Finite Group Databasebeta

← #7686962

Subgroups — #7686962

Order 512.

4804 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59446C213yesmaximal, complemented
2#59331C213yesmaximal, complemented
3#59296C213yesmaximal, complemented
4#59292C213yesmaximal, complemented
5#59260C213yesmaximal, complemented
6#45376C213yesmaximal, complemented
7#45054C213yesmaximal, complemented
8#45030C213yesmaximal, complemented
9#44991C213yesmaximal, complemented
10#38969C213yesmaximal, complemented
11#38926C213yesmaximal, complemented
12#38074C213yesmaximal, complemented
13#38073C213yesmaximal, complemented
14#36475C211yesmaximal, characteristic, complemented
15#36433C211yesmaximal, characteristic
16#36433C211yesmaximal, characteristic
17#36431C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#36201C213yesmaximal, complemented
20#36200C213yesmaximal, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35898C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35868C211yesmaximal, characteristic, complemented
25#34780C213yesmaximal, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34197C211yesmaximal, characteristic, complemented
28#34197C211yesmaximal, characteristic, complemented
29#34193C211yesmaximal, characteristic, complemented
30C4×#550C211yesmaximal, characteristic
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2864C2213yes—
39#2854C2213yes—
40#2854C2213yes—
41#2851C2213yes—
42#2851C2213yes—
43#2765C2216yes—
44#2761C2216yes—
45#2751C2216yes—
46#2751C2216yes—
47#2750C2216yes—
48#2744C2216yes—
49#2743C2216yes—
50#2741C2216yes—
51#2707C2216yes—
52#2702C2216yes—
53#2695C2216yes—
54#2694C2216yes—
55#2694C2216yes—
56#2687C2216yes—
57#2647C2213yes—
58#2647C2213yes—
59#2644C2213yes—
60#2644C2213yes—
61#2611C2216yes—
62#2601C2216yes—
63#2580C2213yes—
64#2580C2213yes—
65#2577C2216yes—
66#2570C2213yes—
67#2570C2213yes—
68#2570C2213yes—
69#2570C2213yes—
70#2566C2213yes—
71#2566C2213yes—
72#2558C2216yes—
73#2552C2213yes—
74#2552C2213yes—
75#2532C2216yes—
76#2530C2216yes—
77#2529C2216yes—
78#2527C2216yes—
79#2525C2216yes—
80#2524C2213yes—
81#2524C2211yescharacteristic
82#2519C2216yes—
83#2515C2213yes—
84#2515C2216yes—
85#2515C2213yes—
86#2514C2213yes—
87#2513C2213yes—
88#2513C2213yes—
89#2512C2213yes—
90#2512C2213yes—
91#2512C2213yes—
92#2512C2213yes—
93#2509C2213yes—
94#2509C2213yes—
95#2509C2213yes—
96#2508C2213yes—
97#2508C2213yes—
98#2507C2213yes—
99#2507C2213yes—
100#2507C2213yes—
101#2506C2213yes—
102#2506C2213yes—
103#2506C2213yes—
104#2506C2213yes—
105#2506C2213yes—
106#2503C2213yes—
107#2500C2213yes—
108#2500C2213yes—
109#2497C2213yes—
110#2497C2213yes—
111#2496C2213yes—
112#2496C2213yes—
113#2495C2213yes—
114#2494C2213yes—
115#2494C2213yes—
116#2493C2213yes—
117#2493C2213yes—
118#2489C2213yes—
119#2486C2213yes—
120#2485C2213yes—
121#2485C2213yes—
122#2481C2216yes—
123#2468C2216yes—
124#2468C2216yes—
125#2460C2216yes—
126#2460C2216yes—
127#2454C2213yes—
128#2454C2213yes—
129#2452C2213yes—
130#2452C2213yes—
131#2445C2213yes—
132#2445C2213yes—
133#2445C2213yes—
134#2445C2213yes—
135#2442C2213yes—
136#2441C2213yes—
137#2441C2213yes—
138#2439C2213yes—
139#2439C2213yes—
140#2422C2213yes—
141#2422C2213yes—
142#2420C2213yes—
143#2420C2213yes—
144#2419C2216yes—
145#2419C2213yes—
146#2419C2213yes—
147#2417C2213yes—
148#2413C2216yes—
149#2402C2213yes—
150#2402C2213yes—
151#2401C2213yes—
152#2401C2213yes—
153#2373C2216yes—
