Finite Group Databasebeta

← #7665653

Subgroups — #7665653

Order 512.

4913 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40166C213yesmaximal, complemented
2#40154C213yesmaximal, complemented
3#40074C213yesmaximal, complemented
4#40058C213yesmaximal, complemented
5#40022C213yesmaximal, complemented
6#40000C213yesmaximal, complemented
7#39930C213yesmaximal, complemented
8#39904C213yesmaximal, complemented
9#39538C213yesmaximal, complemented
10#39403C213yesmaximal, complemented
11#39022C213yesmaximal, complemented
12#39007C213yesmaximal, complemented
13#36577C211yesmaximal, characteristic, complemented
14Q8×#123C211yesmaximal, characteristic, complemented
15#36467C211yesmaximal, characteristic, complemented
16#36467C211yesmaximal, characteristic, complemented
17#36466C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36448C211yesmaximal, characteristic, complemented
20#36446C211yesmaximal, characteristic, complemented
21#36435C211yesmaximal, characteristic, complemented
22#36434C211yesmaximal, characteristic
23#36432C211yesmaximal, characteristic, complemented
24#36431C211yesmaximal, characteristic, complemented
25#35135C213yesmaximal, complemented
26#35117C213yesmaximal, complemented
27#35110C213yesmaximal, complemented
28C4×#557C211yesmaximal, characteristic, complemented
29C4×#548C211yesmaximal, characteristic, complemented
30#34128C211yesmaximal, characteristic, complemented
31C4×#542C213yesmaximal, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#542C2213yes—
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2863C2213yes—
43#2862C2213yes—
44#2861C2213yes—
45#2861C2213yes—
46#2860C2213yes—
47#2859C2213yes—
48#2857C2213yes—
49#2855C2213yes—
50#2855C2213yes—
51#2851C2213yes—
52#2851C2213yes—
53#2850C2213yes—
54#2796C2216yes—
55#2790C2216yes—
56#2777C2216yes—
57#2775C2216yes—
58#2767C2216yes—
59#2765C2216yes—
60#2764C2216yes—
61#2758C2216yes—
62#2757C2216yes—
63#2755C2216yes—
64#2746C2216yes—
65#2738C2216yes—
66#2716C2216yes—
67#2715C2216yes—
68#2700C2216yes—
69#2686C2216yes—
70#2655C2216yes—
71#2654C2216yes—
72#2650C2216yes—
73#2649C2216yes—
74#2638C2216yes—
75#2637C2216yes—
76#2592C2213yes—
77#2592C2213yes—
78#2584C2213yes—
79#2584C2213yes—
80#2582C2213yes—
81#2581C2213yes—
82#2580C2213yes—
83#2568C2213yes—
84#2568C2213yes—
85#2566C2213yes—
86#2565C2213yes—
87#2562C2213yes—
88#2562C2213yes—
89#2552C2213yes—
90#2551C2213yes—
91#2550C2213yes—
92#2550C2213yes—
93#2547C2213yes—
94#2545C2213yes—
95#2536C2213yes—
96#2532C2216yes—
97#2530C2216yes—
98#2530C2216yes—
99#2529C2216yes—
100#2529C2216yes—
101#2527C2216yes—
102#2520C2216yes—
103#2515C2216yes—
104#2514C2213yes—
105#2514C2213yes—
106#2513C2213yes—
107#2512C2213yes—
108#2512C2213yes—
109#2511C2213yes—
110#2502C2213yes—
111#2499C2213yes—
112#2497C2213yes—
113#2496C2213yes—
114#2496C2213yes—
115#2495C2213yes—
116#2495C2213yes—
117#2494C2213yes—
118#2492C2213yes—
119#2492C2213yes—
120#2491C2213yes—
121#2491C2213yes—
122#2490C2213yes—
123#2490C2213yes—
124#2489C2213yes—
125#2489C2213yes—
126#2489C2213yes—
127#2489C2213yes—
128#2489C2213yes—
129#2489C2213yes—
130#2487C2213yes—
131#2485C2213yes—
132#2479C2216yes—
133#2470C2216yes—
134#2468C2216yes—
135#2465C2216yes—
136#2454C2213yes—
137#2453C2213yes—
138#2453C2213yes—
139#2453C2213yes—
140#2452C2213yes—
141#2451C2213yes—
142#2447C2213yes—
143#2447C2213yes—
144#2446C2213yes—
145#2446C2213yes—
146#2442C2213yes—
147#2442C2213yes—
148#2442C2213yes—
149#2441C2213yes—
150#2440C2213yes—
