Finite Group Databasebeta

← #7660342

Subgroups — #7660342

Order 512.

4289 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52251C213yesmaximal, complemented
2#42716C213yesmaximal, complemented
3#42704C213yesmaximal, complemented
4#42638C213yesmaximal, complemented
5#42638C213yesmaximal, complemented
6#42562C213yesmaximal, complemented
7#42509C213yesmaximal, complemented
8#40167C213yesmaximal, complemented
9#40120C213yesmaximal, complemented
10#40059C213yesmaximal, complemented
11#39901C213yesmaximal, complemented
12#39788C213yesmaximal, complemented
13#39607C213yesmaximal, complemented
14#37353C213yesmaximal, complemented
15#37337C213yesmaximal, complemented
16#37295C213yesmaximal, complemented
17Q8×#125C211yesmaximal, characteristic, complemented
18Q8×#125C211yesmaximal, characteristic, complemented
19#36458C211yesmaximal, characteristic
20#36458C211yesmaximal, characteristic
21#36445C211yesmaximal, characteristic
22#36431C211yesmaximal, characteristic
23#35971C211yesmaximal, characteristic, complemented
24#35957C211yesmaximal, characteristic, complemented
25#35898C211yesmaximal, characteristic
26#35898C211yesmaximal, characteristic
27#35868C211yesmaximal, characteristic, complemented
28#35868C211yesmaximal, characteristic, complemented
29#34337C211yesmaximal, characteristic, complemented
30#34336C211yesmaximal, characteristic, complemented
31#34193C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2860C2213yes—
36#2860C2213yes—
37#2859C2213yes—
38#2859C2213yes—
39#2857C2213yes—
40#2851C2213yes—
41#2836C2216yes—
42#2836C2216yes—
43#2798C2216yes—
44#2783C2216yes—
45#2776C2213yes—
46#2776C2216yes—
47#2769C2213yes—
48#2769C2216yes—
49#2766C2213yes—
50#2762C2213yes—
51#2762C2213yes—
52#2758C2213yes—
53#2755C2213yes—
54#2755C2216yes—
55#2754C2216yes—
56#2747C2213yes—
57#2747C2216yes—
58#2744C2213yes—
59#2739C2213yes—
60#2725C2216yes—
61#2725C2216yes—
62#2725C2216yes—
63#2722C2216yes—
64#2722C2213yes—
65#2722C2216yes—
66#2721C2216yes—
67#2721C2216yes—
68#2719C2211yescharacteristic
69#2704C2216yes—
70#2704C2213yes—
71#2704C2216yes—
72#2698C2216yes—
73#2698C2213yes—
74#2690C2213yes—
75#2690C2216yes—
76#2689C2213yes—
77#2689C2216yes—
78#2664C2216yes—
79#2664C2216yes—
80#2660C2213yes—
81#2655C2216yes—
82#2654C2216yes—
83#2647C2213yes—
84#2647C2213yes—
85#2647C2213yes—
86#2644C2213yes—
87#2644C2213yes—
88#2637C2216yes—
89#2629C2216yes—
90#2584C2213yes—
91#2580C2213yes—
92#2571C2213yes—
93#2570C2213yes—
94#2570C2213yes—
95#2570C2213yes—
96#2567C2213yes—
97#2566C2213yes—
98#2552C2213yes—
99#2552C2213yes—
100#2552C2213yes—
101#2552C2213yes—
102#2552C2213yes—
103#2552C2213yes—
104#2552C2213yes—
105#2552C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2542C2213yes—
109#2538C2213yes—
110#2519C2216yes—
111#2513C2213yes—
112#2513C2213yes—
113#2513C2213yes—
114#2513C2213yes—
115#2512C2213yes—
116#2512C2213yes—
117#2512C2213yes—
118#2512C2213yes—
119#2512C2213yes—
120#2512C2213yes—
121#2512C2213yes—
122#2512C2213yes—
123#2509C2213yes—
124#2509C2213yes—
125#2509C2213yes—
126#2508C2213yes—
127#2508C2213yes—
128#2507C2213yes—
129#2507C2213yes—
130#2507C2213yes—
131#2507C2213yes—
132#2507C2213yes—
133#2507C2213yes—
134#2507C2213yes—
135#2507C2213yes—
136#2507C2213yes—
137#2507C2213yes—
138#2507C2213yes—
139#2506C2213yes—
140#2506C2213yes—
141#2506C2213yes—
142#2506C2213yes—
143#2506C2216yes—
144#2497C2213yes—
145#2497C2213yes—
146#2497C2213yes—
147#2497C2213yes—
148#2496C2213yes—
149#2496C2213yes—
150#2496C2213yes—
151#2496C2213yes—
152#2495C2213yes—
153#2495C2213yes—
154#2494C2213yes—
155#2494C2213yes—
156#2478C2216yes—
157#2478C2216yes—
158#2469C2216yes—
159#2454C2213yes—
160#2454C2213yes—
161#2454C2213yes—
162#2453C2216yes—
163#2452C2213yes—
164#2441C2213yes—
165#2441C2213yes—
166#2441C2213yes—
167#2439C2213yes—
168#2402C2213yes—
169#2402C2213yes—
170#2402C2213yes—
171#2401C2213yes—
172#2401C2213yes—
173#2399C2213yes—
174#2370C2213yes—
175#2370C2213yes—
176#2370C2213yes—
177#2370C2213yes—
178#2369C2213yes—
179#2365C2213yes—
180#2355C2213yes—
181#2354C2213yes—
182#2354C2213yes—
