Finite Group Databasebeta

← #7732606

Subgroups — #7732606

Order 512.

7274 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3552C211yesmaximal, characteristic, complemented
3#51202C218yesmaximal, complemented
4#47207C218yesmaximal, complemented
5#45332C214yesmaximal, complemented
6#45241C214yesmaximal, complemented
7#39616C211yesmaximal, characteristic, complemented
8#39488C211yesmaximal, characteristic, complemented
9#39483C212yesmaximal, complemented
10#39174C211yesmaximal, characteristic, complemented
11#38956C211yesmaximal, characteristic, complemented
12#38952C212yesmaximal, complemented
13#38089C212yesmaximal, complemented
14#37862C212yesmaximal, complemented
15#37774C214yesmaximal, complemented
16#37680C214yesmaximal, complemented
17#37616C211yesmaximal, characteristic, complemented
18#37304C212yesmaximal, complemented
19#37301C212yesmaximal, complemented
20#36560C211yesmaximal, characteristic, complemented
21#36465C211yesmaximal, characteristic, complemented
22#36419C211yesmaximal, characteristic, complemented
23#36179C211yesmaximal, characteristic, complemented
24#35535C212yesmaximal, complemented
25#35532C212yesmaximal, complemented
26#35317C211yesmaximal, characteristic, complemented
27#35279C211yesmaximal, characteristic, complemented
28#34910C211yesmaximal, characteristic, complemented
29#34084C211yesmaximal, characteristic, complemented
30#3552—216no—
31C2×#563C2214yes—
32#3517—216no—
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#556C2211yescharacteristic
36C2×#554C2212yes—
37C2×#553C2214yes—
38C2×#553C2212yes—
39C2×#553C2212yes—
40C2×#550C2211yescharacteristic
41C2×#550C2212yes—
42C2×#550C2211yescharacteristic
43C2×#550C2212yes—
44C2×D4×Q8C2212yes—
45C2×D4×Q8C2211yescharacteristic
46C2×#548C2212yes—
47C2×#548C2214yes—
48C2×#547C2212yes—
49C2×#547C2211yescharacteristic
50C2×#547C2211yescharacteristic
51C2×#547C2214yes—
52C2×#544C2212yes—
53C2×#542C2212yes—
54C2×#541C2212yes—
55C2×#540C2214yes—
56C2×#540C2212yes—
57C2×#539C2214yes—
58C2×#536C2212yes—
59C2×#536C2214yes—
60C2×#532C2212yes—
61C2×#532C2211yescharacteristic
62C22×C4⋊Q8C2211yescharacteristic
63C2×#529C2211yescharacteristic
64C2×#529C2212yes—
65C2×#529C2211yescharacteristic
66C2×#520C2212yes—
67C2×C4×#41C2211yescharacteristic
68#2868C2211yescharacteristic
69#2868C2211yescharacteristic
70#2859C2212yes—
71#2858C2211yescharacteristic
72#2858C2212yes—
73#2858C2211yescharacteristic
74#2857C2214yes—
75#2856C2212yes—
76#2850C2212yes—
77#2813C2214yes—
78#2727C2218yes—
79#2721C2218yes—
80#2720C2218yes—
81#2718C2218yes—
82#2711C2218yes—
83#2705C2218yes—
84#2703C2218yes—
85#2694C2218yes—
86#2682C2218yes—
87#2681C2218yes—
88#2681C2218yes—
89#2680C2218yes—
90#2676C2218yes—
91#2674C2218yes—
92#2673C2218yes—
93#2672C2218yes—
94#2672C2218yes—
95#2672C2218yes—
96#2671C2218yes—
97#2671C2218yes—
98#2660C2212yes—
99#2658C2214yes—
100#2641C2212yes—
101#2636C2214yes—
102#2628C2214yes—
103#2620C2212yes—
104#2620C2212yes—
105#2620C2214yes—
106#2619C2212yes—
107#2619C2212yes—
108#2602C2214yes—
109#2601C2214yes—
110#2568C2211yescharacteristic
111#2568C2211yescharacteristic
112#2568C2211yescharacteristic
113#2567C2212yes—
114#2567C2212yes—
115#2566C2212yes—
116#2566C2212yes—
117#2566C2211yescharacteristic
118#2566C2212yes—
119#2565C2211yescharacteristic
120#2565C2212yes—
121#2565C2212yes—
122#2563C2212yes—
123#2559C2218yes—
124#2548C2212yes—
125#2548C2211yescharacteristic
126#2546C2214yes—
127#2545C2211yescharacteristic
128#2544C2214yes—
129#2544C2211yescharacteristic
130#2544C2212yes—
131#2542C2214yes—
132#2542C2211yescharacteristic
133#2542C2214yes—
134#2542C2211yescharacteristic
135#2542C2211yescharacteristic
136#2542C2212yes—
137#2542C2212yes—
138#2542C2212yes—
139#2541C2211yescharacteristic
140#2541C2212yes—
141#2540C2218yes—
142#2540C2214yes—
143#2506C2218yes—
144#2504C2212yes—
145#2502C2212yes—
146#2501C2218yes—
147#2501C2212yes—
148#2501C2212yes—
149#2501C2212yes—
150#2501C2214yes—
