Finite Group Databasebeta

← #7653395

Subgroups — #7653395

Order 512.

4240 conjugacy classes of subgroups.

The subgroup lattice has 1201 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42765C213yesmaximal, complemented
2#42728C213yesmaximal
3#42610C213yesmaximal
4#42553C213yesmaximal, complemented
5#40202C213yesmaximal
6#40096C213yesmaximal
7#40024C213yesmaximal, complemented
8#39999C213yesmaximal, complemented
9#39901C213yesmaximal
10#39901C213yesmaximal
11#39653C213yesmaximal, complemented
12#39241C213yesmaximal, complemented
13#37580C213yesmaximal, complemented
14Q8×#125C211yesmaximal, characteristic, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36475C211yesmaximal, characteristic, complemented
17#36466C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic
19#36448C211yesmaximal, characteristic
20#36435C211yesmaximal, characteristic
21#36435C211yesmaximal, characteristic
22#35971C211yesmaximal, characteristic, complemented
23#35920C211yesmaximal, characteristic
24#35883C211yesmaximal, characteristic
25#35868C211yesmaximal, characteristic, complemented
26#35142C213yesmaximal
27#35115C213yesmaximal, complemented
28#34975C213yesmaximal
29#34336C211yesmaximal, characteristic, complemented
30C4×#557C211yesmaximal, characteristic, complemented
31Q8×#117C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2864C2213yes—
36#2864C2213yes—
37#2863C2213yes—
38#2863C2213yes—
39#2859C2213yes—
40#2859C2213yes—
41#2851C2213yes—
42#2851C2213yes—
43#2839C2216yes—
44#2833C2216yes—
45#2802C2216yes—
46#2794C2216yes—
47#2789C2216yes—
48#2776C2216yes—
49#2766C2216yes—
50#2766C2216yes—
51#2766C2216yes—
52#2758C2216yes—
53#2755C2216yes—
54#2755C2216yes—
55#2722C2216yes—
56#2722C2216yes—
57#2719C2216yes—
58#2713C2216yes—
59#2690C2216yes—
60#2690C2216yes—
61#2666C2216yes—
62#2655C2216yes—
63#2655C2216yes—
64#2655C2216yes—
65#2655C2216yes—
66#2655C2216yes—
67#2652C2216yes—
68#2647C2213yes—
69#2647C2213yes—
70#2645C2213yes—
71#2645C2213yes—
72#2634C2216yes—
73#2584C2213yes—
74#2584C2213yes—
75#2581C2213yes—
76#2581C2213yes—
77#2571C2213yes—
78#2570C2213yes—
79#2570C2213yes—
80#2570C2213yes—
81#2570C2213yes—
82#2570C2213yes—
83#2570C2213yes—
84#2565C2213yes—
85#2565C2213yes—
86#2552C2213yes—
87#2552C2213yes—
88#2552C2213yes—
89#2552C2213yes—
90#2551C2213yes—
91#2550C2213yes—
92#2550C2213yes—
93#2533C2216yes—
94#2533C2213yes—
95#2533C2213yes—
96#2528C2213yes—
97#2528C2216yes—
98#2528C2213yes—
99#2524C2216yes—
100#2514C2213yes—
101#2514C2213yes—
102#2514C2213yes—
103#2514C2213yes—
104#2514C2213yes—
105#2514C2213yes—
106#2514C2213yes—
107#2511C2213yes—
108#2511C2213yes—
109#2511C2213yes—
110#2511C2213yes—
111#2511C2213yes—
112#2511C2213yes—
113#2509C2213yes—
114#2509C2213yes—
115#2509C2213yes—
116#2509C2213yes—
117#2508C2213yes—
118#2508C2213yes—
119#2508C2213yes—
120#2508C2213yes—
121#2507C2213yes—
122#2507C2213yes—
123#2507C2213yes—
124#2507C2213yes—
125#2507C2213yes—
126#2507C2213yes—
127#2507C2213yes—
128#2507C2213yes—
129#2506C2213yes—
130#2506C2213yes—
131#2506C2213yes—
132#2506C2213yes—
133#2506C2213yes—
134#2497C2213yes—
135#2496C2213yes—
136#2496C2213yes—
137#2496C2213yes—
138#2496C2213yes—
139#2496C2213yes—
140#2496C2213yes—
141#2495C2213yes—
142#2495C2213yes—
143#2495C2213yes—
144#2494C2213yes—
145#2494C2213yes—
146#2494C2213yes—
147#2489C2213yes—
148#2478C2216yes—
149#2478C2213yes—
150#2478C2213yes—
151#2475C2213yes—
152#2475C2211yescharacteristic
153#2462C2216yes—
154#2453C2213yes—
155#2453C2213yes—
156#2453C2213yes—
157#2451C2213yes—
158#2451C2213yes—
159#2446C2213yes—
160#2442C2213yes—
161#2442C2213yes—
162#2440C2213yes—
163#2440C2213yes—
164#2429C2213yes—
165#2421C2213yes—
166#2402C2213yes—
167#2402C2213yes—
168#2401C2213yes—
169#2401C2213yes—
170#2370C2213yes—
171#2370C2213yes—
172#2370C2213yes—
173#2370C2213yes—
174#2369C2213yes—
175#2365C2213yes—
176#2355C2213yes—
177#2355C2213yes—
178#2355C2213yes—
179#2355C2213yes—
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
