Finite Group Databasebeta

← #7654148

Subgroups — #7654148

Order 512.

4229 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42689C213yesmaximal, complemented
2#42663C213yesmaximal
3#42527C213yesmaximal, complemented
4#42470C213yesmaximal
5#40189C213yesmaximal, complemented
6#40120C213yesmaximal
7#40082C213yesmaximal, complemented
8#40075C213yesmaximal
9#39788C213yesmaximal
10#39241C213yesmaximal, complemented
11#39011C213yesmaximal
12#39003C213yesmaximal, complemented
13#37597C213yesmaximal
14#36584C211yesmaximal, characteristic, complemented
15Q8×#126C211yesmaximal, characteristic
16Q8×#125C211yesmaximal, characteristic, complemented
17#36475C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic
19#36448C211yesmaximal, characteristic
20#36448C211yesmaximal, characteristic
21#36447C211yesmaximal, characteristic, complemented
22#35957C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35845C211yesmaximal, characteristic
25#35786C211yesmaximal, characteristic
26#35208C213yesmaximal, complemented
27#35115C213yesmaximal, complemented
28#34973C213yesmaximal
29#34262C211yesmaximal, characteristic
30C4×#557C211yesmaximal, characteristic, complemented
31C4×#557C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2864C2213yes—
36#2863C2213yes—
37#2863C2213yes—
38#2863C2213yes—
39#2863C2213yes—
40#2859C2213yes—
41#2859C2213yes—
42#2859C2213yes—
43#2833C2216yes—
44#2831C2216yes—
45#2794C2216yes—
46#2783C2216yes—
47#2776C2216yes—
48#2776C2216yes—
49#2769C2216yes—
50#2769C2216yes—
51#2766C2216yes—
52#2766C2216yes—
53#2762C2216yes—
54#2762C2216yes—
55#2758C2216yes—
56#2754C2216yes—
57#2725C2216yes—
58#2721C2216yes—
59#2719C2216yes—
60#2719C2216yes—
61#2666C2216yes—
62#2666C2216yes—
63#2664C2216yes—
64#2660C2213yes—
65#2655C2216yes—
66#2655C2216yes—
67#2655C2216yes—
68#2654C2216yes—
69#2647C2213yes—
70#2634C2216yes—
71#2629C2213yes—
72#2628C2213yes—
73#2584C2213yes—
74#2582C2213yes—
75#2581C2213yes—
76#2571C2213yes—
77#2571C2213yes—
78#2571C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2570C2213yes—
82#2567C2213yes—
83#2567C2213yes—
84#2565C2213yes—
85#2552C2213yes—
86#2552C2213yes—
87#2552C2213yes—
88#2552C2213yes—
89#2552C2213yes—
90#2552C2213yes—
91#2550C2213yes—
92#2550C2213yes—
93#2533C2216yes—
94#2528C2216yes—
95#2524C2213yes—
96#2524C2213yes—
97#2524C2213yes—
98#2524C2213yes—
99#2519C2213yes—
100#2519C2211yescharacteristic
101#2519C2213yes—
102#2519C2213yes—
103#2514C2213yes—
104#2514C2213yes—
105#2514C2213yes—
106#2514C2213yes—
107#2514C2213yes—
108#2514C2213yes—
109#2511C2213yes—
110#2511C2213yes—
111#2511C2213yes—
112#2511C2213yes—
113#2511C2213yes—
114#2511C2213yes—
115#2509C2213yes—
116#2509C2213yes—
117#2509C2213yes—
118#2509C2213yes—
119#2509C2213yes—
120#2509C2213yes—
121#2508C2213yes—
122#2508C2213yes—
123#2508C2213yes—
124#2507C2213yes—
125#2507C2213yes—
126#2507C2213yes—
127#2507C2213yes—
128#2507C2213yes—
129#2507C2213yes—
130#2506C2213yes—
131#2506C2213yes—
132#2506C2213yes—
133#2506C2213yes—
134#2506C2216yes—
135#2506C2213yes—
136#2497C2213yes—
137#2497C2213yes—
138#2497C2213yes—
139#2496C2213yes—
140#2496C2213yes—
141#2496C2213yes—
142#2495C2213yes—
143#2495C2213yes—
144#2495C2213yes—
145#2494C2213yes—
146#2494C2213yes—
147#2494C2213yes—
148#2469C2213yes—
149#2469C2213yes—
150#2469C2213yes—
151#2469C2213yes—
152#2462C2213yes—
153#2462C2216yes—
154#2462C2213yes—
155#2462C2213yes—
156#2462C2213yes—
157#2453C2213yes—
158#2453C2213yes—
159#2453C2213yes—
160#2453C2216yes—
161#2451C2213yes—
162#2441C2213yes—
163#2441C2213yes—
164#2441C2213yes—
165#2439C2213yes—
166#2402C2213yes—
167#2399C2213yes—
168#2396C2213yes—
169#2396C2213yes—
170#2370C2213yes—
171#2370C2213yes—
172#2370C2213yes—
173#2370C2213yes—
174#2365C2213yes—
175#2365C2213yes—
176#2356C2213yes—
177#2355C2213yes—