151#2501C2212yes—
152#2500C2211yescharacteristic
153#2500C2212yes—
154#2500C2212yes—
155#2499C2211yescharacteristic
156#2487C2214yes—
157#2479C2218yes—
158#2467C2218yes—
159#2464C2218yes—
160#2461C2218yes—
161#2455C2218yes—
162#2455C2218yes—
163#2455C2218yes—
164#2454C2218yes—
165#2449C2218yes—
166#2449C2218yes—
167#2449C2218yes—
168#2449C2218yes—
169#2445C2218yes—
170#2443C2218yes—
171#2441C2218yes—
172#2440C2218yes—
173#2434C2214yes—
174#2432C2214yes—
175#2432C2211yescharacteristic
176#2432C2212yes—
177#2432C2214yes—
178#2431C2214yes—
179#2431C2212yes—
180#2431C2211yescharacteristic
181#2429C2214yes—
182#2429C2214yes—
183#2427C2214yes—
184#2426C2214yes—
185#2409C2214yes—
186#2407C2214yes—
187#2392C2214yes—
188#2367C2214yes—
189#2365C2214yes—
190#2335C2214yes—
191#2334C2214yes—
192#2330C2212yes—
193#2326C2212yes—
194#2326C2212yes—
195#2326C2212yes—
196#2324C2212yes—
197#2323C2212yes—
198#2317C2212yes—
199#2317C2212yes—
200#2311C2212yes—
201#2311C2212yes—
202C4×C4⋊Q8C2212yes—
203C4×C4⋊Q8C2211yescharacteristic
204C4×#127C2212yes—
205C4×#127C2211yescharacteristic
206C4×#124C2211yescharacteristic
207C4×#124C2211yescharacteristic
208#2298C2212yes—
209#2297C2212yes—
210#2296C2212yes—
211#2295C2211yescharacteristic
212#2293C2212yes—
213#2293C2211yescharacteristic
214#2290C2212yes—
215#2290C2214yes—
216#2285C2211yescharacteristic
217C2×#384C2212yes—
218C42×Q8C2211yescharacteristic
219C42×D4C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2312yes—
227C23×Q8C2312yes—
228C23×Q8C2312yes—
229#563—232no—
230#557—28no—
231#557—28no—
232#556—28no—
233#554—216no—
234#553—232no—
235#553—216no—
236#553—216no—
237#550—216no—
238#550—28no—
239#550—28no—
240#550—216no—
241D4×Q8—216no—
242D4×Q8—28no—
243#548—216no—
244#548—416no—
245#547—216no—
246#547—28no—
247#547—28no—
248#547—416no—
249#544—216no—
250#542—216no—
251#541—216no—
252#540—232no—
253#540—216no—
254#539—232no—
255#536—216no—
256#536—416no—
257#532—216no—
258#532—28no—
259C2×C4⋊Q8—28no—
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273C2×#127C2311yescharacteristic
274C2×#127C2312yes—
275C2×#127C2314yes—
276C2×#127C2312yes—
277C2×#127C2311yescharacteristic
278C2×#127C2312yes—
279#529—216no—
280#529—28no—
281#529D4116yescomplemented
282C2×#126C2312yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2312yes—
288C2×#125C2311yescharacteristic
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2314yes—
295C2×#125C2311yescharacteristic
296C2×#124C2311yescharacteristic
297C2×#124C2314yes—
298C2×#124C2312yes—
299C2×#124C2311yescharacteristic
300C2×#124C2314yes—
301C2×#124C2312yes—
302C2×#124C2312yes—
303C2×#124C2314yes—
304C2×#124C2318yes—
305C2×#124C2311yescharacteristic
306C2×#124C2311yescharacteristic
307C2×#123C2312yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2314yes—
313C2×#123C2314yes—
314C2×#123C2314yes—
315C2×#123C2318yes—
316C2×#123C2318yes—
317C2×#123C2318yes—
318C2×#123C2318yes—
319C2×#123C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2311yescharacteristic
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2318yes—
335C2×C22⋊Q8C2318yes—
336C2×C22⋊Q8C2318yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×#121C2312yes—
339C2×#121C2312yes—
340C2×#121C2312yes—
341C2×#121C2311yescharacteristic
342C2×#121C2312yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2312yes—
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#121C2312yes—
349C2×#121C2314yes—
350C2×#121C2314yes—
351C2×#121C2314yes—
352C2×#121C2314yes—
353C2×#121C2318yes—
354C2×#121C2314yes—
355C2×#121C2318yes—
356C2×#121C2311yescharacteristic
357#520—216no—
358C4×#41—28no—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2311yescharacteristic
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2314yes—
385C2×C4×D4C2314yes—
386C2×C4×D4C2314yes—
387C2×C4×D4C2314yes—
388C2×C4×D4C2318yes—
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2312yes—
391C2×#117C2311yescharacteristic
392C2×#117C2312yes—
393C2×#117C2312yes—