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#2345C2213yes—
201#2345C2213yes—
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208#2336C2216yes—
209#2336C2216yes—
210#2336C2216yes—
211#2334C2216yes—
212#2331C2213yes—
213#2330C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×#125C2213yes—
217C4×#125C2213yes—
218C4×#125C2213yes—
219C4×#125C2213yes—
220C4×#125C2213yes—
221C4×#125C2213yes—
222C4×#126C2213yes—
223C4×#126C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226#2295C2213yes—
227#2295C2213yes—
228#2295C2213yes—
229#2285C2213yes—
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C42×Q8C2213yes—
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C23×Q8C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×#126C2313yes—
245C2×#126C2313yes—
246C2×#126C2316yes—
247C2×#125C2311yescharacteristic
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2316yes—
255C2×#125C2316yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C4×Q8—28no—
259C2×C4×Q8C2313yes—
260C2×C4×Q8C2313yes—
261C2×C4×Q8C2313yes—
262C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2313yes—
281C22×C4⋊C4C2313yes—
282C22×C42C2313yes—
283#401C2313yes—
284#401C2316yes—
285#401C2316yes—
286#401C2313yes—
287#401C2316yes—
288#400C2313yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2316yes—
293#400C2316yes—
294#400C2313yes—
295#400C2316yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2313yes—
301#400C2313yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2313yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2313yes—
311#400C2313yes—
312#400C2316yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2311yescharacteristic
318#400C2313yes—
319#400C2313yes—
320#398C2316yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2313yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2313yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2316yes—
341#398C2311yescharacteristic
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#397C2313yes—
346#397C2316yes—
347#397C2316yes—
348#397C2311yescharacteristic
349#397C2313yes—
350#397C2313yes—
351#397C2313yes—
352#397C2313yes—
353#396C2313yes—
354#396C2311yescharacteristic
355#395C2316yes—
356#395C2316yes—
357#395C2316yes—
358#395C2316yes—
359#391C2316yes—
360#391C2313yes—
361#391C2313yes—
362#391C2313yes—
363#391C2313yes—
364#391C2313yes—
365#391C2313yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2316yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
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#389C2311yescharacteristic
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2316yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2316yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2316yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2316yes—
428#389C2316yes—
429#389C2316yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#388C2311yescharacteristic
443#388C2311yescharacteristic
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2316yes—
449#387C2313yes—
450#387C2313yes—
451#387C2313yes—
452#387C2313yes—
453#387C2313yes—
454#387C2313yes—
455#387C2311yescharacteristic
456#387C2311yescharacteristic
457#387C2313yes—
458#387C2313yes—
459#387C2313yes—
460#387C2313yes—
461#387C2313yes—
462#387C2316yes—
463#387C2316yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2316yes—
468#387C2316yes—
469#387C2316yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2313yes—
485#387C2313yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
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#387C2313yes—
507#387C2313yes—
508#387C2311yescharacteristic
509#385C2316yes—
510#385C2316yes—
511#385C2313yes—
512#385C2313yes—
513#385C2311yescharacteristic
514#385C2311yescharacteristic
515#384C2313yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2313yes—
526#383C2313yes—
527#383C2313yes—
528#383C2316yes—
529#383C2316yes—
530#383C2316yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2316yes—
