Finite Group Databasebeta

← #7658657

Subgroups — #7658657

Order 512.

4161 conjugacy classes of subgroups.

The subgroup lattice has 1191 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42755C213yesmaximal, complemented
2#42753C213yesmaximal, complemented
3#42728C213yesmaximal, complemented
4#42723C213yesmaximal, complemented
5#42638C213yesmaximal, complemented
6#42636C213yesmaximal, complemented
7#42626C213yesmaximal, complemented
8#42623C213yesmaximal, complemented
9#42530C213yesmaximal, complemented
10#42509C213yesmaximal, complemented
11#42469C213yesmaximal, complemented
12#42455C213yesmaximal, complemented
13#37637C213yesmaximal, complemented
14#37597C213yesmaximal, complemented
15#37571C213yesmaximal, complemented
16#36700C213yesmaximal, complemented
17#36040C211yesmaximal, characteristic
18#35971C211yesmaximal, characteristic, complemented
19#35971C211yesmaximal, characteristic, complemented
20#35957C211yesmaximal, characteristic, complemented
21#35898C211yesmaximal, characteristic
22#35898C211yesmaximal, characteristic
23#35898C211yesmaximal, characteristic
24#35898C211yesmaximal, characteristic
25#35868C211yesmaximal, characteristic, complemented
26#35868C211yesmaximal, characteristic, complemented
27#35868C211yesmaximal, characteristic, complemented
28#35816C211yesmaximal, characteristic
29#34337C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34263C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2839C2211yescharacteristic
36#2839C2213yes—
37#2839C2213yes—
38#2839C2213yes—
39#2836C2213yes—
40#2836C2213yes—
41#2836C2213yes—
42#2836C2213yes—
43#2833C2213yes—
44#2833C2213yes—
45#2833C2213yes—
46#2833C2213yes—
47#2831C2213yes—
48#2831C2213yes—
49#2831C2216yes—
50#2831C2213yes—
51#2831C2213yes—
52#2802C2216yes—
53#2798C2216yes—
54#2794C2216yes—
55#2789C2216yes—
56#2747C2216yes—
57#2744C2216yes—
58#2739C2216yes—
59#2739C2216yes—
60#2725C2216yes—
61#2725C2216yes—
62#2722C2216yes—
63#2722C2216yes—
64#2721C2216yes—
65#2719C2216yes—
66#2704C2216yes—
67#2698C2216yes—
68#2664C2216yes—
69#2664C2216yes—
70#2660C2213yes—
71#2655C2216yes—
72#2655C2216yes—
73#2654C2216yes—
74#2652C2216yes—
75#2652C2216yes—
76#2650C2216yes—
77#2647C2213yes—
78#2647C2213yes—
79#2647C2213yes—
80#2647C2213yes—
81#2647C2213yes—
82#2644C2213yes—
83#2644C2213yes—
84#2644C2213yes—
85#2644C2213yes—
86#2637C2216yes—
87#2637C2216yes—
88#2629C2216yes—
89#2629C2213yes—
90#2628C2213yes—
91#2625C2216yes—
92#2584C2213yes—
93#2580C2213yes—
94#2571C2213yes—
95#2571C2213yes—
96#2570C2213yes—
97#2570C2213yes—
98#2570C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2567C2213yes—
102#2566C2213yes—
103#2563C2213yes—
104#2552C2213yes—
105#2552C2213yes—
106#2552C2213yes—
107#2552C2213yes—
108#2552C2213yes—
109#2550C2213yes—
110#2550C2213yes—
111#2538C2213yes—
112#2513C2213yes—
113#2513C2213yes—
114#2513C2213yes—
115#2513C2213yes—
116#2512C2213yes—
117#2512C2213yes—
118#2512C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2512C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2509C2213yes—
127#2509C2213yes—
128#2509C2213yes—
129#2508C2213yes—
130#2508C2213yes—
131#2508C2213yes—
132#2508C2213yes—
133#2507C2213yes—
134#2507C2213yes—
135#2507C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2506C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2506C2213yes—
144#2497C2213yes—
145#2497C2213yes—
146#2497C2213yes—
147#2497C2213yes—
148#2496C2216yes—
149#2496C2213yes—
150#2496C2213yes—
151#2496C2213yes—
152#2496C2213yes—
153#2494C2213yes—
154#2494C2213yes—
155#2494C2213yes—
156#2494C2213yes—
157#2489C2216yes—
158#2478C2216yes—
159#2475C2216yes—
160#2469C2216yes—
161#2462C2216yes—
162#2454C2213yes—
163#2454C2213yes—
164#2454C2213yes—
165#2452C2213yes—
166#2442C2213yes—
167#2442C2213yes—
168#2442C2213yes—
169#2440C2213yes—
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#2370C2213yes—
185#2370C2213yes—
186#2369C2213yes—
187#2365C2213yes—
188#2357C2213yes—
189#2355C2213yes—
190#2354C2213yes—
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200Q8×C4⋊C4C2213yes—
