Finite Group Databasebeta

← #7698338

Subgroups — #7698338

Order 512.

4541 conjugacy classes of subgroups.

The subgroup lattice has 1241 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59710C213yesmaximal, complemented
2#59574C213yesmaximal, complemented
3#59426C213yesmaximal, complemented
4#52272C213yesmaximal, complemented
5#45329C213yesmaximal, complemented
6#45232C213yesmaximal, complemented
7#45174C213yesmaximal, complemented
8#45085C213yesmaximal, complemented
9#45067C213yesmaximal, complemented
10#44911C213yesmaximal, complemented
11#39758C213yesmaximal, complemented
12#39515C213yesmaximal, complemented
13#39297C213yesmaximal, complemented
14#39293C213yesmaximal, complemented
15#38237C213yesmaximal, complemented
16#38236C213yesmaximal, complemented
17#36474C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36448C211yesmaximal, characteristic, complemented
20#36040C211yesmaximal, characteristic, complemented
21#35948C211yesmaximal, characteristic
22#35898C211yesmaximal, characteristic, complemented
23#35883C211yesmaximal, characteristic, complemented
24#35854C211yesmaximal, characteristic
25#35845C211yesmaximal, characteristic, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34336C211yesmaximal, characteristic, complemented
28#34335C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic
30#34263C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#2863C2213yes—
39#2862C2213yes—
40#2860C2213yes—
41#2810C2213yes—
42#2808C2213yes—
43#2805C2213yes—
44#2800C2213yes—
45#2800C2213yes—
46#2798C2216yes—
47#2798C2216yes—
48#2798C2211yescharacteristic
49#2798C2213yes—
50#2798C2216yes—
51#2793C2213yes—
52#2793C2213yes—
53#2788C2216yes—
54#2783C2216yes—
55#2777C2216yes—
56#2776C2213yes—
57#2776C2213yes—
58#2767C2216yes—
59#2759C2213yes—
60#2759C2216yes—
61#2759C2213yes—
62#2759C2216yes—
63#2758C2216yes—
64#2745C2216yes—
65#2740C2216yes—
66#2727C2213yes—
67#2716C2213yes—
68#2716C2213yes—
69#2715C2216yes—
70#2645C2213yes—
71#2644C2213yes—
72#2640C2213yes—
73#2640C2213yes—
74#2628C2213yes—
75#2628C2213yes—
76#2604C2216yes—
77#2601C2216yes—
78#2592C2213yes—
79#2592C2213yes—
80#2592C2216yes—
81#2588C2216yes—
82#2581C2213yes—
83#2581C2216yes—
84#2580C2213yes—
85#2577C2216yes—
86#2567C2213yes—
87#2567C2213yes—
88#2563C2213yes—
89#2563C2213yes—
90#2550C2213yes—
91#2550C2213yes—
92#2550C2213yes—
93#2550C2213yes—
94#2547C2213yes—
95#2546C2213yes—
96#2528C2216yes—
97#2527C2216yes—
98#2527C2216yes—
99#2523C2216yes—
100#2523C2216yes—
101#2521C2216yes—
102#2514C2213yes—
103#2514C2213yes—
104#2514C2213yes—
105#2514C2213yes—
106#2514C2216yes—
107#2513C2213yes—
108#2513C2213yes—
109#2512C2213yes—
110#2512C2213yes—
111#2512C2213yes—
112#2512C2213yes—
113#2511C2213yes—
114#2511C2213yes—
115#2497C2213yes—
116#2497C2213yes—
117#2497C2213yes—
118#2496C2213yes—
119#2496C2213yes—
120#2496C2216yes—
121#2496C2213yes—
122#2495C2213yes—
123#2495C2213yes—
124#2495C2213yes—
125#2494C2216yes—
126#2494C2213yes—
127#2494C2213yes—
128#2494C2213yes—
129#2492C2213yes—
130#2492C2213yes—
131#2491C2213yes—
132#2491C2213yes—
133#2490C2213yes—
134#2490C2213yes—
135#2489C2213yes—
136#2489C2213yes—
137#2478C2216yes—
138#2469C2216yes—
139#2469C2216yes—
140#2469C2216yes—
141#2454C2213yes—
142#2454C2213yes—
143#2453C2213yes—
144#2453C2213yes—
145#2448C2216yes—
146#2442C2213yes—
147#2442C2213yes—
148#2441C2213yes—
149#2441C2213yes—
150#2439C2216yes—
151#2401C2213yes—
152#2401C2213yes—
153#2398C2213yes—
154#2398C2213yes—
155#2396C2213yes—
156#2396C2213yes—
