Finite Group Databasebeta

← #7654208

Subgroups — #7654208

Order 512.

4295 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42764C213yesmaximal, complemented
2#42723C213yesmaximal, complemented
3#42614C213yesmaximal, complemented
4#42562C213yesmaximal, complemented
5#40227C213yesmaximal, complemented
6#40120C213yesmaximal, complemented
7#40027C213yesmaximal, complemented
8#39997C213yesmaximal, complemented
9#39907C213yesmaximal, complemented
10#39907C213yesmaximal, complemented
11#39780C213yesmaximal, complemented
12#39217C213yesmaximal, complemented
13#37571C213yesmaximal, complemented
14#36584C211yesmaximal, characteristic, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36475C211yesmaximal, characteristic, complemented
17#36466C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic
19#36458C211yesmaximal, characteristic
20#36431C211yesmaximal, characteristic
21#36431C211yesmaximal, characteristic
22#36059C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35898C211yesmaximal, characteristic
25#35868C211yesmaximal, characteristic, complemented
26#35142C213yesmaximal, complemented
27#35116C213yesmaximal, complemented
28#34975C213yesmaximal, complemented
29#34336C211yesmaximal, characteristic, complemented
30C4×#557C211yesmaximal, characteristic, complemented
31#34125C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2864C2213yes—
36#2864C2213yes—
37#2860C2213yes—
38#2860C2213yes—
39#2859C2213yes—
40#2859C2213yes—
41#2851C2213yes—
42#2851C2213yes—
43#2836C2216yes—
44#2831C2216yes—
45#2798C2216yes—
46#2783C2216yes—
47#2772C2216yes—
48#2769C2216yes—
49#2769C2216yes—
50#2758C2216yes—
51#2758C2216yes—
52#2754C2216yes—
53#2739C2216yes—
54#2739C2216yes—
55#2725C2216yes—
56#2725C2216yes—
57#2721C2216yes—
58#2716C2216yes—
59#2689C2216yes—
60#2689C2216yes—
61#2664C2216yes—
62#2655C2216yes—
63#2654C2216yes—
64#2652C2216yes—
65#2652C2216yes—
66#2652C2216yes—
67#2650C2216yes—
68#2647C2213yes—
69#2647C2213yes—
70#2644C2213yes—
71#2644C2213yes—
72#2637C2216yes—
73#2584C2213yes—
74#2584C2213yes—
75#2580C2213yes—
76#2580C2213yes—
77#2571C2213yes—
78#2571C2213yes—
79#2571C2213yes—
80#2570C2213yes—
81#2570C2213yes—
82#2570C2213yes—
83#2570C2213yes—
84#2570C2213yes—
85#2570C2213yes—
86#2566C2213yes—
87#2566C2213yes—
88#2552C2213yes—
89#2552C2213yes—
90#2551C2213yes—
91#2550C2213yes—
92#2550C2213yes—
93#2533C2216yes—
94#2533C2213yes—
95#2533C2213yes—
96#2528C2213yes—
97#2528C2211yescharacteristic
98#2519C2216yes—
99#2514C2213yes—
100#2513C2213yes—
101#2513C2213yes—
102#2513C2213yes—
103#2513C2213yes—
104#2513C2213yes—
105#2513C2213yes—
106#2512C2213yes—
107#2512C2213yes—
108#2512C2213yes—
109#2512C2213yes—
110#2512C2213yes—
111#2512C2213yes—
112#2509C2213yes—
113#2509C2213yes—
114#2509C2213yes—
115#2509C2213yes—
116#2509C2213yes—
117#2509C2213yes—
118#2509C2213yes—
119#2509C2213yes—
120#2508C2213yes—
121#2508C2213yes—
122#2508C2213yes—
123#2508C2213yes—
124#2507C2213yes—
125#2507C2213yes—
126#2507C2213yes—
127#2507C2213yes—
128#2506C2213yes—
129#2506C2213yes—
130#2506C2213yes—
131#2506C2213yes—
132#2506C2213yes—
133#2497C2213yes—
134#2497C2213yes—
135#2497C2213yes—
136#2496C2213yes—
137#2496C2213yes—
138#2496C2213yes—
139#2496C2213yes—
140#2495C2213yes—
141#2495C2213yes—
142#2495C2213yes—
143#2495C2213yes—
144#2495C2213yes—
145#2494C2213yes—
146#2489C2213yes—
147#2478C2216yes—
148#2478C2213yes—
149#2478C2213yes—
150#2475C2213yes—
151#2475C2216yes—
152#2475C2213yes—
153#2469C2216yes—
154#2454C2213yes—
155#2454C2213yes—
156#2453C2213yes—
157#2452C2213yes—
158#2452C2213yes—
159#2446C2213yes—
160#2441C2213yes—
161#2441C2213yes—
162#2439C2213yes—
163#2439C2213yes—
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#2357C2213yes—
177#2357C2213yes—
178#2355C2213yes—
179#2355C2213yes—
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
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#2347C2213yes—
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2336C2216yes—
209#2334C2216yes—
210#2334C2216yes—
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#2293C2213yes—