178#2355C2213yes—
179#2355C2213yes—
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2347C2213yes—
201#2346C2213yes—
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208#2336C2216yes—
209#2336C2216yes—
210#2330C2216yes—
211#2320C2213yes—
212#2320C2216yes—
213#2314C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×#125C2213yes—
217C4×#125C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×#126C2213yes—
227C4×#126C2213yes—
228#2298C2213yes—
229#2295C2213yes—
230#2276C2211yescharacteristic
231C42×Q8C2213yes—
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2213yes—
238C23×Q8C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×#126C2311yescharacteristic
244C2×#126C2313yes—
245C2×#126C2313yes—
246C2×#126C2313yes—
247C2×#125C2311yescharacteristic
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2316yes—
256C2×#125C2316yes—
257C2×#125C2316yes—
258#519—28no—
259C2×C4×Q8C2313yes—
260C2×C4×Q8C2313yes—
261C2×C4×Q8C2313yes—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2313yes—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2311yescharacteristic
281C2×#117C2313yes—
282C2×#117C2313yes—
283#401C2316yes—
284#401C2316yes—
285#401C2316yes—
286#400C2313yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2316yes—
295#400C2313yes—
296#400C2316yes—
297#400C2316yes—
298#400C2313yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2313yes—
304#400C2316yes—
305#400C2313yes—
306#400C2313yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#399C2316yes—
312#399C2311yescharacteristic
313#399C2313yes—
314#398C2313yes—
315#398C2316yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2316yes—
322#398C2313yes—
323#398C2313yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2313yes—
328#398C2313yes—
329#398C2316yes—
330#398C2311yescharacteristic
331#398C2313yes—
332#398C2313yes—
333#398C2316yes—
334#398C2311yescharacteristic
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2316yes—
339#398C2316yes—
340#397C2316yes—
341#397C2316yes—
342#397C2316yes—
343#396C2313yes—
344#396C2316yes—
345#396C2316yes—
346#396C2311yescharacteristic
347#396C2313yes—
348#396C2313yes—
349#395C2313yes—
350#395C2313yes—
351#395C2316yes—
352#395C2316yes—
353#395C2313yes—
354#395C2313yes—
355#395C2313yes—
356#395C2313yes—
357#393C2313yes—
358#393C2313yes—
359#391C2316yes—
360#391C2316yes—
361#391C2313yes—
362#391C2313yes—
363#391C2316yes—
364#391C2313yes—
365#391C2313yes—
366#391C2316yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#389C2311yescharacteristic
376#389C2313yes—
377#389C2313yes—
378#389C2313yes—
379#389C2313yes—
380#389C2313yes—
381#389C2313yes—
382#389C2313yes—
383#389C2313yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2316yes—
396#389C2316yes—
397#389C2313yes—
398#389C2316yes—
399#389C2316yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2316yes—
411#389C2313yes—
412#389C2313yes—
413#389C2316yes—
414#389C2313yes—
415#389C2313yes—
416#389C2316yes—
417#389C2313yes—
418#389C2313yes—
419#389C2316yes—
420#389C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2316yes—
426#389C2316yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#388C2311yescharacteristic
437#388C2311yescharacteristic
438#388C2311yescharacteristic
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2313yes—
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2313yes—
449#388C2316yes—
450#388C2313yes—
451#388C2313yes—
452#388C2311yescharacteristic
453#387C2313yes—
454#387C2313yes—
455#387C2313yes—
456#387C2313yes—
457#387C2313yes—
458#387C2313yes—
459#387C2313yes—
460#387C2313yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2311yescharacteristic
466#387C2313yes—
467#387C2313yes—
468#387C2316yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#384C2313yes—
514#384C2313yes—
515#384C2313yes—