154#2371C2216yes—
155#2370C2213yes—
156#2370C2213yes—
157#2369C2213yes—
158#2366C2213yes—
159#2363C2213yes—
160#2363C2213yes—
161#2359C2216yes—
162#2357C2213yes—
163#2357C2213yes—
164#2357C2213yes—
165#2357C2213yes—
166#2355C2213yes—
167#2354C2213yes—
168#2354C2213yes—
169#2354C2213yes—
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186#2349C2213yes—
187#2349C2213yes—
188D4×C4⋊C4C2213yes—
189D4×C4⋊C4C2213yes—
190#2347C2213yes—
191#2347C2213yes—
192#2346C2213yes—
193#2346C2213yes—
194#2346C2213yes—
195#2346C2213yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2331C2213yes—
205#2330C2213yes—
206#2319C2213yes—
207#2319C2213yes—
208#2319C2213yes—
209#2319C2213yes—
210#2319C2213yes—
211#2319C2213yes—
212C4×#127C2213yes—
213C4×#125C2213yes—
214C4×#125C2213yes—
215C4×C22⋊Q8C2213yes—
216C4×C22⋊Q8C2213yes—
217C4×#123C2213yes—
218C4×#123C2213yes—
219C4×#121C2213yes—
220C4×#121C2213yes—
221#2296C2213yes—
222#2296C2213yes—
223#2295C2213yes—
224#2285C2213yes—
225#2285C2213yes—
226#2283C2213yes—
227#2283C2213yes—
228#2283C2213yes—
229#2283C2213yes—
230#2283C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#557—28no—
241#550—28no—
242C2×C4⋊Q8C2313yes—
243C2×#127C2313yes—
244C2×#126C2316yes—
245C2×#126C2316yes—
246C2×#125C2313yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2316yes—
250C2×#125C2316yes—
251C2×#123C2316yes—
252C2×#123C2313yes—
253C2×#123C2313yes—
254C2×#123C2316yes—
255C2×C22⋊Q8C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×#121C2313yes—
258C2×#121C2313yes—
259C4×#41—28no—
260C4×#41—28no—
261C4×#41—28no—
262C4×#41—28no—
263C2×C4×Q8C2313yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×C4×D4C2313yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×C4×D4C2313yes—
287C2×C4×D4C2313yes—
288C2×C4×D4C2316yes—
289C2×#117C2313yes—
290C2×#117C2313yes—
291C2×#117C2313yes—
292C2×#117C2313yes—
293C2×#117C2316yes—
294C22×C4⋊C4C2313yes—
295C22×C4⋊C4C2313yes—
296C22×C42C2313yes—
297C22×C42C2313yes—
298C22×C42C2313yes—
299C22×C42C2313yes—
300#401C2313yes—
301#401C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2316yes—
311#400C2311yescharacteristic
312#400C2311yescharacteristic
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#399C2316yes—
321#399C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2313yes—
328#398C2316yes—
329#398C2311yescharacteristic
330#398C2311yescharacteristic
331#398C2313yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#397C2316yes—
337#397C2316yes—
338#397C2313yes—
339#397C2313yes—
340#397C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#397C2313yes—
348#396C2316yes—
349#396C2316yes—
350#396C2316yes—
351#396C2316yes—
352#396C2316yes—
353#396C2316yes—
354#396C2313yes—
355#396C2313yes—
356#394C2316yes—
357#394C2316yes—
358#394C2316yes—
359#394C2316yes—
360#394C2316yes—
361#394C2316yes—
362#393C2316yes—
363#393C2316yes—
364#391C2313yes—
365#391C2316yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#390C2313yes—
370#390C2313yes—
371#390C2316yes—
372#390C2316yes—
373#390C2313yes—
374#390C2313yes—
375#390C2313yes—
376#390C2313yes—
377#390C2313yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
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#389C2316yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2316yes—
425#389C2313yes—
426#389C2316yes—
427#389C2313yes—
428#388C2316yes—
429#388C2316yes—
430#388C2316yes—
431#388C2316yes—
432#388C2316yes—