157#2370C2213yes—
158#2370C2213yes—
159#2370C2213yes—
160#2370C2213yes—
161#2369C2213yes—
162#2369C2213yes—
163#2367C2213yes—
164#2365C2213yes—
165#2365C2213yes—
166#2365C2213yes—
167#2363C2213yes—
168#2360C2213yes—
169#2357C2213yes—
170#2356C2213yes—
171#2355C2213yes—
172#2355C2213yes—
173#2355C2213yes—
174#2354C2213yes—
175#2352C2213yes—
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185Q8×C4⋊C4C2213yes—
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189#2347C2216yes—
190#2347C2213yes—
191#2346C2213yes—
192#2345C2213yes—
193#2344C2213yes—
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2331C2213yes—
205#2331C2213yes—
206#2331C2213yes—
207#2330C2213yes—
208#2330C2213yes—
209#2330C2213yes—
210#2324C2213yes—
211#2323C2213yes—
212#2320C2213yes—
213#2319C2213yes—
214#2314C2213yes—
215#2314C2213yes—
216C4×C4⋊Q8C2213yes—
217C4×C4⋊Q8C2213yes—
218C4×C4⋊Q8C2213yes—
219C4×#125C2213yes—
220C4×#126C2213yes—
221C4×#126C2213yes—
222C4×#124C2213yes—
223#2298C2213yes—
224#2298C2213yes—
225#2295C2213yes—
226#2295C2213yes—
227#2295C2213yes—
228#2295C2213yes—
229#2293C2213yes—
230#2293C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240Q82—28no—
241#557—28no—
242#557—28no—
243#548—28no—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×#126C2313yes—
251C2×#126C2313yes—
252C2×#126C2316yes—
253C2×#126C2316yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#124C2313yes—
259C2×#124C2316yes—
260C2×C22⋊Q8C2313yes—
261C2×#121C2313yes—
262#520—28no—
263#519—28no—
264C2×C4×Q8C2313yes—
265C2×C4×Q8C2313yes—
266C2×C4×Q8C2313yes—
267C2×C4×Q8C2313yes—
268C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2316yes—
281C2×C4×Q8C2316yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×C4×D4C2313yes—
287C2×#117C2313yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C2×#117C2316yes—
291C22×C4⋊C4C2313yes—
292#401C2316yes—
293#401C2313yes—
294#401C2313yes—
295#401C2316yes—
296#400C2316yes—
297#400C2313yes—
298#400C2316yes—
299#400C2316yes—
300#400C2313yes—
301#400C2316yes—
302#400C2313yes—
303#400C2316yes—
304#400C2316yes—
305#400C2311yescharacteristic
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2311yescharacteristic
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2316yes—
315#399C2313yes—
316#399C2316yes—
317#399C2316yes—
318#399C2311yescharacteristic
319#398C2316yes—
320#398C2313yes—
321#398C2316yes—
322#398C2313yes—
323#398C2313yes—
324#398C2313yes—
325#397C2313yes—
326#397C2316yes—
327#397C2313yes—
328#397C2316yes—
329#397C2316yes—
330#397C2316yes—
331#397C2313yes—
332#397C2316yes—
333#397C2316yes—
334#397C2311yescharacteristic
335#397C2313yes—
336#397C2311yescharacteristic
337#397C2313yes—
338#397C2313yes—
339#397C2313yes—
340#397C2313yes—
341#397C2316yes—
342#397C2316yes—
343#396C2313yes—
344#396C2316yes—
345#396C2316yes—
346#396C2313yes—
347#396C2313yes—
348#396C2313yes—
349#396C2313yes—
350#396C2313yes—
351#395C2313yes—
352#395C2316yes—
353#395C2316yes—
354#395C2316yes—
355#395C2313yes—
356#394C2313yes—
357#394C2313yes—
358#394C2313yes—
359#394C2313yes—
360#393C2313yes—
361#393C2313yes—
362#393C2316yes—
363#393C2316yes—
364#393C2313yes—
365#393C2313yes—
366#393C2316yes—
367#393C2313yes—
368#393C2316yes—
369#393C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2313yes—
372#391C2316yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#391C2316yes—
377#391C2313yes—
378#391C2313yes—
379#391C2313yes—
380#391C2316yes—
381#391C2316yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2316yes—
