Finite Group Databasebeta

← #7689387

Subgroups — #7689387

Order 512.

4743 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59719C213yesmaximal, complemented
2#59713C213yesmaximal, complemented
3#59679C213yesmaximal, complemented
4#59250C213yesmaximal, complemented
5#59247C213yesmaximal, complemented
6#45193C213yesmaximal, complemented
7#45166C213yesmaximal, complemented
8#45040C213yesmaximal, complemented
9#44983C213yesmaximal, complemented
10#39756C213yesmaximal, complemented
11#39152C213yesmaximal, complemented
12#38242C213yesmaximal, complemented
13#38238C213yesmaximal, complemented
14#36503C213yesmaximal, complemented
15#36466C211yesmaximal, characteristic, complemented
16#36458C211yesmaximal, characteristic, complemented
17#36458C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#36431C211yesmaximal, characteristic, complemented
20#36196C213yesmaximal, complemented
21#36049C211yesmaximal, characteristic
22#36049C211yesmaximal, characteristic
23#35898C211yesmaximal, characteristic, complemented
24#35898C211yesmaximal, characteristic, complemented
25#34803C213yesmaximal, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34336C211yesmaximal, characteristic, complemented
28#34336C211yesmaximal, characteristic, complemented
29#34197C211yesmaximal, characteristic, complemented
30C4×#550C211yesmaximal, characteristic
31#34125C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2860C2213yes—
39#2860C2213yes—
40#2859C2213yes—
41#2851C2213yes—
42#2851C2213yes—
43#2808C2216yes—
44#2808C2216yes—
45#2800C2216yes—
46#2800C2216yes—
47#2786C2216yes—
48#2783C2216yes—
49#2777C2216yes—
50#2775C2216yes—
51#2759C2216yes—
52#2740C2216yes—
53#2727C2216yes—
54#2727C2216yes—
55#2715C2216yes—
56#2700C2216yes—
57#2644C2213yes—
58#2644C2213yes—
59#2641C2213yes—
60#2641C2213yes—
61#2604C2216yes—
62#2601C2216yes—
63#2594C2216yes—
64#2584C2213yes—
65#2584C2213yes—
66#2580C2213yes—
67#2580C2213yes—
68#2573C2216yes—
69#2573C2216yes—
70#2566C2213yes—
71#2566C2213yes—
72#2562C2213yes—
73#2562C2213yes—
74#2560C2216yes—
75#2552C2213yes—
76#2551C2213yes—
77#2550C2213yes—
78#2550C2213yes—
79#2548C2213yes—
80#2548C2213yes—
81#2545C2216yes—
82#2533C2213yes—
83#2533C2216yes—
84#2533C2211yescharacteristic
85#2532C2216yes—
86#2527C2213yes—
87#2527C2213yes—
88#2523C2213yes—
89#2523C2213yes—
90#2521C2216yes—
91#2514C2213yes—
92#2513C2213yes—
93#2513C2213yes—
94#2513C2213yes—
95#2513C2213yes—
96#2512C2213yes—
97#2512C2216yes—
98#2512C2213yes—
99#2512C2213yes—
100#2512C2213yes—
101#2512C2213yes—
102#2512C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2509C2213yes—
106#2499C2213yes—
107#2497C2213yes—
108#2497C2213yes—
109#2497C2213yes—
110#2497C2213yes—
111#2496C2213yes—
112#2496C2213yes—
113#2496C2213yes—
114#2496C2213yes—
115#2496C2213yes—
116#2495C2213yes—
117#2495C2213yes—
118#2494C2213yes—
119#2494C2213yes—
120#2492C2213yes—
121#2491C2213yes—
122#2491C2213yes—
123#2491C2213yes—
124#2491C2213yes—
125#2490C2213yes—
126#2490C2213yes—
127#2490C2213yes—
128#2490C2213yes—
129#2485C2213yes—
130#2474C2216yes—
131#2469C2216yes—
132#2466C2213yes—
133#2466C2216yes—
134#2466C2213yes—
135#2466C2216yes—
136#2466C2216yes—
137#2466C2216yes—
138#2454C2213yes—
139#2454C2213yes—
140#2452C2213yes—
141#2452C2213yes—
142#2447C2216yes—
143#2441C2213yes—
144#2441C2213yes—
145#2439C2213yes—
146#2439C2213yes—
147#2439C2213yes—
148#2415C2213yes—
149#2401C2213yes—
150#2401C2213yes—
151#2398C2213yes—
152#2398C2213yes—
153#2373C2216yes—
154#2373C2216yes—
155#2370C2213yes—
156#2370C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2370C2213yes—
160#2370C2213yes—
161#2369C2213yes—
162#2369C2213yes—
163#2367C2216yes—
164#2366C2213yes—
165#2365C2213yes—
166#2363C2213yes—
167#2363C2213yes—
168#2357C2213yes—
169#2357C2213yes—
170#2357C2213yes—
171#2357C2213yes—
172#2355C2213yes—
173#2355C2213yes—
174#2354C2213yes—
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181Q8×C4⋊C4C2213yes—
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188#2347C2213yes—
189#2347C2213yes—
190#2346C2213yes—
191#2346C2213yes—
192#2341C2211yescharacteristic
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2331C2213yes—
203#2331C2213yes—
204#2330C2213yes—
205#2330C2213yes—