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2211yescharacteristic
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189Q8×C4⋊C4C2213yes—
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
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204#2347C2213yes—
205#2347C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2336C2216yes—
213#2331C2213yes—
214#2330C2213yes—
215#2330C2213yes—
216#2330C2213yes—
217#2323C2216yes—
218#2319C2213yes—
219#2319C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×#125C2213yes—
222C4×#125C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×#126C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228#2295C2213yes—
229#2295C2213yes—
230#2285C2213yes—
231#2283C2213yes—
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239#557—28no—
240#557—28no—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×#126C2313yes—
244C2×#126C2313yes—
245C2×#126C2316yes—
246C2×#126C2316yes—
247C2×#126C2316yes—
248C2×#126C2316yes—
249C2×#125C2311yescharacteristic
250C2×#125C2311yescharacteristic
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2316yes—
256C2×#125C2316yes—
257C2×#125C2316yes—
258C2×#125C2316yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2316yes—
262C4×#41—28no—
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2316yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×#117C2313yes—
283C2×#117C2316yes—
284C22×C42C2313yes—
285#401C2313yes—
286#401C2313yes—
287#400C2313yes—
288#400C2313yes—
289#400C2316yes—
290#400C2313yes—
291#400C2313yes—
292#400C2313yes—
293#400C2316yes—
294#400C2313yes—
295#400C2313yes—
296#400C2316yes—
297#400C2316yes—
298#400C2313yes—
299#400C2313yes—
300#400C2316yes—
301#400C2316yes—
302#400C2311yescharacteristic
303#400C2311yescharacteristic
304#400C2313yes—
305#400C2313yes—
306#400C2313yes—
307#400C2311yescharacteristic
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#399C2316yes—
312#399C2316yes—
313#399C2316yes—
314#398C2313yes—
315#398C2316yes—
316#398C2316yes—
317#398C2313yes—
318#398C2316yes—
319#398C2316yes—
320#398C2316yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2313yes—
325#398C2313yes—
326#398C2313yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2316yes—
332#398C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2311yescharacteristic
336#398C2313yes—
337#398C2311yescharacteristic
338#398C2311yescharacteristic
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2313yes—
343#398C2313yes—
344#398C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#397C2316yes—
350#397C2316yes—
351#397C2313yes—
352#397C2313yes—
353#397C2316yes—
354#397C2316yes—
355#397C2313yes—
356#397C2313yes—
357#397C2316yes—
358#397C2316yes—
359#396C2316yes—
360#396C2316yes—
361#396C2316yes—
362#396C2316yes—
363#396C2316yes—
364#396C2316yes—
365#396C2316yes—
366#396C2313yes—
367#396C2313yes—
368#396C2316yes—
369#395C2313yes—
370#395C2316yes—
371#395C2313yes—
372#395C2313yes—
373#395C2313yes—
374#393C2316yes—
375#391C2313yes—
376#391C2316yes—
377#391C2313yes—
378#391C2316yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2316yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2316yes—
416#389C2313yes—
417#389C2313yes—
418#389C2316yes—
419#389C2316yes—
420#389C2313yes—
421#389C2313yes—
422#389C2316yes—
423#389C2316yes—
424#389C2316yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2316yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2316yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2316yes—
443#389C2313yes—
444#389C2316yes—
445#389C2316yes—
446#389C2316yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2311yescharacteristic
458#389C2311yescharacteristic
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2313yes—
463#388C2313yes—
464#388C2313yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#387C2311yescharacteristic
478#387C2311yescharacteristic
479#387C2313yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2316yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2313yes—
503#387C2316yes—
504#387C2316yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2311yescharacteristic
516#387C2311yescharacteristic