433#388C2316yes—
434#388C2316yes—
435#388C2316yes—
436#388C2316yes—
437#388C2316yes—
438#388C2316yes—
439#388C2316yes—
440#388C2313yes—
441#388C2313yes—
442#388C2316yes—
443#388C2316yes—
444#388C2316yes—
445#388C2316yes—
446#388C2316yes—
447#388C2316yes—
448#388C2316yes—
449#388C2316yes—
450#388C2313yes—
451#388C2313yes—
452#387C2311yescharacteristic
453#387C2313yes—
454#387C2313yes—
455#387C2313yes—
456#387C2316yes—
457#387C2313yes—
458#387C2316yes—
459#387C2316yes—
460#387C2316yes—
461#387C2316yes—
462#387C2316yes—
463#387C2313yes—
464#387C2316yes—
465#387C2316yes—
466#387C2316yes—
467#387C2316yes—
468#387C2313yes—
469#387C2316yes—
470#387C2316yes—
471#387C2316yes—
472#387C2316yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2311yescharacteristic
478#387C2311yescharacteristic
479#387C2311yescharacteristic
480#387C2311yescharacteristic
481#387C2311yescharacteristic
482#386C2316yes—
483#386C2316yes—
484#386C2313yes—
485#386C2316yes—
486#386C2316yes—
487#386C2313yes—
488#385C2313yes—
489#385C2313yes—
490#385C2316yes—
491#385C2316yes—
492#385C2313yes—
493#385C2313yes—
494#385C2316yes—
495#385C2316yes—
496#385C2316yes—
497#385C2316yes—
498#385C2316yes—
499#385C2316yes—
500#385C2313yes—
501#385C2313yes—
502#384C2313yes—
503#384C2313yes—
504#384C2313yes—
505#384C2313yes—
506#384C2313yes—
507#384C2313yes—
508#384C2313yes—
509#384C2313yes—
510#383C2313yes—
511#383C2313yes—
512#383C2313yes—
513#383C2311yescharacteristic
514#383C2311yescharacteristic
515#383C2313yes—
516#382C2313yes—
517#382C2313yes—
518#382C2313yes—
519#382C2313yes—
520#382C2313yes—
521#382C2313yes—
522#382C2313yes—
523#382C2313yes—
524#382C2313yes—
525#382C2313yes—
526#382C2313yes—
527#382C2313yes—
528#382C2313yes—
529#382C2311yescharacteristic
530#382C2313yes—
531#381C2316yes—
532#381C2313yes—
533#381C2316yes—
534#381C2313yes—
535#381C2313yes—
536#381C2313yes—
537#381C2313yes—
538#381C2313yes—
539#381C2313yes—
540#381C2313yes—
541#380C2313yes—
542#380C2313yes—
543#380C2313yes—
544#380C2316yes—
545#380C2313yes—
546#380C2316yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2316yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2316yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2316yes—
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⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2311yescharacteristic
600C4×C4⋊C4C2311yescharacteristic
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2316yes—
620#376C2316yes—
621C2×#95C2313yes—
622C2×#95C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41#4118yes—
630C22×Q8C2413yes—
631C22×Q8C2411yescharacteristic
632C22×D4C2413yes—
633C22×D4C2413yes—
634C22×D4C2413yes—
635C22×D4C2416yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C23×C4C2413yes—
645C23×C4C2413yes—
646C4⋊Q8—212no—
647#127—212no—
648#126—412no—
649#126—86no—
650#125—212no—
651#125—212no—
652#125—46no—
653#125—412no—
654#125—86no—
655#123—412no—
656#123—46no—
657#123—46no—
658#123—86no—
659C22⋊Q8—46no—
660C22⋊Q8—46no—
661#121—212no—
662#121—212no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—212no—
676C4×Q8#4118yes—
677C4×D4—212no—
678C4×D4—212no—
679C4×D4—212no—
680C4×D4—212no—
681C4×D4—212no—
682C4×D4—212no—
683C4×D4—212no—
684C4×D4—212no—
685C4×D4—212no—
686C4×D4—46no—
687C4×D4—46no—
688C4×D4—86no—
689#117—212no—
690#117—212no—
691#117—212no—
692#117—212no—
693#117—86no—
694C2×C4⋊C4—46no—