206#2330C2213yes—
207#2330C2213yes—
208#2319C2213yes—
209#2319C2213yes—
210C4×C4⋊Q8C2213yes—
211C4×C4⋊Q8C2213yes—
212C4×#127C2213yes—
213C4×#125C2213yes—
214C4×#125C2213yes—
215C4×#126C2213yes—
216C4×#126C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×#121C2213yes—
220C4×#121C2213yes—
221#2295C2213yes—
222#2295C2213yes—
223#2295C2213yes—
224#2293C2213yes—
225#2293C2213yes—
226#2283C2213yes—
227#2283C2213yes—
228#2283C2213yes—
229#2276C2211yescharacteristic
230#2276C2211yescharacteristic
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#557—28no—
241#557—28no—
242#557—28no—
243#550—28no—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×#127C2313yes—
249C2×#126C2313yes—
250C2×#126C2313yes—
251C2×#126C2316yes—
252C2×#126C2316yes—
253C2×#126C2316yes—
254C2×#126C2316yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2316yes—
262C2×#124C2316yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C4×#41—28no—
268C4×#41—28no—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2313yes—
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2316yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2313yes—
287C2×C4×D4C2313yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2316yes—
294C2×#117C2313yes—
295C2×#117C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C22×C42C2313yes—
299C22×C42C2313yes—
300#401C2313yes—
301#401C2313yes—
302#400C2313yes—
303#400C2313yes—
304#400C2313yes—
305#400C2313yes—
306#400C2316yes—
307#400C2316yes—
308#400C2311yescharacteristic
309#400C2311yescharacteristic
310#400C2311yescharacteristic
311#400C2311yescharacteristic
312#400C2313yes—
313#400C2313yes—
314#399C2316yes—
315#399C2316yes—
316#398C2316yes—
317#398C2316yes—
318#397C2316yes—
319#397C2316yes—
320#397C2316yes—
321#397C2313yes—
322#397C2313yes—
323#397C2313yes—
324#397C2316yes—
325#397C2316yes—
326#397C2313yes—
327#397C2313yes—
328#397C2313yes—
329#397C2313yes—
330#397C2313yes—
331#397C2313yes—
332#397C2313yes—
333#397C2316yes—
334#397C2316yes—
335#397C2316yes—
336#396C2316yes—
337#396C2316yes—
338#396C2316yes—
339#396C2316yes—
340#396C2316yes—
341#396C2316yes—
342#396C2316yes—
343#396C2313yes—
344#396C2313yes—
345#396C2316yes—
346#395C2316yes—
347#395C2316yes—
348#394C2316yes—
349#394C2316yes—
350#394C2316yes—
351#394C2316yes—
352#394C2313yes—
353#394C2313yes—
354#394C2316yes—
355#394C2316yes—
356#394C2313yes—
357#394C2313yes—
358#393C2316yes—
359#393C2316yes—
360#393C2313yes—
361#393C2313yes—
362#393C2313yes—
363#393C2313yes—
364#391C2316yes—
365#391C2313yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2316yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#390C2316yes—
377#390C2313yes—
378#390C2313yes—
379#390C2316yes—
380#390C2316yes—
381#390C2313yes—
382#390C2313yes—
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#390C2313yes—
396#390C2313yes—
397#390C2313yes—
398#390C2313yes—
399#390C2316yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2311yescharacteristic
405#389C2313yes—
406#389C2313yes—
407#389C2316yes—
408#389C2313yes—
409#389C2313yes—
410#389C2316yes—
411#389C2316yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2316yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2316yes—
432#389C2316yes—
433#389C2313yes—
434#389C2316yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2311yescharacteristic
443#389C2313yes—
444#388C2313yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2313yes—
449#388C2313yes—
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#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#387C2311yescharacteristic
473#387C2311yescharacteristic
474#387C2313yes—
475#387C2313yes—
476#387C2313yes—
477#387C2313yes—
478#387C2313yes—
479#387C2313yes—
480#387C2313yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2316yes—
485#387C2313yes—
486#387C2316yes—
487#387C2313yes—
488#387C2313yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2313yes—
495#387C2316yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2316yes—
502#387C2311yescharacteristic
503#387C2311yescharacteristic
504#387C2311yescharacteristic
505#387C2311yescharacteristic
506#386C2316yes—
507#386C2316yes—
508#385C2313yes—
509#385C2313yes—
510#385C2316yes—
511#385C2316yes—
512#385C2316yes—
513#385C2313yes—