544#382C2313yes—
545#382C2316yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2316yes—
553#380C2313yes—
554#380C2313yes—
555C4×C4⋊C4C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2316yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
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⋊C4C2316yes—
579C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
591C4×C4⋊C4C2313yes—
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⋊C4C2311yescharacteristic
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617C43C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C22×Q8—24no—
622C22×Q8—24no—
623C22×Q8—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2413yes—
627C22×Q8C2411yescharacteristic
628C23×C4C2413yes—
629C23×C4C2411yescharacteristic
630C23×C4C2413yes—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—46no—
634#126—46no—
635#126—46no—
636#126—412no—
637#125—212no—
638#125—212no—
639#125—24no—
640#125—212no—
641#125—212no—
642#125—212no—
643#125—412no—
644#125—46no—
645#125—412no—
646C22⋊Q8—46no—
647C22⋊Q8—46no—
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—24no—
660C4×Q8—24no—
661C4×Q8—212no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—212no—
665C4×Q8—46no—
666C4×Q8—46no—
667C4×Q8#4118yes—
668#117—24no—
669#117—46no—
670C2×C4⋊C4—212no—
671C2×C4⋊C4C2413yes—
672C2×C4⋊C4C2416yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2416yes—
700C2×C4⋊C4C2416yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2411yescharacteristic
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2411yescharacteristic
749C2×C22⋊C4C2411yescharacteristic
750C2×C22⋊C4C2411yescharacteristic
751C2×C22⋊C4C2411yescharacteristic
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C42—212no—
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2413yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
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×C42C2411yescharacteristic
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2416yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2416yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791#95C2411yescharacteristic
792#95C2411yescharacteristic
793#95C2413yes—
794#95C2413yes—
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#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2416yes—
818#95C2416yes—
819#95C2411yescharacteristic
820#95C2411yescharacteristic
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2413yes—
830#95C2411yescharacteristic
831#95C2416yes—
832#95C2411yescharacteristic
833#95C2413yes—
834#95C2416yes—
835#95C2413yes—
836#95C2413yes—
837#95C2416yes—
838#95C2416yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2416yes—
846#95C2413yes—
847#95C2413yes—
848#95C2416yes—
849#95C2413yes—
850#95C2416yes—
851#95C2416yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2416yes—
862#95C2416yes—
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—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—26no—
889C22×C4—26no—
890C22×C4—26no—
891C22×C4—26no—
892C22×C4—43no—
893C22×C4—43no—
894C22×C4C2513yes—
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2511yescharacteristic
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2511yescharacteristic
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2511yescharacteristic
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2513yes—
914C22×C4C2513yes—
915C22×C4C2513yes—
916C22×C4C2511yescharacteristic
917C22×C4C2513yes—
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2513yes—
924C4⋊C4—26no—
925C4⋊C4—212no—
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—26no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—212no—
937C4⋊C4—212no—
938C4⋊C4—22no—
939C4⋊C4—26no—
940C4⋊C4—26no—
941C4⋊C4—26no—
942C4⋊C4—26no—
943C4⋊C4—26no—
944C4⋊C4—26no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—26no—
951C4⋊C4—26no—
952C4⋊C4—22no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—22no—