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
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#2345C2213yes—
213#2344C2213yes—
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2331C2213yes—
221#2330C2213yes—
222#2330C2213yes—
223#2330C2213yes—
224#2319C2213yes—
225#2314C2213yes—
226C4×C4⋊Q8C2213yes—
227C4×#125C2213yes—
228#2298C2213yes—
229#2295C2213yes—
230#2295C2213yes—
231#2293C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×#126C2316yes—
244C2×#126C2316yes—
245C2×#126C2316yes—
246C2×#126C2316yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2316yes—
252C2×#125C2316yes—
253C2×#125C2316yes—
254C2×C22⋊Q8C2316yes—
255#520—28no—
256C2×C4×Q8C2313yes—
257C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2316yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×#117C2313yes—
276C2×#117C2316yes—
277C22×C4⋊C4C2313yes—
278#401C2313yes—
279#401C2313yes—
280#401C2313yes—
281#401C2313yes—
282#400C2313yes—
283#400C2313yes—
284#400C2313yes—
285#400C2316yes—
286#400C2316yes—
287#400C2313yes—
288#400C2313yes—
289#400C2311yescharacteristic
290#400C2313yes—
291#400C2313yes—
292#400C2313yes—
293#400C2313yes—
294#400C2313yes—
295#400C2313yes—
296#400C2313yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2311yescharacteristic
301#400C2311yescharacteristic
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2311yescharacteristic
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2311yescharacteristic
316#400C2311yescharacteristic
317#400C2311yescharacteristic
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#399C2313yes—
325#399C2313yes—
326#399C2316yes—
327#398C2313yes—
328#398C2313yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2311yescharacteristic
333#398C2311yescharacteristic
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2316yes—
340#398C2311yescharacteristic
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2311yescharacteristic
352#398C2311yescharacteristic
353#398C2313yes—
354#398C2313yes—
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#398C2313yes—
359#398C2316yes—
360#398C2316yes—
361#398C2316yes—
362#398C2316yes—
363#398C2316yes—
364#398C2316yes—
365#398C2316yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2313yes—
372#397C2313yes—
373#397C2313yes—
374#397C2316yes—
375#397C2316yes—
376#397C2316yes—
377#397C2313yes—
378#397C2313yes—
379#397C2313yes—
380#397C2313yes—
381#397C2316yes—
382#397C2316yes—
383#397C2316yes—
384#397C2316yes—
385#397C2316yes—
386#396C2313yes—
387#396C2316yes—
388#396C2313yes—
389#396C2313yes—
390#396C2313yes—
391#396C2313yes—
392#396C2313yes—
393#396C2313yes—
394#396C2313yes—
395#396C2316yes—
396#396C2316yes—
397#396C2316yes—
398#396C2316yes—
399#396C2316yes—
400#395C2313yes—
401#395C2316yes—
402#395C2313yes—
403#395C2313yes—
404#395C2313yes—
405#395C2313yes—
406#395C2313yes—
407#393C2313yes—
408#393C2316yes—
409#393C2313yes—
410#391C2313yes—
411#391C2316yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2316yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#389C2313yes—
429#389C2313yes—
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#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#389C2311yescharacteristic
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2316yes—
460#389C2316yes—
461#389C2313yes—
462#389C2313yes—
463#389C2316yes—
464#389C2316yes—
465#389C2313yes—
466#389C2316yes—
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#389C2316yes—
483#388C2316yes—
484#388C2316yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2316yes—
490#388C2316yes—
491#388C2316yes—
492#388C2316yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2316yes—
497#387C2313yes—
498#387C2316yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2311yescharacteristic
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2311yescharacteristic
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#385C2316yes—
530#385C2316yes—
531#385C2316yes—
532#385C2316yes—
533#384C2313yes—
534#384C2313yes—
535#384C2316yes—
536#384C2313yes—
537#384C2313yes—