514#385C2313yes—
515#385C2316yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#383C2313yes—
524#383C2313yes—
525#383C2313yes—
526#383C2316yes—
527#383C2311yescharacteristic
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#381C2316yes—
537#381C2316yes—
538#381C2313yes—
539#381C2313yes—
540#380C2313yes—
541#380C2313yes—
542#380C2313yes—
543#380C2313yes—
544#380C2313yes—
545#380C2313yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554C4×C4⋊C4C2313yes—
555C4×C4⋊C4C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2313yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2316yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2316yes—
564C4×C4⋊C4C2316yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2316yes—
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⋊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⋊C4C2311yescharacteristic
596C4×C22⋊C4C2313yes—
597C4×C22⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2316yes—
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⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2316yes—
619#376C2313yes—
620#376C2311yescharacteristic
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2411yescharacteristic
634C22×D4C2413yes—
635C22×D4C2413yes—
636C22×D4C2413yes—
637C22×D4C2416yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646C4⋊Q8—212no—
647C4⋊Q8—46no—
648#127—212no—
649#126—412no—
650#126—46no—
651#126—46no—
652#126—412no—
653#126—86no—
654#126—86no—
655#125—212no—
656#125—212no—
657#125—212no—
658#125—212no—
659#125—212no—
660#125—212no—
661#124—412no—
662#124—86no—
663C22⋊Q8—46no—
664C22⋊Q8—46no—
665#121—212no—
666#121—212no—
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—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—212no—
679C4×Q8—212no—
680C4×Q8—212no—
681C4×Q8—86no—
682C4×Q8#4118yes—
683C4×Q8#4118yes—
684C4×D4—212no—
685C4×D4—212no—
686C4×D4—212no—
687C4×D4—212no—
688C4×D4—212no—
689C4×D4—46no—
690C4×D4—46no—
691C4×D4—86no—
692#117—212no—
693#117—212no—
694#117—46no—
695#117—46no—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊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⋊C4C2413yes—
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2416yes—
765C2×C22⋊C4C2416yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2416yes—
773C2×C22⋊C4C2416yes—
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2416yes—
786C2×C42—212no—
787C2×C42—212no—
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2411yescharacteristic
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×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2416yes—
812C2×C42C2416yes—
813C2×C42C2416yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2416yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2411yescharacteristic
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2416yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
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#95C2416yes—
867#95C2411yescharacteristic
868#95C2411yescharacteristic
869#95C2413yes—
870#95C2411yescharacteristic
871#95C2416yes—
872#95C2416yes—
873#95C2413yes—
874#95C2416yes—
875#95C2413yes—
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890C24C2513yes—
891C24C2513yes—
892#41—416no—
893#41—416no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—26no—
898C2×Q8—43no—
899C2×Q8—43no—
900C2×Q8—43no—
901C2×Q8—43no—
902C2×Q8—43no—
903C2×Q8C2×#4114yes—
904C2×Q8C2×#4114yes—
905C2×Q82−1+414yes—
906C2×D4—26no—
907C2×D4—26no—
908C2×D4—26no—
909C2×D4—26no—
910C2×D4—26no—
911C2×D4—212no—
912C2×D4—26no—
913C2×D4—26no—
914C2×D4—43no—
915C2×D4—43no—
916C2×D4—46no—
917C2×D4—46no—
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—26no—
928C22×C4—26no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4—43no—
932C22×C4—43no—
933C22×C4—43no—
934C22×C4—43no—
935C22×C4—43no—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2511yescharacteristic
941C22×C4C2513yes—
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2513yes—
945C22×C4C2513yes—
946C22×C4C2513yes—
947C22×C4C2511yescharacteristic
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2513yes—
954C22×C4C2513yes—
955C22×C4C2511yescharacteristic
956C22×C4C2513yes—
957C22×C4C2511yescharacteristic