516#384C2313yes—
517#384C2313yes—
518#384C2316yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#383C2313yes—
526#383C2313yes—
527#383C2313yes—
528#383C2313yes—
529#383C2316yes—
530#383C2316yes—
531#383C2316yes—
532#383C2316yes—
533#382C2311yescharacteristic
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2316yes—
546#382C2313yes—
547#382C2316yes—
548#382C2316yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555C4×C4⋊C4C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
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⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
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⋊C4C2311yescharacteristic
607C4×C4⋊C4C2311yescharacteristic
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2316yes—
615#376C2313yes—
616C43C2313yes—
617C43C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2413yes—
627C22×Q8C2411yescharacteristic
628C23×C4C2413yes—
629C4⋊Q8—212no—
630C4⋊Q8—212no—
631#126—24no—
632#126—46no—
633#126—46no—
634#126—46no—
635#125—212no—
636#125—212no—
637#125—212no—
638#125—24no—
639#125—212no—
640#125—412no—
641#125—46no—
642#125—412no—
643#125—412no—
644#125—46no—
645#125—46no—
646C4×Q8—24no—
647C4×Q8—24no—
648C4×Q8—24no—
649C4×Q8—24no—
650C4×Q8—24no—
651C4×Q8—24no—
652C4×Q8—24no—
653C4×Q8—24no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—24no—
658C4×Q8—24no—
659C4×Q8—212no—
660C4×Q8—212no—
661C4×Q8—212no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—46no—
665C4×Q8—46no—
666C4×Q8—46no—
667C4×Q8#4118yes—
668#117—212no—
669#117—212no—
670C2×C4⋊C4C2413yes—
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2413yes—
677C2×C4⋊C4C2413yes—
678C2×C4⋊C4C2413yes—
679C2×C4⋊C4C2413yes—
680C2×C4⋊C4C2413yes—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2413yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C22⋊C4C2411yescharacteristic
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2411yescharacteristic
749C2×C22⋊C4C2411yescharacteristic
750C2×C22⋊C4C2411yescharacteristic
751C2×C22⋊C4C2411yescharacteristic
752C2×C22⋊C4C2411yescharacteristic
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C42C2416yes—
760C2×C42C2413yes—
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2413yes—
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2413yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2411yescharacteristic
780C2×C42C2413yes—
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2416yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795#95C2411yescharacteristic
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2416yes—
802#95C2416yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2411yescharacteristic
824#95C2416yes—
825#95C2413yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2416yes—
833#95C2416yes—
834#95C2416yes—
835#95C2416yes—
836#95C2416yes—
837#95C2413yes—
838#95C2413yes—
839#95C2416yes—
840#95C2416yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2416yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2416yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2416yes—
864#95C2416yes—
865#95C2416yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871C24C2511yescharacteristic
872C2×Q8—26no—
873C2×Q8—26no—
874C2×Q8—26no—
875C2×Q8—26no—
876C2×Q8—26no—
877C2×Q8—26no—
878C2×Q8—43no—
879C2×Q8—43no—
880C2×Q8—43no—
881C2×Q8—416no—
882C2×Q8C2×#4114yes—
883C2×Q82−1+414yes—
884C2×Q82−1+414yes—
885C22×C4—26no—
886C22×C4—26no—
887C22×C4—26no—
888C22×C4C2513yes—
889C22×C4C2511yescharacteristic
890C22×C4C2513yes—
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2513yes—
894C22×C4C2513yes—
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2513yes—
898C22×C4C2511yescharacteristic
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2513yes—
906C22×C4C2511yescharacteristic