386#391C2316yes—
387#391C2316yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2316yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2311yescharacteristic
396#390C2313yes—
397#390C2313yes—
398#390C2316yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2313yes—
405#390C2313yes—
406#390C2313yes—
407#390C2313yes—
408#390C2313yes—
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#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2316yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2313yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2316yes—
438#389C2316yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2311yescharacteristic
451#388C2311yescharacteristic
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2316yes—
459#388C2316yes—
460#388C2316yes—
461#388C2313yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2313yes—
472#388C2313yes—
473#388C2316yes—
474#388C2316yes—
475#388C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2311yescharacteristic
481#388C2313yes—
482#388C2311yescharacteristic
483#387C2311yescharacteristic
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2316yes—
491#387C2313yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2313yes—
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2313yes—
514#387C2313yes—
515#387C2316yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2311yescharacteristic
526#387C2311yescharacteristic
527#386C2316yes—
528#385C2316yes—
529#385C2316yes—
530#385C2316yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#384C2313yes—
535#384C2313yes—
536#384C2313yes—
537#383C2313yes—
538#383C2313yes—
539#383C2316yes—
540#383C2316yes—
541#383C2316yes—
542#382C2313yes—
543#382C2316yes—
544#382C2313yes—
545#382C2313yes—
546#382C2313yes—
547#382C2316yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#381C2316yes—
552#380C2313yes—
553#380C2313yes—
554#380C2316yes—
555#380C2313yes—
556#380C2313yes—
557#380C2316yes—
558#380C2313yes—
559#380C2313yes—
560#380C2316yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2316yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊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⋊C4C2316yes—
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×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620#376C2316yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2413yes—
631C22×Q8C2411yescharacteristic
632C22×Q8C2413yes—
633C22×Q8C2416yes—
634C22×Q8C2413yes—
635C22×Q8C2411yescharacteristic
636C22×D4C2413yes—
637C22×D4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2416yes—
641C4⋊Q8—212no—
642C4⋊Q8—212no—
643C4⋊Q8—212no—
644C4⋊Q8—212no—
645C4⋊Q8—212no—
646C4⋊Q8—46no—
647#126—46no—
648#126—46no—
649#126—86no—
650#126—86no—
651#125—212no—
652#125—212no—
653#125—212no—
654#125—212no—
655#124—212no—
656#124—86no—
657C22⋊Q8—212no—
658#121—212no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—212no—
671C4×Q8—212no—
672C4×Q8—212no—
673C4×Q8—212no—
674C4×Q8—212no—
675C4×Q8—86no—
676C4×Q8—86no—
677C4×Q8#4118yes—
678C4×Q8#4118yes—
679C4×D4—212no—
680C4×D4—212no—
681C4×D4—212no—
682#117—212no—
683#117—212no—
684#117—212no—
685#117—412no—
686C2×C4⋊C4—212no—
687C2×C4⋊C4C2413yes—
688C2×C4⋊C4C2413yes—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2416yes—
714C2×C4⋊C4C2416yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2411yescharacteristic
747C2×C22⋊C4C2413yes—
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2411yescharacteristic
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2416yes—
