Finite Group Databasebeta

← #7696999

Subgroups — #7696999

Order 512.

4412 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59718C213yesmaximal, complemented
2#59433C213yesmaximal
3#59246C213yesmaximal, complemented
4#52233C213yesmaximal
5#45431C213yesmaximal, complemented
6#45232C213yesmaximal
7#45219C213yesmaximal, complemented
8#45218C213yesmaximal, complemented
9#45183C213yesmaximal, complemented
10#45174C213yesmaximal, complemented
11#39802C213yesmaximal, complemented
12#39296C213yesmaximal, complemented
13#39157C213yesmaximal, complemented
14#38986C213yesmaximal, complemented
15#38243C213yesmaximal, complemented
16#37963C213yesmaximal
17#36577C211yesmaximal, characteristic, complemented
18#36448C211yesmaximal, characteristic, complemented
19#36446C211yesmaximal, characteristic
20#35957C211yesmaximal, characteristic, complemented
21#35920C211yesmaximal, characteristic, complemented
22#35910C211yesmaximal, characteristic
23#35883C211yesmaximal, characteristic, complemented
24#35883C211yesmaximal, characteristic, complemented
25#35845C211yesmaximal, characteristic, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34336C211yesmaximal, characteristic, complemented
28#34336C211yesmaximal, characteristic, complemented
29#34291C211yesmaximal, characteristic
30#34262C211yesmaximal, characteristic, complemented
31#34192C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2863C2213yes—
39#2862C2213yes—
40#2857C2213yes—
41#2810C2216yes—
42#2798C2216yes—
43#2793C2216yes—
44#2789C2213yes—
45#2789C2216yes—
46#2788C2213yes—
47#2787C2213yes—
48#2786C2213yes—
49#2783C2213yes—
50#2777C2213yes—
51#2777C2216yes—
52#2776C2216yes—
53#2775C2213yes—
54#2767C2213yes—
55#2767C2216yes—
56#2762C2213yes—
57#2762C2216yes—
58#2762C2216yes—
59#2759C2213yes—
60#2758C2213yes—
61#2758C2216yes—
62#2758C2216yes—
63#2758C2216yes—
64#2745C2213yes—
65#2740C2211yescharacteristic
66#2715C2213yes—
67#2700C2213yes—
68#2689C2213yes—
69#2689C2216yes—
70#2660C2213yes—
71#2645C2213yes—
72#2645C2213yes—
73#2645C2213yes—
74#2642C2213yes—
75#2628C2213yes—
76#2605C2216yes—
77#2605C2216yes—
78#2596C2216yes—
79#2594C2216yes—
80#2588C2216yes—
81#2584C2213yes—
82#2582C2213yes—
83#2581C2213yes—
84#2577C2216yes—
85#2571C2216yes—
86#2570C2216yes—
87#2568C2213yes—
88#2568C2213yes—
89#2568C2213yes—
90#2567C2213yes—
91#2567C2213yes—
92#2562C2213yes—
93#2552C2213yes—
94#2552C2213yes—
95#2550C2213yes—
96#2550C2213yes—
97#2547C2213yes—
98#2533C2216yes—
99#2532C2216yes—
100#2528C2216yes—
101#2528C2216yes—
102#2528C2216yes—
103#2524C2216yes—
104#2523C2216yes—
105#2521C2216yes—
106#2514C2213yes—
107#2514C2213yes—
108#2514C2213yes—
109#2514C2213yes—
110#2514C2213yes—
111#2514C2216yes—
112#2514C2216yes—
113#2514C2213yes—
114#2511C2213yes—
115#2511C2213yes—
116#2511C2213yes—
117#2511C2213yes—
118#2511C2213yes—
119#2511C2213yes—
120#2509C2216yes—
121#2497C2213yes—
122#2497C2213yes—
123#2496C2213yes—
124#2496C2213yes—
125#2496C2216yes—
126#2496C2213yes—
127#2496C2213yes—
128#2495C2213yes—
129#2495C2213yes—
130#2495C2213yes—
131#2494C2213yes—
132#2494C2213yes—
133#2494C2213yes—
134#2494C2216yes—
135#2492C2213yes—
136#2492C2213yes—
137#2489C2213yes—
138#2489C2213yes—
139#2489C2213yes—
140#2489C2213yes—
141#2489C2213yes—
142#2489C2213yes—
143#2453C2213yes—
144#2453C2213yes—
145#2453C2213yes—
146#2453C2213yes—
147#2442C2213yes—
148#2442C2213yes—
149#2441C2213yes—
150#2441C2213yes—
151#2401C2213yes—
152#2401C2213yes—
153#2401C2213yes—
154#2399C2213yes—
155#2398C2213yes—
156#2396C2213yes—
157#2373C2216yes—
158#2370C2213yes—
159#2370C2213yes—
160#2370C2213yes—
161#2370C2213yes—
162#2370C2213yes—
163#2370C2213yes—
164#2369C2213yes—
165#2369C2213yes—
166#2369C2213yes—