151#2439C2213yes—
152#2429C2213yes—
153#2426C2213yes—
154#2423C2213yes—
155#2423C2213yes—
156#2422C2213yes—
157#2420C2213yes—
158#2417C2213yes—
159#2416C2213yes—
160#2370C2213yes—
161#2370C2213yes—
162#2367C2213yes—
163#2365C2213yes—
164#2362C2213yes—
165#2361C2213yes—
166#2356C2213yes—
167#2356C2213yes—
168#2355C2213yes—
169#2352C2213yes—
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180#2344C2213yes—
181#2344C2213yes—
182#2341C2211yescharacteristic
183#2341C2211yescharacteristic
184#2341C2211yescharacteristic
185#2341C2211yescharacteristic
186Q8×C22⋊C4C2211yescharacteristic
187Q8×C22⋊C4C2211yescharacteristic
188Q8×C22⋊C4C2211yescharacteristic
189Q8×C22⋊C4C2211yescharacteristic
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2211yescharacteristic
192Q8×C22⋊C4C2211yescharacteristic
193Q8×C22⋊C4C2211yescharacteristic
194#2337C2213yes—
195#2337C2213yes—
196#2335C2211yescharacteristic
197#2335C2213yes—
198#2334C2216yes—
199#2334C2213yes—
200#2334C2213yes—
201#2332C2213yes—
202#2332C2213yes—
203#2331C2213yes—
204#2326C2213yes—
205#2324C2213yes—
206#2323C2213yes—
207#2320C2213yes—
208#2319C2213yes—
209#2314C2213yes—
210C4×C4⋊Q8C2213yes—
211C4×C4⋊Q8C2213yes—
212C4×#125C2213yes—
213C4×#125C2213yes—
214C4×#126C2213yes—
215C4×#126C2213yes—
216C4×#124C2213yes—
217C4×#124C2213yes—
218C4×#124C2213yes—
219C4×#124C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×C22⋊Q8C2213yes—
222C4×C22⋊Q8C2213yes—
223C4×C22⋊Q8C2213yes—
224C4×#123C2213yes—
225C4×#123C2213yes—
226C4×#121C2213yes—
227C4×#121C2213yes—
228#2295C2213yes—
229#2295C2213yes—
230#2283C2213yes—
231C42×Q8C2213yes—
232C42×Q8C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—28no—
242#557—44no—
243#557—44no—
244D4×Q8—44no—
245#548—28no—
246#548—44no—
247#542—224no—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×#126C2313yes—
254C2×#126C2313yes—
255C2×#126C2316yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#123C2313yes—
268C2×#123C2311yescharacteristic
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×#121C2313yes—
277C2×#121C2313yes—
278C2×#121C2313yes—
279C4×#41—44no—
280C2×C4×Q8—28no—
281C2×C4×Q8—44no—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2311yescharacteristic
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C42C2313yes—
316C22×C42C2313yes—
317C22×C42C2313yes—
318#401C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2316yes—
330#399C2316yes—
331#399C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#397C2316yes—
349#397C2316yes—
350#397C2316yes—
351#396C2316yes—
352#396C2316yes—
353#396C2316yes—
354#396C2316yes—
355#396C2316yes—
356#395C2316yes—
357#395C2316yes—
358#395C2316yes—
359#394C2316yes—
360#394C2316yes—
361#394C2316yes—
362#394C2316yes—
363#393C2316yes—
364#393C2316yes—
365#393C2316yes—
366#391C2313yes—
367#391C2313yes—
368#391C2316yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2316yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2316yes—
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#391C2313yes—
392#391C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#390C2313yes—
397#390C2311yescharacteristic
398#390C2313yes—
399#390C2313yes—
400#390C2313yes—
401#390C2313yes—
402#390C2313yes—
403#390C2313yes—
404#390C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2311yescharacteristic
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2316yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2316yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2316yes—