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2416yes—
755C2×C22⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2416yes—
758C2×C22⋊C4C2416yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2416yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2416yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2416yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2416yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2416yes—
794C2×C42C2416yes—
795C2×C42C2416yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2411yescharacteristic
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807#95C2411yescharacteristic
808#95C2411yescharacteristic
809#95C2411yescharacteristic
810#95C2411yescharacteristic
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2413yes—
820#95C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2416yes—
826#95C2416yes—
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2413yes—
834#95C2413yes—
835#95C2416yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2416yes—
843#95C2416yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2416yes—
853#95C2416yes—
854#95C2411yescharacteristic
855#95C2413yes—
856#95C2413yes—
857#95C2416yes—
858#95C2411yescharacteristic
859#95C2411yescharacteristic
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2416yes—
880#95C2416yes—
881#95C2416yes—
882C24C2511yescharacteristic
883C24C2513yes—
884#41—416no—
885C2×Q8—22no—
886C2×Q8—26no—
887C2×Q8—26no—
888C2×Q8—26no—
889C2×Q8—26no—
890C2×Q8—212no—
891C2×Q8—26no—
892C2×Q8—22no—
893C2×Q8—43no—
894C2×Q8—41no—
895C2×Q8—43no—
896C2×Q8—46no—
897C2×Q8—43no—
898C2×Q8—46no—
899C2×Q8—43no—
900C2×Q8—416no—
901C2×Q8C2×#4114yes—
902C2×Q8C2×#4114yes—
903C2×Q82−1+414yes—
904C2×D4—26no—
905C2×D4—26no—
906C2×D4—26no—
907C2×D4—26no—
908C2×D4—43no—
909C2×D4—43no—
910C22×C4—26no—
911C22×C4—26no—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—212no—
917C22×C4—46no—
918C22×C4—46no—
919C22×C4C2513yes—
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2513yes—
925C22×C4C2511yescharacteristic
926C22×C4C2513yes—
927C22×C4C2513yes—
928C22×C4C2513yes—
929C22×C4C2513yes—
930C22×C4C2511yescharacteristic
931C22×C4C2513yes—
932C22×C4C2513yes—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2513yes—
936C22×C4C2513yes—
937C22×C4C2513yes—
938C22×C4C2511yescharacteristic
939C22×C4C2513yes—
940C22×C4C2511yescharacteristic
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2511yescharacteristic
944C22×C4C2513yes—
945C22×C4C2513yes—
946C22×C4C2511yescharacteristic
947C22×C4C2513yes—
948C4⋊C4—26no—
949C4⋊C4—26no—
950C4⋊C4—22no—
951C4⋊C4—26no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—212no—
971C4⋊C4—212no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—22no—
977C4⋊C4—26no—
978C4⋊C4—43no—
979C4⋊C4—43no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—43no—
986C4⋊C4—46no—
987C4⋊C4—41no—
988C4⋊C4—43no—
989C4⋊C4—46no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—46no—
994C4⋊C4—46no—
995C4⋊C4—46no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4C2×#41112yes—
1005C4⋊C4C2×#41112yes—
1006C22⋊C4—26no—
1007C22⋊C4—22no—
1008C22⋊C4—26no—
1009C22⋊C4—26no—
1010C22⋊C4—22no—
1011C22⋊C4—26no—
1012C22⋊C4—212no—
1013C22⋊C4—26no—
1014C22⋊C4—22no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—43no—
1019C22⋊C4—43no—
1020C22⋊C4—43no—
1021C22⋊C4—46no—
1022C22⋊C4—43no—
1023C22⋊C4—43no—
1024C22⋊C4—43no—
1025C22⋊C4—41no—
1026C22⋊C4—46no—
1027C22⋊C4—43no—
1028C22⋊C4—43no—
1029C22⋊C4—46no—
1030C22⋊C4—46no—