517#385C2313yes—
518#385C2316yes—
519#385C2313yes—
520#385C2316yes—
521#385C2313yes—
522#385C2313yes—
523#384C2313yes—
524#384C2313yes—
525#384C2316yes—
526#384C2313yes—
527#384C2313yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#384C2313yes—
538#383C2313yes—
539#383C2313yes—
540#383C2313yes—
541#383C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2313yes—
548#382C2313yes—
549#382C2313yes—
550#382C2316yes—
551#382C2311yescharacteristic
552#382C2313yes—
553#381C2313yes—
554#381C2313yes—
555#380C2316yes—
556#380C2316yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
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⋊C4C2316yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
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⋊C4C2316yes—
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×C4⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
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—
633#126—46no—
634#126—46no—
635#126—86no—
636#126—86no—
637#126—86no—
638#126—86no—
639#125—212no—
640#125—212no—
641#125—212no—
642#125—24no—
643#125—24no—
644#125—212no—
645#125—412no—
646#125—86no—
647#125—86no—
648#125—86no—
649C22⋊Q8—212no—
650C22⋊Q8—46no—
651C22⋊Q8—86no—
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—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—212no—
666C4×Q8—212no—
667C4×Q8—86no—
668C4×Q8#4118yes—
669C4×D4—212no—
670C4×D4—212no—
671#117—212no—
672#117—86no—
673C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2416yes—
715C2×C4⋊C4C2416yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2416yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2416yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C22⋊C4C2416yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2413yes—
753C2×C22⋊C4C2416yes—
754C2×C22⋊C4C2416yes—
755C2×C22⋊C4C2416yes—
756C2×C22⋊C4C2416yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2416yes—
763C2×C22⋊C4C2416yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C42—212no—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2416yes—
788C2×C42C2416yes—
789C2×C42C2413yes—
790C2×C42C2416yes—
791C2×C42C2413yes—
792C2×C42C2416yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797#95C2411yescharacteristic
798#95C2411yescharacteristic
799#95C2411yescharacteristic
800#95C2411yescharacteristic
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#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816#95C2411yescharacteristic
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2411yescharacteristic
826#95C2413yes—
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2411yescharacteristic
830#95C2413yes—
831#95C2413yes—
832#95C2416yes—
833#95C2416yes—
834#95C2411yescharacteristic
835#95C2411yescharacteristic
836#95C2411yescharacteristic
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2416yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2416yes—
870#95C2416yes—
871#95C2416yes—
872#95C2416yes—
873C24C2513yes—
874#41—416no—
875C2×Q8—26no—
876C2×Q8—26no—
877C2×Q8—26no—
878C2×Q8—43no—
879C2×Q8—43no—
880C2×Q8—43no—
881C2×Q8C2×#4114yes—
882C2×Q82−1+414yes—
883C2×Q82−1+414yes—
884C2×D4—26no—
885C2×D4—26no—
886C2×D4—26no—
887C22×C4—26no—
888C22×C4—26no—
889C22×C4—26no—
890C22×C4—26no—
891C22×C4—26no—
892C22×C4—26no—
893C22×C4—43no—
894C22×C4—43no—
895C22×C4—43no—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2511yescharacteristic
899C22×C4C2511yescharacteristic
900C22×C4C2511yescharacteristic
901C22×C4C2511yescharacteristic
902C22×C4C2513yes—
903C22×C4C2513yes—
904C22×C4C2511yescharacteristic
905C22×C4C2513yes—
906C22×C4C2511yescharacteristic
907C22×C4C2511yescharacteristic
908C22×C4C2513yes—
909C22×C4C2513yes—
910C22×C4C2513yes—
911C22×C4C2513yes—
912C22×C4C2513yes—
913C22×C4C2513yes—
914C22×C4C2513yes—
915C22×C4C2513yes—
916C22×C4C2513yes—
917C22×C4C2511yescharacteristic
918C22×C4C2513yes—
919C22×C4C2511yescharacteristic
920C22×C4C2513yes—
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2513yes—
926C4⋊C4—26no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—26no—
930C4⋊C4—26no—
931C4⋊C4—26no—
932C4⋊C4—26no—