438#388C2311yescharacteristic
439#388C2313yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2313yes—
444#388C2313yes—
445#388C2313yes—
446#388C2316yes—
447#388C2316yes—
448#388C2311yescharacteristic
449#388C2313yes—
450#388C2313yes—
451#388C2313yes—
452#388C2313yes—
453#388C2311yescharacteristic
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2311yescharacteristic
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2316yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#387C2311yescharacteristic
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#387C2311yescharacteristic
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#386C2313yes—
509#386C2313yes—
510#386C2311yescharacteristic
511#386C2313yes—
512#386C2316yes—
513#386C2316yes—
514#385C2313yes—
515#385C2316yes—
516#385C2313yes—
517#385C2313yes—
518#385C2313yes—
519#385C2313yes—
520#385C2313yes—
521#385C2316yes—
522#385C2316yes—
523#385C2311yescharacteristic
524#385C2313yes—
525#385C2316yes—
526#385C2316yes—
527#385C2316yes—
528#384C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#383C2313yes—
534#383C2313yes—
535#383C2316yes—
536#383C2316yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2313yes—
541#382C2313yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2316yes—
546#382C2316yes—
547#382C2313yes—
548#381C2313yes—
549#381C2313yes—
550#381C2316yes—
551#381C2316yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2311yescharacteristic
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2316yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2316yes—
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⋊C4C2311yescharacteristic
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×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2311yescharacteristic
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2311yescharacteristic
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2316yes—
621#376C2313yes—
622#376C2313yes—
623#376C2316yes—
624C43C2313yes—
625C43C2313yes—
626C43C2313yes—
627C43C2313yes—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8—24no—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2413yes—
640C22×Q8C2413yes—
641C22×Q8C2413yes—
642C22×Q8C2411yescharacteristic
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2413yes—
646C22×D4C2411yescharacteristic
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2411yescharacteristic
653C23×C4C2413yes—
654C23×C4C2413yes—
655C23×C4C2411yescharacteristic
656C4⋊Q8—212no—
657C4⋊Q8—212no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660C4⋊Q8—46no—
661#126—212no—
662#126—212no—
663#126—412no—
664#125—212no—
665#125—212no—
666#125—46no—
667#125—46no—
668#125—46no—
669#125—46no—
670#124—212no—
671#124—212no—
672#124—212no—
673#124—212no—
674#124—46no—
675#123—212no—
676#123#4118yescomplemented
677C22⋊Q8—212no—
678C22⋊Q8—212no—
679C22⋊Q8—212no—
680C22⋊Q8—212no—
681C22⋊Q8—46no—
682C22⋊Q8—46no—
683C22⋊Q8—46no—
684#121—212no—
685#121—212no—
686#121—46no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—212no—
699C4×Q8—212no—
700C4×Q8—212no—
701C4×Q8—212no—
702C4×Q8—46no—
703C4×Q8—46no—
704C4×Q8—46no—
705C4×Q8—46no—
706C4×Q8—46no—
707C4×Q8#4118yes—
708C4×D4—212no—
709C4×D4—212no—
710C4×D4—46no—
711C4×D4—46no—
712C4×D4—46no—
713C4×D4—46no—
714C4×D4—46no—
715#117—212no—
716#117—46no—
717#117—46no—
718C2×C4⋊C4—212no—
