C2×Q8—26no—
867C2×Q8—26no—
868C2×Q8—41no—
869C2×Q8—41no—
870C2×Q8—46no—
871C2×Q8—43no—
872C2×Q8—43no—
873C2×Q8—46no—
874C2×Q8—416no—
875C2×Q8C2×#4114yes—
876C2×Q82−1+414yes—
877C2×Q82−1+414yes—
878C22×C4—26no—
879C22×C4—26no—
880C22×C4—26no—
881C22×C4C2513yes—
882C22×C4C2511yescharacteristic
883C22×C4C2513yes—
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2513yes—
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2513yes—
895C22×C4C2513yes—
896C22×C4C2511yescharacteristic
897C22×C4C2513yes—
898C22×C4C2511yescharacteristic
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2513yes—
910C22×C4C2513yes—
911C4⋊C4—26no—
912C4⋊C4—26no—
913C4⋊C4—26no—
914C4⋊C4—22no—
915C4⋊C4—26no—
916C4⋊C4—26no—
917C4⋊C4—26no—
918C4⋊C4—26no—
919C4⋊C4—26no—
920C4⋊C4—26no—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—212no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—41no—
934C4⋊C4—43no—
935C4⋊C4—43no—
936C4⋊C4—41no—
937C4⋊C4—43no—
938C4⋊C4—43no—
939C4⋊C4—43no—
940C4⋊C4—43no—
941C4⋊C4—43no—
942C4⋊C4—43no—
943C4⋊C4—43no—
944C4⋊C4—43no—
945C4⋊C4—43no—
946C4⋊C4—43no—
947C4⋊C4—43no—
948C4⋊C4—43no—
949C4⋊C4—43no—
950C4⋊C4—41no—
951C4⋊C4—43no—
952C4⋊C4—46no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—43no—
959C4⋊C4—46no—
960C4⋊C4—46no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—41no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—46no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—46no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—46no—
977C4⋊C4—46no—
978C4⋊C4—46no—
979C4⋊C4—46no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4C2×#41112yes—
983C22⋊C4—26no—
984C22⋊C4—22no—
985C22⋊C4—41no—
986C22⋊C4—43no—
987C22⋊C4—43no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—43no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—43no—
995C22⋊C4—43no—
996C22⋊C4—43no—
997C42—26no—
998C42—212no—
999C42—26no—
1000C42—26no—
1001C42—26no—
1002C42—26no—
1003C42—26no—
1004C42—26no—
1005C42—26no—
1006C42—26no—
1007C42—26no—
1008C42—26no—
1009C42—26no—
1010C42—26no—
1011C42—43no—
1012C42—41no—
1013C42—43no—
1014C42—46no—
1015C42—46no—
1016C42—43no—
1017C42—46no—
1018C42—46no—
1019C42—46no—
1020C42C2×#41112yes—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23C2611yescharacteristic
1029Q8—44no—
1030Q8—412no—
1031Q8—86no—
1032Q8—812no—
1033Q8#541116yes—
1034C2×C4—23no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—23no—
1038C2×C4—23no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—23no—
1045C2×C4—23no—
1046C2×C4—23no—
1047C2×C4—23no—
1048C2×C4—23no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—23no—
1058C2×C4—23no—
1059C2×C4—23no—
1060C2×C4—23no—
1061C2×C4—23no—
1062C2×C4—23no—
1063C2×C4—23no—
1064C2×C4—23no—
1065C2×C4—23no—
1066C2×C4—23no—
1067C2×C4—23no—
1068C2×C4—21no—
1069C2×C4—23no—
1070C2×C4—23no—
1071C2×C4—23no—
1072C2×C4—23no—
1073C2×C4—23no—
1074C2×C4—23no—
1075C2×C4—23no—
1076C2×C4—23no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—23no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—21no—
1099C2×C4—23no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—23no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—412no—
1120C2×C4C22×#4116yes—
1121C2×C4C22×#4112yes—
1122C2×C4C22×#4116yes—
1123C2×C4C2×2−1+416yes—
1124C2×C4C2×2−1+416yes—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22C23×#4111yescharacteristic
1133C22C22×2−1+411yescharacteristic
1134C22C22×2−1+411yescharacteristic
1135C22H(7,𝔽2)11yescharacteristic
1136C222−1+611yescharacteristic
1137C222−1+611yescharacteristic
1138C222−1+611yescharacteristic
1139C4—22no—
1140C4—26no—
1141C4—41no—
1142C4—41no—
1143C4—41no—
1144C4—41no—
1145C4—41no—
1146C4—41no—
1147C4—43no—
1148C4—43no—
1149C4—41no—
1150C4—41no—
1151C4—43no—
1152C4—43no—
1153C4—43no—
1154C4—43no—
1155C4—43no—
1156C4—43no—
1157C4—43no—
1158C4—41no—
1159C4—43no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—43no—
1164C4—43no—
1165C4—43no—
1166C4—41no—
1167C4—43no—
1168C4C2×#541112yes—
1169C2—81no—
1170C2C22×#54111yescharacteristic
1171C2#6285011yescharacteristic
1172C2#6285711yescharacteristic
1173C2#6305711yescharacteristic
1174C2#6305711yescharacteristic
1175C2#6306111yescharacteristic
1176C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42744C2semidirect
4. #42733C2semidirect
5. #42703C2semidirect
6. #42689C2semidirect
9. #42600C2semidirect
12. #42553C2semidirect
13. #37630C2semidirect
15. #37580C2semidirect
17. #35971C2semidirect
18. #35971C2semidirect
19. #35971C2semidirect
20. #35937C2semidirect
25. #35868C2semidirect
26. #35868C2semidirect
29. #34336C2semidirect
30. #34335C2semidirect

Maximal subgroups

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

subgroupindex
#427482
#427442
#427382
#427332
#427032
#426892
#426702
#426632
#426002
#425972
#425622
#425532
#376302
#375922
#375802
#367002
#359712
#359372
#359202
#358832
#358682
#357862
#357112
#343362
#343352
#342622