933C4⋊C4—26no—
934C4⋊C4—26no—
935C4⋊C4—26no—
936C4⋊C4—26no—
937C4⋊C4—212no—
938C4⋊C4—212no—
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—26no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—43no—
965C4⋊C4—43no—
966C4⋊C4—43no—
967C4⋊C4—46no—
968C4⋊C4—46no—
969C4⋊C4—43no—
970C4⋊C4—43no—
971C4⋊C4—46no—
972C4⋊C4—46no—
973C4⋊C4—46no—
974C4⋊C4—46no—
975C4⋊C4—46no—
976C4⋊C4—46no—
977C4⋊C4—43no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—46no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—46no—
987C4⋊C4—46no—
988C4⋊C4—46no—
989C4⋊C4—46no—
990C4⋊C4—46no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4C2×#41112yes—
1001C4⋊C42−1+414yes—
1002C22⋊C4—212no—
1003C22⋊C4—26no—
1004C22⋊C4—26no—
1005C22⋊C4—26no—
1006C22⋊C4—46no—
1007C22⋊C4—46no—
1008C22⋊C4—43no—
1009C22⋊C4—46no—
1010C22⋊C4—46no—
1011C22⋊C4—43no—
1012C22⋊C4—43no—
1013C22⋊C4—43no—
1014C22⋊C4—43no—
1015C22⋊C4—43no—
1016C22⋊C4—43no—
1017C22⋊C4—43no—
1018C22⋊C4—46no—
1019C22⋊C4—46no—
1020C22⋊C4—43no—
1021C42—22no—
1022C42—26no—
1023C42—26no—
1024C42—26no—
1025C42—26no—
1026C42—26no—
1027C42—26no—
1028C42—26no—
1029C42—26no—
1030C42—26no—
1031C42—26no—
1032C42—26no—
1033C42—26no—
1034C42—26no—
1035C42—26no—
1036C42—22no—
1037C42—22no—
1038C42—26no—
1039C42—46no—
1040C42—46no—
1041C42—43no—
1042C42—46no—
1043C42—43no—
1044C42—46no—
1045C42—43no—
1046C42—43no—
1047C42—43no—
1048C42C2×#41112yes—
1049C23—23no—
1050C23—23no—
1051C23—23no—
1052C23—23no—
1053C23—23no—
1054C23—23no—
1055C23—23no—
1056C23C2611yescharacteristic
1057Q8—412no—
1058Q8—86no—
1059Q8#541116yes—
1060D4—412no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—23no—
1067C2×C4—21no—
1068C2×C4—23no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
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—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—23no—
1091C2×C4—23no—
1092C2×C4—23no—
1093C2×C4—23no—
1094C2×C4—21no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—23no—
1108C2×C4—23no—
1109C2×C4—21no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—412no—
1143C2×C4—412no—
1144C2×C4—86no—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4116yes—
1147C2×C4C22×#4116yes—
1148C2×C4C2×2−1+412yes—
1149C2×C4C2×2−1+412yes—
1150C2×C4C2×2−1+412yes—
1151C2×C4C2×2−1+416yes—
1152C2×C4C2×2−1+416yes—
1153C2×C4#58512yes—
1154C22—43no—
1155C22—43no—
1156C22—43no—
1157C22—43no—
1158C22—43no—
1159C22—43no—
1160C22—43no—
1161C22C23×#4111yescharacteristic
1162C22C22×2−1+411yescharacteristic
1163C22C22×2−1+411yescharacteristic
1164C22C22×2−1+411yescharacteristic
1165C22C2×#58511yescharacteristic
1166C22H(7,𝔽2)11yescharacteristic
1167C22H(7,𝔽2)11yescharacteristic
1168C4—22no—
1169C4—26no—
1170C4—22no—
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—41no—
1175C4—41no—
1176C4—43no—
1177C4—41no—
1178C4—43no—
1179C4—43no—
1180C4—43no—
1181C4—43no—
1182C4—41no—
1183C4—41no—
1184C4—41no—
1185C4—43no—
1186C4—43no—
1187C4—43no—
1188C4—43no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—43no—
1193C4—41no—
1194C4—43no—
1195C4—43no—
1196C4—43no—
1197C4C2×#541112yes—
1198C2—83no—
1199C2C22×#54111yescharacteristic
1200C2#6294311yescharacteristic
1201C2#6295211yescharacteristic
1202C2#6300011yescharacteristic
1203C2#6300611yescharacteristic
1204C2#6303811yescharacteristic
1205C2#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. #52251C2semidirect
2. #42716C2semidirect
3. #42704C2semidirect
4. #42638C2semidirect
5. #42638C2semidirect
6. #42562C2semidirect
7. #42509C2semidirect
8. #40167C2semidirect
9. #40120C2semidirect
10. #40059C2semidirect
11. #39901C2semidirect
12. #39788C2semidirect
13. #39607C2semidirect
14. #37353C2semidirect
15. #37337C2semidirect
16. #37295C2semidirect
17. Q8×#125C2semidirect
18. Q8×#125C2semidirect
23. #35971C2semidirect
24. #35957C2semidirect
27. #35868C2semidirect
28. #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
#522512
#427162
#427042
#426382
#425622
#425092
#401672
#401202
#400592
#399012
#397882
#396072
#373532
#373372
#372952
Q8×#1252
#364582
#364452
#364312
#359712
#359572
#358982
#358682
#343372
#343362
#341932