719C2×C4⋊C4—46no—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2416yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2416yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2416yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2416yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C42—212no—
812C2×C42—46no—
813C2×C42—46no—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2411yescharacteristic
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2411yescharacteristic
839C2×C42C2411yescharacteristic
840C2×C42C2411yescharacteristic
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2411yescharacteristic
847C2×C42C2413yes—
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2416yes—
857#95C2416yes—
858#95C2416yes—
859#95C2416yes—
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2416yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2413yes—
887#95C2416yes—
888#95C2416yes—
889#95C2413yes—
890#95C2413yes—
891#95C2411yescharacteristic
892#95C2413yes—
893#95C2416yes—
894#95C2416yes—
895#95C2416yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2416yes—
902#95C2413yes—
903#95C2413yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907#95C2416yes—
908#95C2416yes—
909#95C2416yes—
910C24C2513yes—
911C24C2511yescharacteristic
912C24C2511yescharacteristic
913#41—416no—
914C2×Q8—26no—
915C2×Q8—26no—
916C2×Q8—26no—
917C2×Q8—26no—
918C2×Q8—26no—
919C2×Q8—26no—
920C2×Q8—26no—
921C2×Q8—26no—
922C2×Q8—26no—
923C2×Q8—26no—
924C2×Q8—43no—
925C2×Q8—43no—
926C2×Q8—43no—
927C2×Q8—43no—
928C2×Q8—43no—
929C2×Q8—416no—
930C2×Q8—416no—
931C2×Q8C2×#4114yes—
932C2×Q8H(5,𝔽2)14yes—
933C2×Q82−1+414yes—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—26no—
937C2×D4—26no—
938C2×D4—26no—
939C2×D4—26no—
940C2×D4—41no—
941C2×D4—43no—
942C2×D4—41no—
943C2×D4—43no—
944C2×D4—43no—
945C2×D4C2×#4114yes—
946C22×C4—26no—
947C22×C4—22no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—26no—
959C22×C4—41no—
960C22×C4—43no—
961C22×C4—41no—
962C22×C4—41no—
963C22×C4—41no—
964C22×C4—43no—
965C22×C4—43no—
966C22×C4—43no—
967C22×C4—43no—
968C22×C4—43no—
969C22×C4—43no—
970C22×C4—43no—
971C22×C4—43no—
972C22×C4C2×#4114yes—
973C22×C4C2513yes—
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2513yes—
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2513yes—
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2513yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2513yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2513yes—
1001C4⋊C4—26no—
1002C4⋊C4—212no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—22no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—212no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—46no—
1028C4⋊C4—41no—
1029C4⋊C4—43no—
1030C4⋊C4—41no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—46no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—46no—
1048C4⋊C4—46no—
1049C4⋊C4—46no—
1050C4⋊C4—46no—
1051C4⋊C4—46no—
1052C4⋊C4C2×#41112yes—
1053C4⋊C4C2×#4114yes—
1054C4⋊C4C2×#4114yes—
1055C22⋊C4—26no—
1056C22⋊C4—26no—
1057C22⋊C4—26no—
1058C22⋊C4—26no—
1059C22⋊C4—26no—
1060C22⋊C4—22no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—212no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—26no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—26no—
1070C22⋊C4—41no—
1071C22⋊C4—46no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—46no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—46no—
1082C22⋊C4—41no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—46no—
1087C22⋊C4—46no—
1088C22⋊C4—46no—
1089C22⋊C4C2×#4114yes—
1090C22⋊C4C2×#4114yes—