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2511yescharacteristic
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2513yes—
918C4⋊C4—26no—
919C4⋊C4—26no—
920C4⋊C4—26no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—212no—
932C4⋊C4—212no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—26no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—43no—
969C4⋊C4—46no—
970C4⋊C4—46no—
971C4⋊C4—46no—
972C4⋊C4—46no—
973C4⋊C4—46no—
974C4⋊C4—46no—
975C4⋊C4—46no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—46no—
979C4⋊C4—46no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—46no—
984C4⋊C4—46no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4C2×#41112yes—
992C4⋊C42−1+414yes—
993C22⋊C4—26no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—43no—
1002C22⋊C4—43no—
1003C22⋊C4—43no—
1004C22⋊C4—43no—
1005C22⋊C4—43no—
1006C22⋊C4—43no—
1007C42—26no—
1008C42—212no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—26no—
1014C42—26no—
1015C42—26no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—22no—
1025C42—22no—
1026C42—22no—
1027C42—22no—
1028C42—26no—
1029C42—22no—
1030C42—26no—
1031C42—43no—
1032C42—43no—
1033C42—43no—
1034C42—43no—
1035C42—43no—
1036C42—43no—
1037C42—43no—
1038C42—46no—
1039C42—43no—
1040C42—43no—
1041C42—43no—
1042C42C2×#41112yes—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23C2611yescharacteristic
1051Q8—412no—
1052Q8—412no—
1053Q8—412no—
1054Q8#541116yes—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—23no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—23no—
1070C2×C4—21no—
1071C2×C4—23no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—21no—
1082C2×C4—23no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—21no—
1097C2×C4—23no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—23no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—21no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—412no—
1135C2×C4C22×#4116yes—
1136C2×C4C22×#4112yes—
1137C2×C4C22×#4116yes—
1138C2×C4C2×2−1+412yes—
1139C2×C4C2×2−1+412yes—
1140C2×C4C2×2−1+412yes—
1141C2×C4C2×2−1+416yes—
1142C2×C4C2×2−1+416yes—
1143C2×C4#58512yes—
1144C2×C4#58512yes—
1145C2×C4#58512yes—
1146C22—41no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22C23×#4111yescharacteristic
1154C22C22×2−1+411yescharacteristic
1155C22C22×2−1+411yescharacteristic
1156C22C22×2−1+411yescharacteristic
1157C22C2×#58511yescharacteristic
1158C22C2×#58511yescharacteristic
1159C22C2×#58511yescharacteristic
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—22no—
1166C4—26no—
1167C4—22no—
1168C4—41no—
1169C4—43no—
1170C4—43no—
1171C4—43no—
1172C4—43no—
1173C4—43no—
1174C4—43no—
1175C4—43no—
1176C4—41no—
1177C4—43no—
1178C4—41no—
1179C4—43no—
1180C4—41no—
1181C4—43no—
1182C4—43no—
1183C4—43no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—43no—
1188C4—43no—
1189C4C2×#541112yes—
1190C2—81no—
1191C2C22×#54111yescharacteristic
1192C2#6279311yescharacteristic
1193C2#6280511yescharacteristic
1194C2#6303211yescharacteristic
1195C2#6303311yescharacteristic
1196C2#6303311yescharacteristic
1197C2#6303811yescharacteristic
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
1. #42689C2semidirect
3. #42527C2semidirect
5. #40189C2semidirect
7. #40082C2semidirect
10. #39241C2semidirect
12. #39003C2semidirect
14. #36584C2semidirect
16. Q8×#125C2semidirect
17. #36475C2semidirect
21. #36447C2semidirect
22. #35957C2semidirect
23. #35868C2semidirect
26. #35208C2semidirect
27. #35115C2semidirect
30. C4×#557C2semidirect
31. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#426892
#426632
#425272
#424702
#401892
#401202
#400822
#400752
#397882
#392412
#390112
#390032
#375972
#365842
Q8×#1262
Q8×#1252
#364752
#364482
#364472
#359572
#358682
#358452
#357862
#352082
#351152
#349732
#342622
C4×#5572