958C22×C4C2513yes—
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—212no—
984C4⋊C4—212no—
985C4⋊C4—212no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—26no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—22no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—46no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—46no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—46no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4C2×#41112yes—
1020C4⋊C4C2×#41112yes—
1021C22⋊C4—212no—
1022C22⋊C4—212no—
1023C22⋊C4—26no—
1024C22⋊C4—26no—
1025C22⋊C4—26no—
1026C22⋊C4—26no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—26no—
1030C22⋊C4—43no—
1031C22⋊C4—43no—
1032C22⋊C4—43no—
1033C22⋊C4—43no—
1034C22⋊C4—46no—
1035C22⋊C4—46no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—46no—
1040C22⋊C4—46no—
1041C22⋊C4—43no—
1042C22⋊C4—43no—
1043C22⋊C4—46no—
1044C22⋊C4—46no—
1045C22⋊C4—46no—
1046C22⋊C4—46no—
1047C22⋊C4—43no—
1048C22⋊C4—46no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4—46no—
1052C22⋊C4—43no—
1053C22⋊C4—43no—
1054C22⋊C4—43no—
1055C42—22no—
1056C42—22no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—22no—
1071C42—22no—
1072C42—26no—
1073C42—22no—
1074C42—43no—
1075C42—43no—
1076C42—43no—
1077C42—43no—
1078C42—46no—
1079C42—46no—
1080C42—46no—
1081C42—43no—
1082C42—46no—
1083C42—43no—
1084C42—43no—
1085C42—43no—
1086C42C2×#41112yes—
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—
1101C23—23no—
1102C23C2611yescharacteristic
1103Q8—412no—
1104Q8—86no—
1105Q8—86no—
1106Q8#556116yes—
1107D4—412no—
1108D4—412no—
1109D4—412no—
1110D4—812no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—412no—
1189C2×C4—412no—
1190C2×C4—412no—
1191C2×C4—86no—
1192C2×C4—86no—
1193C2×C4—86no—
1194C2×C4C22×#4112yes—
1195C2×C4C22×#4116yes—
1196C2×C4C22×#4112yes—
1197C2×C4C22×#4116yes—
1198C2×C4C22×#4116yes—
1199C2×C4C22×#4116yes—
1200C2×C4C2×2−1+416yes—
1201C2×C4#58512yes—
1202C2×C4#58512yes—
1203C2×C4#58512yes—
1204C22—43no—
1205C22—43no—
1206C22—43no—
1207C22—43no—
1208C22—43no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22—43no—
1213C22—43no—
1214C22—43no—
1215C22—43no—
1216C22—43no—
1217C22—43no—
1218C22C23×#4111yescharacteristic
1219C22C23×#4111yescharacteristic
1220C22C22×2−1+411yescharacteristic
1221C22C2×#58511yescharacteristic
1222C22C2×#58511yescharacteristic
1223C22C2×#58511yescharacteristic
1224C22H(7,𝔽2)11yescharacteristic
1225C4—22no—
1226C4—26no—
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—26no—
1232C4—41no—
1233C4—43no—
1234C4—43no—
1235C4—43no—
1236C4—43no—
1237C4—43no—
1238C4—41no—
1239C4—41no—
1240C4—43no—
1241C4—41no—
1242C4—41no—
1243C4—43no—
1244C4—43no—
1245C4—41no—
1246C4—43no—
1247C4—41no—
1248C4—41no—
1249C4—43no—
1250C4—43no—
1251C4—41no—
1252C4—41no—
1253C4C2×#556112yes—
1254C2—83no—
1255C2—83no—
1256C2C22×#55611yescharacteristic
1257C2#6279311yescharacteristic
1258C2#6281611yescharacteristic
1259C2#6295211yescharacteristic
1260C2#6300611yescharacteristic
1261C2#6300811yescharacteristic
1262C2#6303311yescharacteristic
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. #59719C2semidirect
2. #59713C2semidirect
3. #59679C2semidirect
4. #59250C2semidirect
5. #59247C2semidirect
6. #45193C2semidirect
7. #45166C2semidirect
8. #45040C2semidirect
9. #44983C2semidirect
10. #39756C2semidirect
11. #39152C2semidirect
12. #38242C2semidirect
13. #38238C2semidirect
14. #36503C2semidirect
15. #36466C2semidirect
16. #36458C2semidirect
17. #36458C2semidirect
18. #36431C2semidirect
19. #36431C2semidirect
20. #36196C2semidirect
23. #35898C2semidirect
24. #35898C2semidirect
25. #34803C2semidirect
26. #34337C2semidirect
27. #34336C2semidirect
28. #34336C2semidirect
29. #34197C2semidirect
31. #34125C2semidirect

Maximal subgroups

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

subgroupindex
#597192
#597132
#596792
#592502
#592472
#451932
#451662
#450402
#449832
#397562
#391522
#382422
#382382
#365032
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#364582
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#360492
#358982
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C4×#5502
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