228#2293C2213yes—
229#2283C2213yes—
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C42×Q8C2213yes—
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×#126C2313yes—
245C2×#126C2313yes—
246C2×#126C2316yes—
247C2×#126C2316yes—
248C2×#126C2316yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2316yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C4×#41—28no—
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×Q8C2311yescharacteristic
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×#117C2313yes—
281C2×#117C2313yes—
282C2×#117C2313yes—
283C22×C42C2313yes—
284#401C2313yes—
285#401C2311yescharacteristic
286#400C2313yes—
287#400C2316yes—
288#400C2316yes—
289#400C2316yes—
290#400C2316yes—
291#400C2316yes—
292#400C2313yes—
293#400C2316yes—
294#400C2316yes—
295#400C2316yes—
296#400C2316yes—
297#400C2313yes—
298#400C2316yes—
299#400C2316yes—
300#400C2313yes—
301#400C2313yes—
302#400C2313yes—
303#400C2316yes—
304#400C2316yes—
305#400C2311yescharacteristic
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2311yescharacteristic
311#400C2313yes—
312#400C2313yes—
313#399C2316yes—
314#399C2316yes—
315#398C2313yes—
316#398C2316yes—
317#398C2316yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2316yes—
322#398C2313yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2313yes—
327#398C2313yes—
328#398C2311yescharacteristic
329#398C2313yes—
330#398C2313yes—
331#398C2313yes—
332#397C2316yes—
333#397C2316yes—
334#397C2316yes—
335#397C2313yes—
336#397C2316yes—
337#397C2316yes—
338#397C2316yes—
339#397C2316yes—
340#397C2316yes—
341#397C2316yes—
342#397C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#396C2316yes—
348#396C2316yes—
349#396C2316yes—
350#396C2316yes—
351#396C2313yes—
352#396C2316yes—
353#396C2313yes—
354#396C2316yes—
355#396C2316yes—
356#395C2316yes—
357#395C2316yes—
358#393C2316yes—
359#393C2316yes—
360#391C2316yes—
361#391C2313yes—
362#391C2313yes—
363#391C2313yes—
364#391C2316yes—
365#391C2313yes—
366#391C2313yes—
367#391C2313yes—
368#390C2313yes—
369#390C2313yes—
370#390C2313yes—
371#390C2313yes—
372#390C2313yes—
373#390C2313yes—
374#390C2313yes—
375#390C2313yes—
376#390C2313yes—
377#390C2313yes—
378#390C2313yes—
379#390C2313yes—
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#389C2311yescharacteristic
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2316yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2316yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2316yes—
428#389C2313yes—
429#389C2316yes—
430#389C2316yes—
431#389C2316yes—
432#389C2316yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#388C2313yes—
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2313yes—
449#388C2316yes—
450#388C2316yes—
451#388C2316yes—
452#388C2316yes—
453#388C2316yes—
454#388C2316yes—
455#388C2316yes—
456#388C2316yes—
457#388C2316yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2316yes—
462#387C2311yescharacteristic
463#387C2311yescharacteristic
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2311yescharacteristic
469#387C2311yescharacteristic
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2316yes—
476#387C2316yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2313yes—
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#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2311yescharacteristic
506#387C2311yescharacteristic
507#387C2311yescharacteristic
508#385C2313yes—
509#385C2313yes—
510#385C2316yes—
511#385C2316yes—
512#385C2313yes—
513#385C2313yes—
514#385C2316yes—
515#385C2316yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#384C2313yes—
525#383C2313yes—
526#383C2313yes—
527#383C2316yes—
528#383C2316yes—
529#382C2311yescharacteristic
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2316yes—
543#382C2313yes—
544#382C2316yes—
545#382C2313yes—
546#381C2316yes—
547#380C2313yes—
548#380C2313yes—
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⋊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⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2316yes—