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#384C2313yes—
544#384C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2313yes—
553#382C2313yes—
554#382C2316yes—
555#382C2316yes—
556#381C2316yes—
557#380C2316yes—
558#380C2316yes—
559#380C2313yes—
560#380C2313yes—
561#380C2316yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2316yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2316yes—
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⋊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—
614C4×C22⋊C4C2316yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620C43C2313yes—
621C2×#41—24no—
622C2×#41—24no—
623C2×#41—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2411yescharacteristic
627C22×D4C2413yes—
628C23×C4C2413yes—
629C23×C4C2416yes—
630C4⋊Q8—212no—
631C4⋊Q8—212no—
632#126—86no—
633#126—86no—
634#126—86no—
635#126—86no—
636#125—212no—
637#125—212no—
638#125—212no—
639#125—212no—
640#125—86no—
641#125—86no—
642#125—86no—
643C22⋊Q8—86no—
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—24no—
654C4×Q8—24no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—212no—
658C4×Q8—212no—
659C4×Q8—86no—
660C4×Q8#4118yes—
661C4×D4—212no—
662C4×D4—212no—
663#117—212no—
664#117—86no—
665C2×C4⋊C4—212no—
666C2×C4⋊C4C2413yes—
667C2×C4⋊C4C2413yes—
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2416yes—
688C2×C4⋊C4C2416yes—
689C2×C4⋊C4C2413yes—
690C2×C4⋊C4C2416yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2416yes—
693C2×C4⋊C4C2416yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2416yes—
696C2×C4⋊C4C2416yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2416yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2413yes—
741C2×C22⋊C4C2413yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2416yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2416yes—
747C2×C22⋊C4C2416yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2416yes—
753C2×C22⋊C4C2416yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2416yes—
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×C42C2416yes—
776C2×C42C2413yes—
777C2×C42C2416yes—
778C2×C42C2416yes—
779C2×C42C2416yes—
780C2×C42C2416yes—
781C2×C42C2411yescharacteristic
782C2×C42C2413yes—
783C2×C42C2413yes—
784#95C2411yescharacteristic
785#95C2411yescharacteristic
786#95C2411yescharacteristic
787#95C2411yescharacteristic
788#95C2411yescharacteristic
789#95C2413yes—
790#95C2413yes—
791#95C2413yes—
792#95C2413yes—
793#95C2413yes—
794#95C2413yes—
795#95C2413yes—
796#95C2413yes—
797#95C2413yes—
798#95C2413yes—
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2413yes—
804#95C2411yescharacteristic
805#95C2411yescharacteristic
806#95C2411yescharacteristic
807#95C2411yescharacteristic
808#95C2411yescharacteristic
809#95C2411yescharacteristic
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2416yes—
818#95C2416yes—
819#95C2413yes—
820#95C2411yescharacteristic
821#95C2411yescharacteristic
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2416yes—
845#95C2416yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864#95C2416yes—
865#95C2416yes—
866C24C2513yes—
867#41—416no—
868C2×Q8—26no—
869C2×Q8—26no—
870C2×Q8—43no—
871C2×Q8—43no—
872C2×Q8—43no—
873C2×Q8—43no—
874C2×Q8C2×#4114yes—
875C2×Q82−1+414yes—
876C2×Q82−1+414yes—
877C2×D4—26no—
878C2×D4—26no—
879C2×D4—26no—
880C22×C4—26no—
881C22×C4—26no—
882C22×C4—26no—
883C22×C4—212no—
884C22×C4—46no—
885C22×C4—46no—
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2513yes—
894C22×C4C2511yescharacteristic
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2513yes—
898C22×C4C2513yes—
899C22×C4C2513yes—
900C22×C4C2513yes—
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2513yes—
905C22×C4C2511yescharacteristic
906C22×C4C2511yescharacteristic
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2511yescharacteristic
914C22×C4C2513yes—
915C22×C4C2513yes—
916C4⋊C4—26no—
917C4⋊C4—26no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—26no—
922C4⋊C4—26no—
923C4⋊C4—26no—
924C4⋊C4—26no—
925C4⋊C4—26no—
926C4⋊C4—26no—
927C4⋊C4—26no—
928C4⋊C4—26no—