695C2×C4⋊C4—46no—
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
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⋊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⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C22⋊C4C2416yes—
755C2×C22⋊C4C2416yes—
756C2×C22⋊C4C2416yes—
757C2×C22⋊C4C2416yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2416yes—
763C2×C22⋊C4C2416yes—
764C2×C22⋊C4C2416yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2416yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2416yes—
784C2×C42—212no—
785C2×C42—212no—
786C2×C42—212no—
787C2×C42—212no—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2411yescharacteristic
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2416yes—
810C2×C42C2416yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2416yes—
815C2×C42C2416yes—
816C2×C42C2413yes—
817#95C2411yescharacteristic
818#95C2411yescharacteristic
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2416yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2416yes—
847#95C2416yes—
848#95C2416yes—
849#95C2411yescharacteristic
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2411yescharacteristic
872#95C2416yes—
873#95C2413yes—
874#95C2413yes—
875#95C2416yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2413yes—
887#95C2413yes—
888#95C2416yes—
889#95C2416yes—
890C24C2513yes—
891C24C2513yes—
892#41—232no—
893#41—416no—
894C2×Q8—26no—
895C2×Q8—43no—
896C2×Q8—43no—
897C2×Q8C2×#4114yes—
898C2×Q8C2×#4114yes—
899C2×Q82−1+414yes—
900C2×D4—26no—
901C2×D4—212no—
902C2×D4—26no—
903C2×D4—26no—
904C2×D4—26no—
905C2×D4—26no—
906C2×D4—26no—
907C2×D4—26no—
908C2×D4—43no—
909C2×D4—46no—
910C2×D4—46no—
911C2×D4C2×#41112yes—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—26no—
924C22×C4—26no—
925C22×C4—26no—
926C22×C4—26no—
927C22×C4—43no—
928C22×C4—43no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4—43no—
932C22×C4—43no—
933C22×C4—43no—
934C22×C4—43no—
935C22×C4—43no—
936C22×C4—43no—
937C22×C4—43no—
938C22×C4—43no—
939C22×C4—43no—
940C22×C4—43no—
941C22×C4C2×#41112yes—
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2513yes—
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C22×C4C2513yes—
956C22×C4C2513yes—
957C22×C4C2513yes—
958C22×C4C2513yes—
959C22×C4C2513yes—
960C22×C4C2513yes—
961C22×C4C2513yes—
962C22×C4C2511yescharacteristic
963C22×C4C2513yes—
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2513yes—
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2513yes—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—212no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—22no—
993C4⋊C4—26no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—26no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—22no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—46no—
1013C4⋊C4—43no—
1014C4⋊C4—46no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—46no—
1018C4⋊C4—46no—
1019C4⋊C4—46no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—46no—
1025C4⋊C4—46no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4C2×#41112yes—
1029C22⋊C4—212no—
1030C22⋊C4—212no—
1031C22⋊C4—26no—
1032C22⋊C4—212no—
1033C22⋊C4—212no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—26no—
1037C22⋊C4—46no—
1038C22⋊C4—46no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—46no—
1043C22⋊C4—43no—
1044C22⋊C4—43no—