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⋊C4C2311yescharacteristic
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2311yescharacteristic
616#376C2313yes—
617C43C2313yes—
618C43C2313yes—
619C43C2313yes—
620C43C2313yes—
621C2×#41—24no—
622C2×#41—24no—
623C2×#41—24no—
624C22×Q8C2413yes—
625C22×Q8C2413yes—
626C22×Q8C2411yescharacteristic
627C22×D4C2413yes—
628C23×C4C2413yes—
629C23×C4C2413yes—
630C23×C4C2413yes—
631C4⋊Q8—212no—
632C4⋊Q8—212no—
633C4⋊Q8—46no—
634#126—412no—
635#126—412no—
636#126—46no—
637#126—46no—
638#126—412no—
639#125—212no—
640#125—212no—
641#125—212no—
642#125—212no—
643#125—46no—
644#125—46no—
645#125—412no—
646#125—46no—
647C22⋊Q8—46no—
648C22⋊Q8—46no—
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—24no—
662C4×Q8—212no—
663C4×Q8—212no—
664C4×Q8—46no—
665C4×Q8—46no—
666C4×Q8#4118yes—
667C4×D4—212no—
668C4×D4—212no—
669#117—212no—
670#117—46no—
671#117—46no—
672C2×C4⋊C4C2413yes—
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2416yes—
703C2×C4⋊C4C2416yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2411yescharacteristic
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⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C22⋊C4C2416yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2413yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2416yes—
752C2×C22⋊C4C2416yes—
753C2×C22⋊C4C2413yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2416yes—
758C2×C22⋊C4C2416yes—
759C2×C22⋊C4C2416yes—
760C2×C22⋊C4C2416yes—
761C2×C42—212no—
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2413yes—
765C2×C42C2413yes—
766C2×C42C2411yescharacteristic
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×C42C2413yes—
780C2×C42C2411yescharacteristic
781C2×C42C2413yes—
782C2×C42C2411yescharacteristic
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2416yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2416yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796#95C2411yescharacteristic
797#95C2411yescharacteristic
798#95C2411yescharacteristic
799#95C2411yescharacteristic
800#95C2411yescharacteristic
801#95C2411yescharacteristic
802#95C2413yes—
803#95C2413yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2411yescharacteristic
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2416yes—
821#95C2416yes—
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2416yes—
827#95C2416yes—
828#95C2413yes—
829#95C2411yescharacteristic
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2416yes—
837#95C2411yescharacteristic
838#95C2413yes—
839#95C2413yes—
840#95C2416yes—
841#95C2411yescharacteristic
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2416yes—
852#95C2413yes—
853#95C2413yes—
854#95C2416yes—
855#95C2416yes—
856#95C2416yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2416yes—
871#95C2416yes—
872C24C2513yes—
873#41—416no—
874C2×Q8—26no—
875C2×Q8—26no—
876C2×Q8—26no—
877C2×Q8—43no—
878C2×Q8—43no—
879C2×Q8—43no—
880C2×Q8C2×#4114yes—
881C2×Q82−1+414yes—
882C2×Q82−1+414yes—
883C2×D4—26no—
884C2×D4—26no—
885C2×D4—26no—
886C22×C4—26no—
887C22×C4—26no—
888C22×C4—26no—
889C22×C4—26no—
890C22×C4—26no—
891C22×C4—43no—
892C22×C4—43no—
893C22×C4—43no—
894C22×C4—43no—
895C22×C4C2511yescharacteristic
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2511yescharacteristic
900C22×C4C2511yescharacteristic
901C22×C4C2513yes—
902C22×C4C2513yes—
903C22×C4C2511yescharacteristic
904C22×C4C2511yescharacteristic
905C22×C4C2513yes—
906C22×C4C2513yes—
907C22×C4C2513yes—
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2513yes—
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2513yes—
917C22×C4C2513yes—
918C22×C4C2511yescharacteristic
919C22×C4C2513yes—
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2513yes—
925C4⋊C4—26no—
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—26no—
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—26no—
948C4⋊C4—22no—
949C4⋊C4—26no—
950C4⋊C4—26no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—26no—
962C4⋊C4—22no—