1091C22⋊C4C2×#4114yes—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—22no—
1111C42—26no—
1112C42—41no—
1113C42—43no—
1114C42—43no—
1115C42—43no—
1116C42—41no—
1117C42—41no—
1118C42—43no—
1119C42—41no—
1120C42—43no—
1121C42—43no—
1122C42—43no—
1123C42—43no—
1124C42—43no—
1125C42C2×#41112yes—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23—23no—
1143C23—23no—
1144C23—23no—
1145C23C22×#4112yes—
1146C23C22×#4112yes—
1147C23C2611yescharacteristic
1148Q8—412no—
1149Q8—412no—
1150Q8—412no—
1151Q8—86no—
1152Q8—86no—
1153Q8#542116yescomplemented
1154D4—44no—
1155D4—412no—
1156D4—412no—
1157D4—86no—
1158C2×C4—21no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—23no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—21no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—21no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—21no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—21no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—21no—
1227C2×C4—23no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—44no—
1232C2×C4—412no—
1233C2×C4—44no—
1234C2×C4—412no—
1235C2×C4—412no—
1236C2×C4—412no—
1237C2×C4—86no—
1238C2×C4—86no—
1239C2×C4—86no—
1240C2×C4C22×#4112yes—
1241C2×C4C22×#4112yes—
1242C2×C4C22×#4112yes—
1243C2×C4C22×#4112yes—
1244C2×C4C22×#4112yes—
1245C2×C4C22×#4116yes—
1246C2×C4C22×#4112yes—
1247C2×C4C22×#4116yes—
1248C2×C4C2×H(5,𝔽2)16yes—
1249C2×C4C2×2−1+416yes—
1250C2×C4#58512yes—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22—43no—
1271C22—43no—
1272C22C23×#4111yescharacteristic
1273C22C23×#4111yescharacteristic
1274C22C22×H(5,𝔽2)11yescharacteristic
1275C22C22×2−1+411yescharacteristic
1276C22C2×#58511yescharacteristic
1277C222−1+611yescharacteristic
1278C222−1+611yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—26no—
1286C4—22no—
1287C4—43no—
1288C4—43no—
1289C4—43no—
1290C4—43no—
1291C4—41no—
1292C4—43no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—43no—
1297C4—43no—
1298C4—43no—
1299C4—41no—
1300C4—41no—
1301C4—43no—
1302C4—43no—
1303C4—43no—
1304C4—43no—
1305C4—43no—
1306C4C2×#542112yes—
1307C2—42no—
1308C2—42no—
1309C2—83no—
1310C2C22×#54211yescharacteristic
1311C2#41211yescharacteristic
1312C2#6285011yescharacteristic
1313C2#6292211yescharacteristic
1314C2#6294911yescharacteristic
1315C2#6298411yescharacteristic
1316C2#6300111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36434C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40166C2semidirect
2. #40154C2semidirect
3. #40074C2semidirect
4. #40058C2semidirect
5. #40022C2semidirect
6. #40000C2semidirect
7. #39930C2semidirect
8. #39904C2semidirect
9. #39538C2semidirect
10. #39403C2semidirect
11. #39022C2semidirect
12. #39007C2semidirect
13. #36577C2semidirect
14. Q8×#123C2semidirect
15. #36467C2semidirect
16. #36467C2semidirect
17. #36466C2semidirect
18. #36458C2semidirect
19. #36448C2semidirect
20. #36446C2semidirect
21. #36435C2semidirect
23. #36432C2semidirect
24. #36431C2semidirect
25. #35135C2semidirect
26. #35117C2semidirect
27. #35110C2semidirect
28. C4×#557C2semidirect
29. C4×#548C2semidirect
30. #34128C2semidirect
31. C4×#542C2semidirect
676. #123#41semidirect
1153. Q8#542semidirect

Maximal subgroups

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

subgroupindex
#401662
#401542
#400742
#400582
#400222
#400002
#399302
#399042
#395382
#394032
#390222
#390072
#365772
Q8×#1232
#364672
#364662
#364582
#364482
#364462
#364352
#364342
#364322
#364312
#351352
#351172
#351102
C4×#5572
C4×#5482
#341282
C4×#5422