167#2365C2213yes—
168#2362C2213yes—
169#2360C2213yes—
170#2356C2213yes—
171#2356C2213yes—
172#2356C2213yes—
173#2355C2213yes—
174#2355C2213yes—
175#2355C2213yes—
176#2355C2213yes—
177#2352C2213yes—
178#2351C2211yescharacteristic
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2211yescharacteristic
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185Q8×C4⋊C4C2211yescharacteristic
186Q8×C4⋊C4C2211yescharacteristic
187Q8×C4⋊C4C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190#2347C2213yes—
191#2346C2213yes—
192#2345C2213yes—
193#2345C2213yes—
194Q8×C22⋊C4C2211yescharacteristic
195Q8×C22⋊C4C2211yescharacteristic
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
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#2327C2213yes—
211#2323C2213yes—
212#2320C2213yes—
213#2320C2213yes—
214#2320C2213yes—
215#2314C2213yes—
216C4×#125C2213yes—
217C4×#125C2213yes—
218C4×#125C2213yes—
219C4×#126C2213yes—
220C4×#124C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×C22⋊Q8C2213yes—
223#2298C2213yes—
224#2295C2213yes—
225#2295C2213yes—
226#2295C2213yes—
227#2295C2213yes—
228#2290C2213yes—
229#2283C2213yes—
230#2283C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240#557—28no—
241#557—28no—
242#557—28no—
243D4×Q8—28no—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×#126C2313yes—
249C2×#126C2316yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2313yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#124C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260#519—28no—
261C2×C4×Q8—28no—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×D4C2313yes—
283C2×#117C2313yes—
284C2×#117C2313yes—
285C22×C4⋊C4C2313yes—
286C22×C42C2313yes—
287#401C2316yes—
288#401C2313yes—
289#401C2316yes—
290#401C2316yes—
291#401C2313yes—
292#401C2313yes—
293#400C2316yes—
294#400C2313yes—
295#400C2316yes—
296#400C2316yes—
297#400C2316yes—
298#400C2316yes—
299#400C2316yes—
300#400C2316yes—
301#400C2313yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2313yes—
307#400C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2316yes—
312#400C2316yes—
313#400C2313yes—
314#400C2316yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#399C2316yes—
323#399C2311yescharacteristic
324#398C2313yes—
325#398C2316yes—
326#398C2316yes—
327#398C2316yes—
328#398C2313yes—
329#398C2313yes—
330#398C2311yescharacteristic
331#398C2313yes—
332#398C2313yes—
333#398C2316yes—
334#397C2313yes—
335#397C2316yes—
336#397C2313yes—
337#397C2313yes—
338#397C2313yes—
339#397C2313yes—
340#397C2311yescharacteristic
341#397C2311yescharacteristic
342#397C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2316yes—
347#397C2316yes—
348#396C2313yes—
349#396C2313yes—
350#396C2311yescharacteristic
351#396C2313yes—
352#396C2313yes—
353#395C2313yes—
354#395C2313yes—
355#395C2316yes—
356#395C2316yes—
357#395C2313yes—
358#395C2313yes—
359#395C2313yes—
360#394C2313yes—
361#394C2311yescharacteristic
362#393C2313yes—
363#393C2313yes—
364#393C2313yes—
365#391C2313yes—
366#391C2313yes—
367#391C2316yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2316yes—
375#391C2316yes—
376#391C2313yes—
377#391C2316yes—
378#391C2313yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2316yes—
392#391C2316yes—
393#391C2316yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#390C2311yescharacteristic
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2316yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2316yes—
413#389C2313yes—
414#389C2316yes—
415#389C2313yes—
416#389C2316yes—
417#389C2316yes—
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#389C2313yes—
434#389C2316yes—
435#389C2316yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#388C2311yescharacteristic