956C4⋊C4—26no—
957C4⋊C4—22no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—22no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—22no—
966C4⋊C4—43no—
967C4⋊C4—43no—
968C4⋊C4—43no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—46no—
976C4⋊C4—46no—
977C4⋊C4—46no—
978C4⋊C4—46no—
979C4⋊C4—43no—
980C4⋊C4—46no—
981C4⋊C4—46no—
982C4⋊C4—46no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—46no—
989C4⋊C4—46no—
990C4⋊C4—46no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4C2×#41112yes—
996C4⋊C42−1+414yes—
997C22⋊C4—26no—
998C22⋊C4—26no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—26no—
1002C22⋊C4—26no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—22no—
1007C22⋊C4—43no—
1008C22⋊C4—43no—
1009C42—26no—
1010C42—26no—
1011C42—26no—
1012C42—26no—
1013C42—26no—
1014C42—26no—
1015C42—26no—
1016C42—22no—
1017C42—22no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—26no—
1026C42—22no—
1027C42—26no—
1028C42—22no—
1029C42—26no—
1030C42—43no—
1031C42—43no—
1032C42—43no—
1033C42—43no—
1034C42—43no—
1035C42—43no—
1036C42—43no—
1037C42—46no—
1038C42—43no—
1039C42—43no—
1040C42—46no—
1041C42—43no—
1042C42C2×#41112yes—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23#58512yes—
1050C23C2611yescharacteristic
1051Q8—412no—
1052Q8—412no—
1053Q8—86no—
1054Q8#541116yes—
1055C2×C4—28no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—23no—
1068C2×C4—23no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—23no—
1074C2×C4—23no—
1075C2×C4—23no—
1076C2×C4—23no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—23no—
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—21no—
1096C2×C4—23no—
1097C2×C4—21no—
1098C2×C4—23no—
1099C2×C4—21no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—21no—
1105C2×C4—23no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—23no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—23no—
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—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—21no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—21no—
1136C2×C4—412no—
1137C2×C4—86no—
1138C2×C4C22×#4112yes—
1139C2×C4C22×#4116yes—
1140C2×C4C22×#4116yes—
1141C2×C4C2×2−1+412yes—
1142C2×C4C2×2−1+412yes—
1143C2×C4C2×2−1+412yes—
1144C2×C4C2×2−1+416yes—
1145C2×C4C2×2−1+416yes—
1146C2×C4#58512yes—
1147C2×C4#58512yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22C23×#4111yescharacteristic
1156C22C22×2−1+411yescharacteristic
1157C22C22×2−1+411yescharacteristic
1158C22C22×2−1+411yescharacteristic
1159C22C2×#58511yescharacteristic
1160C22C2×#58511yescharacteristic
1161C22C2×#58511yescharacteristic
1162C4—22no—
1163C4—22no—
1164C4—22no—
1165C4—22no—
1166C4—22no—
1167C4—26no—
1168C4—22no—
1169C4—41no—
1170C4—43no—
1171C4—41no—
1172C4—41no—
1173C4—43no—
1174C4—43no—
1175C4—43no—
1176C4—43no—
1177C4—43no—
1178C4—43no—
1179C4—41no—
1180C4—41no—
1181C4—43no—
1182C4—41no—
1183C4—41no—
1184C4—43no—
1185C4—43no—
1186C4—43no—
1187C4—43no—
1188C4—43no—
1189C4—41no—
1190C4—43no—
1191C4C2×#541112yes—
1192C2—42no—
1193C2C22×#54111yescharacteristic
1194C2#6278811yescharacteristic
1195C2#6281611yescharacteristic
1196C2#6303211yescharacteristic
1197C2#6303311yescharacteristic
1198C2#6303311yescharacteristic
1199C2#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. #42765C2semidirect
4. #42553C2semidirect
7. #40024C2semidirect
8. #39999C2semidirect
11. #39653C2semidirect
12. #39241C2semidirect
13. #37580C2semidirect
14. Q8×#125C2semidirect
15. #36475C2semidirect
16. #36475C2semidirect
17. #36466C2semidirect
22. #35971C2semidirect
25. #35868C2semidirect
27. #35115C2semidirect
29. #34336C2semidirect
30. C4×#557C2semidirect

Maximal subgroups

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

subgroupindex
#427652
#427282
#426102
#425532
#402022
#400962
#400242
#399992
#399012
#396532
#392412
#375802
Q8×#1252
#364752
#364662
#364482
#364352
#359712
#359202
#358832
#358682
#351422
#351152
#349752
#343362
C4×#5572
Q8×#1172