929C4⋊C4—212no—
930C4⋊C4—212no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—26no—
938C4⋊C4—26no—
939C4⋊C4—43no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—46no—
945C4⋊C4—43no—
946C4⋊C4—41no—
947C4⋊C4—43no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—43no—
955C4⋊C4—43no—
956C4⋊C4—43no—
957C4⋊C4—43no—
958C4⋊C4—46no—
959C4⋊C4—43no—
960C4⋊C4—43no—
961C4⋊C4—43no—
962C4⋊C4—46no—
963C4⋊C4—43no—
964C4⋊C4—46no—
965C4⋊C4—46no—
966C4⋊C4—43no—
967C4⋊C4—46no—
968C4⋊C4—46no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—46no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—46no—
980C4⋊C4—46no—
981C4⋊C4—46no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4C2×#41112yes—
991C22⋊C4—26no—
992C22⋊C4—26no—
993C22⋊C4—43no—
994C22⋊C4—43no—
995C22⋊C4—43no—
996C22⋊C4—43no—
997C22⋊C4—43no—
998C22⋊C4—43no—
999C22⋊C4—46no—
1000C22⋊C4—43no—
1001C22⋊C4—46no—
1002C22⋊C4—43no—
1003C22⋊C4—46no—
1004C22⋊C4—46no—
1005C22⋊C4—43no—
1006C22⋊C4—46no—
1007C22⋊C4—46no—
1008C22⋊C4—43no—
1009C22⋊C4—43no—
1010C22⋊C4—43no—
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—43no—
1025C42—41no—
1026C42—43no—
1027C42—46no—
1028C42—43no—
1029C42—46no—
1030C42—46no—
1031C42—46no—
1032C42—46no—
1033C42C2×#41112yes—
1034C23—23no—
1035C23—23no—
1036C23—23no—
1037C23—23no—
1038C23—23no—
1039C23—23no—
1040C23—23no—
1041C23C2611yescharacteristic
1042Q8—412no—
1043Q8—86no—
1044Q8#541116yes—
1045D4—412no—
1046C2×C4—23no—
1047C2×C4—21no—
1048C2×C4—23no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—23no—
1056C2×C4—23no—
1057C2×C4—23no—
1058C2×C4—23no—
1059C2×C4—23no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
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—23no—
1080C2×C4—21no—
1081C2×C4—23no—
1082C2×C4—23no—
1083C2×C4—23no—
1084C2×C4—23no—
1085C2×C4—23no—
1086C2×C4—23no—
1087C2×C4—23no—
1088C2×C4—23no—
1089C2×C4—23no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—23no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
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—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—23no—
1130C2×C4—21no—
1131C2×C4—412no—
1132C2×C4—812no—
1133C2×C4C22×#4112yes—
1134C2×C4C22×#4116yes—
1135C2×C4C22×#4116yes—
1136C2×C4C2×2−1+416yes—
1137C2×C4C2×2−1+416yes—
1138C22—43no—
1139C22—43no—
1140C22—43no—
1141C22—43no—
1142C22—43no—
1143C22—43no—
1144C22—43no—
1145C22C23×#4111yescharacteristic
1146C22C22×2−1+411yescharacteristic
1147C22C22×2−1+411yescharacteristic
1148C22H(7,𝔽2)11yescharacteristic
1149C22H(7,𝔽2)11yescharacteristic
1150C222−1+611yescharacteristic
1151C222−1+611yescharacteristic
1152C4—22no—
1153C4—26no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—43no—
1163C4—43no—
1164C4—43no—
1165C4—43no—
1166C4—43no—
1167C4—43no—
1168C4—43no—
1169C4—43no—
1170C4—41no—
1171C4—41no—
1172C4—43no—
1173C4—43no—
1174C4—43no—
1175C4—41no—
1176C4—41no—
1177C4—43no—
1178C4—43no—
1179C4—41no—
1180C4—41no—
1181C4C2×#541112yes—
1182C2—83no—
1183C2C22×#54111yescharacteristic
1184C2#6285111yescharacteristic
1185C2#6285711yescharacteristic
1186C2#6305711yescharacteristic
1187C2#6306111yescharacteristic
1188C2#6306111yescharacteristic
1189C2#6307011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42755C2semidirect
2. #42753C2semidirect
3. #42728C2semidirect
4. #42723C2semidirect
5. #42638C2semidirect
6. #42636C2semidirect
7. #42626C2semidirect
8. #42623C2semidirect
9. #42530C2semidirect
10. #42509C2semidirect
11. #42469C2semidirect
12. #42455C2semidirect
13. #37637C2semidirect
14. #37597C2semidirect
15. #37571C2semidirect
16. #36700C2semidirect
18. #35971C2semidirect
19. #35971C2semidirect
20. #35957C2semidirect
25. #35868C2semidirect
26. #35868C2semidirect
27. #35868C2semidirect
29. #34337C2semidirect
30. #34336C2semidirect

Maximal subgroups

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

subgroupindex
#427552
#427532
#427282
#427232
#426382
#426362
#426262
#426232
#425302
#425092
#424692
#424552
#376372
#375972
#375712
#367002
#360402
#359712
#359572
#358982
#358682
#358162
#343372
#343362
#342632