442#388C2313yes—
443#388C2313yes—
444#388C2316yes—
445#388C2316yes—
446#388C2313yes—
447#388C2316yes—
448#388C2313yes—
449#388C2316yes—
450#388C2313yes—
451#388C2316yes—
452#388C2313yes—
453#388C2313yes—
454#388C2316yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2311yescharacteristic
460#387C2313yes—
461#387C2313yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2316yes—
467#387C2316yes—
468#387C2316yes—
469#387C2316yes—
470#387C2316yes—
471#387C2316yes—
472#387C2316yes—
473#387C2313yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2313yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2313yes—
496#387C2316yes—
497#387C2316yes—
498#387C2313yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2313yes—
508#387C2311yescharacteristic
509#387C2311yescharacteristic
510#387C2311yescharacteristic
511#387C2313yes—
512#386C2313yes—
513#386C2311yescharacteristic
514#385C2313yes—
515#385C2313yes—
516#385C2313yes—
517#385C2313yes—
518#384C2316yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#384C2313yes—
523#384C2313yes—
524#383C2313yes—
525#383C2316yes—
526#383C2316yes—
527#383C2316yes—
528#383C2316yes—
529#383C2316yes—
530#383C2313yes—
531#383C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2316yes—
537#382C2313yes—
538#382C2313yes—
539#382C2316yes—
540#382C2313yes—
541#382C2316yes—
542#382C2316yes—
543#382C2313yes—
544#382C2313yes—
545#382C2313yes—
546#381C2311yescharacteristic
547#381C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2316yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2311yescharacteristic
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2316yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2316yes—
575C4×C4⋊C4C2316yes—
576C4×C4⋊C4C2316yes—
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⋊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⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2316yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620#376C2316yes—
621#376C2316yes—
622C43C2313yes—
623C43C2313yes—
624C22×Q8—24no—
625C22×Q8—24no—
626C22×Q8—24no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2413yes—
634C22×Q8C2413yes—
635C22×Q8C2411yescharacteristic
636C22×D4C2411yescharacteristic
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2411yescharacteristic
640C23×C4C2413yes—
641C4⋊Q8—212no—
642C4⋊Q8—212no—
643C4⋊Q8—212no—
644C4⋊Q8—212no—
645#126—46no—
646#126—412no—
647#125—212no—
648#125—212no—
649#125—212no—
650#125—212no—
651#125—212no—
652#125—212no—
653#124—46no—
654C22⋊Q8—212no—
655C22⋊Q8—212no—
656C22⋊Q8—46no—
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—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—212no—
669C4×Q8—212no—
670C4×Q8—212no—
671C4×Q8—212no—
672C4×Q8—212no—
673C4×Q8—212no—
674C4×Q8—212no—
675C4×Q8#4118yes—
676C4×Q8#4118yes—
677C4×D4—212no—
678#117—212no—
679#117—212no—
680C2×C4⋊C4—212no—
681C2×C4⋊C4C2413yes—
682C2×C4⋊C4C2416yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2413yes—
685C2×C4⋊C4C2413yes—
686C2×C4⋊C4C2413yes—
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2413yes—
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
706C2×C4⋊C4C2416yes—
707C2×C4⋊C4C2416yes—
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2416yes—
715C2×C4⋊C4C2416yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2416yes—
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⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C22⋊C4C2411yescharacteristic
741C2×C22⋊C4C2413yes—
742C2×C22⋊C4C2413yes—
743C2×C22⋊C4C2413yes—
744C2×C22⋊C4C2413yes—
745C2×C22⋊C4C2413yes—
746C2×C22⋊C4C2413yes—
747C2×C22⋊C4C2411yescharacteristic
748C2×C22⋊C4C2413yes—
749C2×C22⋊C4C2413yes—