1045C22⋊C4—43no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—46no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—46no—
1053C22⋊C4—43no—
1054C22⋊C4—43no—
1055C22⋊C4—46no—
1056C22⋊C4—46no—
1057C22⋊C4—46no—
1058C22⋊C4—43no—
1059C42—22no—
1060C42—22no—
1061C42—22no—
1062C42—22no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42—26no—
1074C42—26no—
1075C42—26no—
1076C42—26no—
1077C42—26no—
1078C42—26no—
1079C42—22no—
1080C42—46no—
1081C42—46no—
1082C42—43no—
1083C42—43no—
1084C42—43no—
1085C42—46no—
1086C42—46no—
1087C42C2×#41112yes—
1088C23—23no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23—23no—
1096C23—23no—
1097C23—23no—
1098C23—23no—
1099C23—23no—
1100C23—23no—
1101C23C22×#4116yes—
1102C23C2611yescharacteristic
1103Q8—86no—
1104Q8#552116yes—
1105D4—224no—
1106D4—412no—
1107D4—412no—
1108D4—812no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—224no—
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—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—23no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—412no—
1189C2×C4—412no—
1190C2×C4—412no—
1191C2×C4—86no—
1192C2×C4—86no—
1193C2×C4—86no—
1194C2×C4—86no—
1195C2×C4—86no—
1196C2×C4—86no—
1197C2×C4C22×#4112yes—
1198C2×C4C22×#4112yes—
1199C2×C4C22×#4116yes—
1200C2×C4C22×#4116yes—
1201C2×C4C22×#4116yes—
1202C2×C4C2×2−1+416yes—
1203C2×C4#58512yes—
1204C2×C4#58512yes—
1205C2×C4#58512yes—
1206C22—26no—
1207C22—26no—
1208C22—26no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22—43no—
1213C22—43no—
1214C22—43no—
1215C22—43no—
1216C22—43no—
1217C22—43no—
1218C22—43no—
1219C22—43no—
1220C22C23×#4111yescharacteristic
1221C22C23×#4111yescharacteristic
1222C22C22×2−1+411yescharacteristic
1223C22C2×#58511yescharacteristic
1224C22C2×#58511yescharacteristic
1225C22C2×#58511yescharacteristic
1226C22H(7,𝔽2)11yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—26no—
1231C4—22no—
1232C4—22no—
1233C4—41no—
1234C4—43no—
1235C4—43no—
1236C4—43no—
1237C4—43no—
1238C4—43no—
1239C4—41no—
1240C4—43no—
1241C4—41no—
1242C4—41no—
1243C4—43no—
1244C4—43no—
1245C4—43no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—43no—
1250C4—41no—
1251C4—41no—
1252C4—43no—
1253C4—43no—
1254C4—41no—
1255C4C2×#552112yes—
1256C2—46no—
1257C2—83no—
1258C2C22×#55211yescharacteristic
1259C2#6281611yescharacteristic
1260C2#6281611yescharacteristic
1261C2#6295211yescharacteristic
1262C2#6300611yescharacteristic
1263C2#6300811yescharacteristic
1264C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59446C2semidirect
2. #59331C2semidirect
3. #59296C2semidirect
4. #59292C2semidirect
5. #59260C2semidirect
6. #45376C2semidirect
7. #45054C2semidirect
8. #45030C2semidirect
9. #44991C2semidirect
10. #38969C2semidirect
11. #38926C2semidirect
12. #38074C2semidirect
13. #38073C2semidirect
14. #36475C2semidirect
17. #36431C2semidirect
18. #36431C2semidirect
19. #36201C2semidirect
20. #36200C2semidirect
21. #35898C2semidirect
22. #35898C2semidirect
23. #35868C2semidirect
24. #35868C2semidirect
25. #34780C2semidirect
26. #34336C2semidirect
27. #34197C2semidirect
28. #34197C2semidirect
29. #34193C2semidirect
31. C4⋊C4×#41C2semidirect

Maximal subgroups

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

subgroupindex
#594462
#593312
#592962
#592922
#592602
#453762
#450542
#450302
#449912
#389692
#389262
#380742
#380732
#364752
#364332
#364312
#362012
#362002
#358982
#358682
#347802
#343362
#341972
#341932
C4×#5502
C4⋊C4×#412