1031C22⋊C4—43no—
1032C22⋊C4—43no—
1033C22⋊C4—43no—
1034C22⋊C4—43no—
1035C22⋊C4—43no—
1036C22⋊C4—43no—
1037C22⋊C4—46no—
1038C42—26no—
1039C42—26no—
1040C42—212no—
1041C42—26no—
1042C42—26no—
1043C42—26no—
1044C42—26no—
1045C42—26no—
1046C42—26no—
1047C42—26no—
1048C42—26no—
1049C42—26no—
1050C42—26no—
1051C42—41no—
1052C42—43no—
1053C42—41no—
1054C42—43no—
1055C42—43no—
1056C42—41no—
1057C42—46no—
1058C42—43no—
1059C42—46no—
1060C42—43no—
1061C42—46no—
1062C42—46no—
1063C42—43no—
1064C42—43no—
1065C42—43no—
1066C42C2×#41112yes—
1067C42C2×#41112yes—
1068C23—21no—
1069C23—23no—
1070C23—23no—
1071C23—21no—
1072C23—21no—
1073C23—23no—
1074C23—21no—
1075C23—23no—
1076C23—23no—
1077C23—21no—
1078C23—23no—
1079C23—21no—
1080C23—23no—
1081C23—21no—
1082C23C2611yescharacteristic
1083Q8—44no—
1084Q8—412no—
1085Q8—412no—
1086Q8—86no—
1087Q8—812no—
1088Q8#556116yes—
1089D4—412no—
1090D4—86no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—23no—
1094C2×C4—23no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—23no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—21no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—21no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—412no—
1171C2×C4—412no—
1172C2×C4—812no—
1173C2×C4C22×#4116yes—
1174C2×C4C22×#4112yes—
1175C2×C4C22×#4112yes—
1176C2×C4C22×#4116yes—
1177C2×C4C22×#4116yes—
1178C2×C4C22×#4116yes—
1179C2×C4C2×2−1+416yes—
1180C2×C4#58512yes—
1181C22—43no—
1182C22—41no—
1183C22—43no—
1184C22—41no—
1185C22—41no—
1186C22—43no—
1187C22—41no—
1188C22—43no—
1189C22—41no—
1190C22—43no—
1191C22—41no—
1192C22—43no—
1193C22—41no—
1194C22—43no—
1195C22C23×#4111yescharacteristic
1196C22C23×#4111yescharacteristic
1197C22C22×2−1+411yescharacteristic
1198C22C2×#58511yescharacteristic
1199C22H(7,𝔽2)11yescharacteristic
1200C222−1+611yescharacteristic
1201C222−1+611yescharacteristic
1202C4—26no—
1203C4—22no—
1204C4—22no—
1205C4—22no—
1206C4—26no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—43no—
1211C4—41no—
1212C4—43no—
1213C4—43no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—43no—
1219C4—43no—
1220C4—43no—
1221C4—41no—
1222C4—41no—
1223C4—43no—
1224C4—43no—
1225C4—43no—
1226C4—43no—
1227C4—43no—
1228C4—41no—
1229C4—43no—
1230C4C2×#556112yes—
1231C2—83no—
1232C2—81no—
1233C2C22×#55611yescharacteristic
1234C2#6285111yescharacteristic
1235C2#6285711yescharacteristic
1236C2#6295211yescharacteristic
1237C2#6299511yescharacteristic
1238C2#6300511yescharacteristic
1239C2#6305711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59710C2semidirect
2. #59574C2semidirect
3. #59426C2semidirect
4. #52272C2semidirect
5. #45329C2semidirect
6. #45232C2semidirect
7. #45174C2semidirect
8. #45085C2semidirect
9. #45067C2semidirect
10. #44911C2semidirect
11. #39758C2semidirect
12. #39515C2semidirect
13. #39297C2semidirect
14. #39293C2semidirect
15. #38237C2semidirect
16. #38236C2semidirect
17. #36474C2semidirect
18. #36458C2semidirect
19. #36448C2semidirect
20. #36040C2semidirect
22. #35898C2semidirect
23. #35883C2semidirect
25. #35845C2semidirect
26. #34337C2semidirect
27. #34336C2semidirect
28. #34335C2semidirect
30. #34263C2semidirect
31. #34262C2semidirect

Maximal subgroups

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

subgroupindex
#597102
#595742
#594262
#522722
#453292
#452322
#451742
#450852
#450672
#449112
#397582
#395152
#392972
#392932
#382372
#382362
#364742
#364582
#364482
#360402
#359482
#358982
#358832
#358542
#358452
#343372
#343362
#343352
#343122
#342632
#342622