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2413yes—
752C2×C22⋊C4C2411yescharacteristic
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2411yescharacteristic
755C2×C22⋊C4C2411yescharacteristic
756C2×C22⋊C4C2411yescharacteristic
757C2×C22⋊C4C2411yescharacteristic
758C2×C22⋊C4C2411yescharacteristic
759C2×C22⋊C4C2411yescharacteristic
760C2×C22⋊C4C2411yescharacteristic
761C2×C22⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C42—212no—
765C2×C42C2413yes—
766C2×C42C2416yes—
767C2×C42C2413yes—
768C2×C42C2413yes—
769C2×C42C2413yes—
770C2×C42C2413yes—
771C2×C42C2413yes—
772C2×C42C2413yes—
773C2×C42C2413yes—
774C2×C42C2413yes—
775C2×C42C2413yes—
776C2×C42C2413yes—
777C2×C42C2413yes—
778C2×C42C2413yes—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2416yes—
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2413yes—
787C2×C42C2413yes—
788C2×C42C2416yes—
789C2×C42C2416yes—
790C2×C42C2416yes—
791C2×C42C2416yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794#95C2411yescharacteristic
795#95C2411yescharacteristic
796#95C2411yescharacteristic
797#95C2411yescharacteristic
798#95C2411yescharacteristic
799#95C2413yes—
800#95C2413yes—
801#95C2413yes—
802#95C2413yes—
803#95C2416yes—
804#95C2413yes—
805#95C2413yes—
806#95C2413yes—
807#95C2413yes—
808#95C2413yes—
809#95C2413yes—
810#95C2413yes—
811#95C2413yes—
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2413yes—
819#95C2416yes—
820#95C2416yes—
821#95C2416yes—
822#95C2416yes—
823#95C2413yes—
824#95C2413yes—
825#95C2416yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2416yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2416yes—
852#95C2411yescharacteristic
853#95C2413yes—
854#95C2411yescharacteristic
855#95C2416yes—
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2413yes—
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2413yes—
864#95C2413yes—
865#95C2416yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2416yes—
873#95C2416yes—
874#95C2416yes—
875#95C2416yes—
876#95C2416yes—
877C24C2511yescharacteristic
878C24C2511yescharacteristic
879C2×Q8—26no—
880C2×Q8—26no—
881C2×Q8—26no—
882C2×Q8—26no—
883C2×Q8—26no—
884C2×Q8—26no—
885C2×Q8—26no—
886C2×Q8—26no—
887C2×Q8—26no—
888C2×Q8—43no—
889C2×Q8—43no—
890C2×Q8—43no—
891C2×Q8—43no—
892C2×Q8—43no—
893C2×Q8—43no—
894C2×Q8—416no—
895C2×Q8—416no—
896C2×Q8C2×#4114yes—
897C2×Q8C2×#4114yes—
898C2×Q82−1+414yes—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—41no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—26no—
905C22×C4—26no—
906C22×C4—26no—
907C22×C4—26no—
908C22×C4—26no—
909C22×C4—26no—
910C22×C4—26no—
911C22×C4—41no—
912C22×C4—43no—
913C22×C4—43no—
914C22×C4C2511yescharacteristic
915C22×C4C2513yes—
916C22×C4C2513yes—
917C22×C4C2511yescharacteristic
918C22×C4C2513yes—
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2513yes—
922C22×C4C2513yes—
923C22×C4C2513yes—
924C22×C4C2513yes—
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2513yes—
932C22×C4C2513yes—
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2513yes—
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C4⋊C4—26no—
944C4⋊C4—212no—
945C4⋊C4—26no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—212no—
965C4⋊C4—212no—
966C4⋊C4—212no—
967C4⋊C4—212no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—43no—
972C4⋊C4—43no—
973C4⋊C4—43no—
974C4⋊C4—43no—
975C4⋊C4—43no—
976C4⋊C4—43no—
977C4⋊C4—46no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—43no—
981C4⋊C4—43no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—46no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4—46no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—46no—
998C4⋊C4—46no—
999C4⋊C4—43no—
1000C4⋊C4C2×#41112yes—