963C4⋊C4—43no—
964C4⋊C4—43no—
965C4⋊C4—43no—
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—43no—
976C4⋊C4—43no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—46no—
981C4⋊C4—43no—
982C4⋊C4—46no—
983C4⋊C4—46no—
984C4⋊C4—43no—
985C4⋊C4—46no—
986C4⋊C4—46no—
987C4⋊C4—46no—
988C4⋊C4—46no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—46no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4C2×#41112yes—
995C22⋊C4—212no—
996C22⋊C4—26no—
997C22⋊C4—26no—
998C22⋊C4—26no—
999C22⋊C4—26no—
1000C22⋊C4—43no—
1001C22⋊C4—43no—
1002C22⋊C4—43no—
1003C22⋊C4—43no—
1004C22⋊C4—46no—
1005C22⋊C4—46no—
1006C22⋊C4—46no—
1007C22⋊C4—46no—
1008C22⋊C4—43no—
1009C22⋊C4—43no—
1010C22⋊C4—46no—
1011C22⋊C4—46no—
1012C22⋊C4—43no—
1013C22⋊C4—43no—
1014C42—22no—
1015C42—26no—
1016C42—26no—
1017C42—26no—
1018C42—26no—
1019C42—26no—
1020C42—26no—
1021C42—26no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—26no—
1026C42—26no—
1027C42—26no—
1028C42—26no—
1029C42—22no—
1030C42—22no—
1031C42—22no—
1032C42—26no—
1033C42—22no—
1034C42—26no—
1035C42—43no—
1036C42—43no—
1037C42—43no—
1038C42—43no—
1039C42—43no—
1040C42—43no—
1041C42—43no—
1042C42—46no—
1043C42—43no—
1044C42—43no—
1045C42—46no—
1046C42—43no—
1047C42C2×#41112yes—
1048C23—23no—
1049C23—23no—
1050C23—23no—
1051C23—23no—
1052C23—23no—
1053C23—23no—
1054C23—23no—
1055C23C2611yescharacteristic
1056Q8—412no—
1057Q8—86no—
1058Q8#541116yes—
1059D4—412no—
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—21no—
1070C2×C4—23no—
1071C2×C4—23no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—23no—
1078C2×C4—23no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—21no—
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—21no—
1096C2×C4—21no—
1097C2×C4—23no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—23no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—23no—
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—23no—
1132C2×C4—23no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—412no—
1142C2×C4—412no—
1143C2×C4—86no—
1144C2×C4C22×#4112yes—
1145C2×C4C22×#4116yes—
1146C2×C4C22×#4116yes—
1147C2×C4C2×2−1+416yes—
1148C2×C4C2×2−1+416yes—
1149C2×C4#58512yes—
1150C2×C4#58512yes—
1151C2×C4#58512yes—
1152C2×C4#58512yes—
1153C22—43no—
1154C22—43no—
1155C22—43no—
1156C22—43no—
1157C22—43no—
1158C22—43no—
1159C22—43no—
1160C22C23×#4111yescharacteristic
1161C22C22×2−1+411yescharacteristic
1162C22C22×2−1+411yescharacteristic
1163C22C2×#58511yescharacteristic
1164C22C2×#58511yescharacteristic
1165C22C2×#58511yescharacteristic
1166C22C2×#58511yescharacteristic
1167C4—22no—
1168C4—22no—
1169C4—22no—
1170C4—22no—
1171C4—26no—
1172C4—22no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—43no—
1177C4—43no—
1178C4—43no—
1179C4—43no—
1180C4—43no—
1181C4—43no—
1182C4—41no—
1183C4—41no—
1184C4—43no—
1185C4—43no—
1186C4—41no—
1187C4—41no—
1188C4—43no—
1189C4—43no—
1190C4—43no—
1191C4—41no—
1192C4—43no—
1193C4—43no—
1194C4—41no—
1195C4—41no—
1196C4C2×#541112yes—
1197C2—83no—
1198C2C22×#54111yescharacteristic
1199C2#6279311yescharacteristic
1200C2#6281611yescharacteristic
1201C2#6303311yescharacteristic
1202C2#6303311yescharacteristic
1203C2#6303311yescharacteristic
1204C2#6303411yescharacteristic
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. #42764C2semidirect
2. #42723C2semidirect
3. #42614C2semidirect
4. #42562C2semidirect
5. #40227C2semidirect
6. #40120C2semidirect
7. #40027C2semidirect
8. #39997C2semidirect
9. #39907C2semidirect
10. #39907C2semidirect
11. #39780C2semidirect
12. #39217C2semidirect
13. #37571C2semidirect
14. #36584C2semidirect
15. #36475C2semidirect
16. #36475C2semidirect
17. #36466C2semidirect
23. #35971C2semidirect
25. #35868C2semidirect
26. #35142C2semidirect
27. #35116C2semidirect
28. #34975C2semidirect
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
#427642
#427232
#426142
#425622
#402272
#401202
#400272
#399972
#399072
#397802
#392172
#375712
#365842
#364752
#364662
#364582
#364312
#360592
#359712
#358982
#358682
#351422
#351162
#349752
#343362
C4×#5572
#341252