1001C4⋊C4C2×#41112yes—
1002C22⋊C4—26no—
1003C22⋊C4—26no—
1004C22⋊C4—26no—
1005C22⋊C4—22no—
1006C22⋊C4—26no—
1007C22⋊C4—22no—
1008C22⋊C4—26no—
1009C22⋊C4—26no—
1010C22⋊C4—26no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—43no—
1016C22⋊C4—41no—
1017C22⋊C4—43no—
1018C22⋊C4—43no—
1019C22⋊C4—43no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—43no—
1025C22⋊C4—43no—
1026C42—26no—
1027C42—26no—
1028C42—26no—
1029C42—26no—
1030C42—212no—
1031C42—26no—
1032C42—26no—
1033C42—26no—
1034C42—26no—
1035C42—26no—
1036C42—26no—
1037C42—26no—
1038C42—26no—
1039C42—26no—
1040C42—46no—
1041C42—43no—
1042C42—43no—
1043C42—46no—
1044C42—41no—
1045C42—43no—
1046C42—43no—
1047C42—46no—
1048C42—46no—
1049C42—41no—
1050C42—43no—
1051C42—46no—
1052C42—43no—
1053C42C2×#41112yes—
1054C42C2×#41112yes—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23#58512yes—
1069C23C2611yescharacteristic
1070Q8—412no—
1071Q8—412no—
1072Q8—86no—
1073Q8—86no—
1074Q8—86no—
1075Q8#556116yes—
1076D4—44no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—23no—
1080C2×C4—23no—
1081C2×C4—23no—
1082C2×C4—21no—
1083C2×C4—23no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—23no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—23no—
1095C2×C4—23no—
1096C2×C4—23no—
1097C2×C4—23no—
1098C2×C4—23no—
1099C2×C4—23no—
1100C2×C4—23no—
1101C2×C4—23no—
1102C2×C4—23no—
1103C2×C4—23no—
1104C2×C4—23no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—23no—
1109C2×C4—23no—
1110C2×C4—23no—
1111C2×C4—23no—
1112C2×C4—23no—
1113C2×C4—23no—
1114C2×C4—23no—
1115C2×C4—21no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—23no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—44no—
1158C2×C4—412no—
1159C2×C4—412no—
1160C2×C4—86no—
1161C2×C4C22×#4112yes—
1162C2×C4C22×#4116yes—
1163C2×C4C22×#4112yes—
1164C2×C4C22×#4116yes—
1165C2×C4C22×#4116yes—
1166C2×C4C22×#4116yes—
1167C2×C4C2×2−1+416yes—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22C23×#4111yescharacteristic
1183C22C23×#4111yescharacteristic
1184C22C22×2−1+411yescharacteristic
1185C22C2×#58511yescharacteristic
1186C222−1+611yescharacteristic
1187C222−1+611yescharacteristic
1188C222−1+611yescharacteristic
1189C4—22no—
1190C4—22no—
1191C4—26no—
1192C4—26no—
1193C4—43no—
1194C4—41no—
1195C4—43no—
1196C4—41no—
1197C4—43no—
1198C4—43no—
1199C4—43no—
1200C4—43no—
1201C4—41no—
1202C4—41no—
1203C4—43no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—43no—
1210C4—43no—
1211C4—41no—
1212C4—41no—
1213C4—43no—
1214C4—43no—
1215C4—43no—
1216C4—43no—
1217C4C2×#556112yes—
1218C2—42no—
1219C2—81no—
1220C2C22×#55611yescharacteristic
1221C2#6286111yescharacteristic
1222C2#6286111yescharacteristic
1223C2#6294911yescharacteristic
1224C2#6300511yescharacteristic
1225C2#6300511yescharacteristic
1226C2#6305711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59718C2semidirect
3. #59246C2semidirect
5. #45431C2semidirect
7. #45219C2semidirect
8. #45218C2semidirect
9. #45183C2semidirect
10. #45174C2semidirect
11. #39802C2semidirect
12. #39296C2semidirect
13. #39157C2semidirect
14. #38986C2semidirect
15. #38243C2semidirect
17. #36577C2semidirect
18. #36448C2semidirect
20. #35957C2semidirect
21. #35920C2semidirect
23. #35883C2semidirect
24. #35883C2semidirect
25. #35845C2semidirect
26. #34336C2semidirect
27. #34336C2semidirect
28. #34336C2semidirect
30. #34262C2semidirect
31. #34192C2semidirect

Maximal subgroups

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

subgroupindex
#597182
#594332
#592462
#522332
#454312
#452322
#452192
#452182
#451832
#451742
#398022
#392962
#391572
#389862
#382432
#379632
#365772
#364482
#364462
#359572
#359202
#359102
#358832
#358452
#343362
#342912
#342622
#341922