394C2×#117C2312yes—
395C2×#117C2312yes—
396C2×#117C2314yes—
397C2×#117C2312yes—
398C2×#117C2312yes—
399C2×#117C2312yes—
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2314yes—
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2318yes—
406C22×C42C2312yes—
407C22×C42C2312yes—
408C22×C42C2311yescharacteristic
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#399C2314yes—
413#399C2314yes—
414#399C2314yes—
415#399C2318yes—
416#399C2318yes—
417#399C2318yes—
418#399C2318yes—
419#399C2318yes—
420#399C2318yes—
421#399C2318yes—
422#398C2314yes—
423#398C2318yes—
424#398C2318yes—
425#398C2318yes—
426#398C2318yes—
427#397C2314yes—
428#397C2318yes—
429#396C2314yes—
430#396C2318yes—
431#396C2318yes—
432#396C2318yes—
433#396C2314yes—
434#396C2318yes—
435#396C2318yes—
436#395C2318yes—
437#395C2318yes—
438#395C2318yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2318yes—
443#394C2318yes—
444#394C2318yes—
445#394C2318yes—
446#394C2318yes—
447#394C2314yes—
448#394C2318yes—
449#394C2318yes—
450#394C2318yes—
451#394C2318yes—
452#394C2318yes—
453#394C2318yes—
454#393C2318yes—
455#392C2314yes—
456#392C2318yes—
457#392C2318yes—
458#392C2314yes—
459#392C2318yes—
460#392C2318yes—
461#391C2311yescharacteristic
462#391C2311yescharacteristic
463#391C2312yes—
464#391C2312yes—
465#391C2311yescharacteristic
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2312yes—
471#391C2311yescharacteristic
472#390C2311yescharacteristic
473#390C2311yescharacteristic
474#390C2314yes—
475#390C2312yes—
476#390C2318yes—
477#390C2312yes—
478#390C2312yes—
479#390C2311yescharacteristic
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2311yescharacteristic
485#390C2312yes—
486#390C2314yes—
487#390C2312yes—
488#390C2312yes—
489#390C2318yes—
490#390C2318yes—
491#390C2314yes—
492#390C2314yes—
493#390C2314yes—
494#390C2318yes—
495#389C2314yes—
496#389C2318yes—
497#389C2318yes—
498#389C2318yes—
499#389C2318yes—
500#389C2318yes—
501#389C2312yes—
502#389C2314yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2318yes—
507#389C2318yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2318yes—
514#388C2318yes—
515#388C2314yes—
516#388C2318yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2318yes—
522#388C2318yes—
523#387C2314yes—
524#387C2318yes—
525#387C2318yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#386C2318yes—
532#386C2318yes—
533#386C2314yes—
534#386C2318yes—
535#386C2314yes—
536#386C2314yes—
537#386C2318yes—
538#386C2318yes—
539#386C2318yes—
540#386C2318yes—
541#385C2314yes—
542#385C2318yes—
543#385C2318yes—
544#385C2318yes—
545#385C2318yes—
546#385C2318yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2318yes—
551#385C2318yes—
552#385C2314yes—
553#385C2318yes—
554#385C2318yes—
555#384C2311yescharacteristic
556#384C2312yes—
557#384C2311yescharacteristic
558#384C2312yes—
559#384C2312yes—
560#384C2312yes—
561#384C2312yes—
562#384C2312yes—
563#384C2312yes—
564#384C2312yes—
565#384C2314yes—
566#384C2314yes—
567#384C2318yes—
568#382C2312yes—
569#382C2312yes—
570#382C2311yescharacteristic
571#382C2312yes—
572#382C2311yescharacteristic
573#382C2312yes—
574#380C2318yes—
575#380C2318yes—
576#380C2318yes—
577#380C2312yes—
578#380C2312yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2318yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2311yescharacteristic
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2311yescharacteristic
586C4×C4⋊C4C2311yescharacteristic
587C4×C4⋊C4C2311yescharacteristic
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2318yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2311yescharacteristic
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2311yescharacteristic
600C4×C22⋊C4C2312yes—
601#376C2312yes—
602#376C2312yes—
603C43C2312yes—
604C43C2311yescharacteristic
605C43C2311yescharacteristic
606C2×#41—28no—
607C2×#41—24no—
608C2×#41—28no—
609C2×#41—28no—
610C2×#41—28no—
611C2×#41—24no—
612C2×#41—28no—
613C2×#41—28no—
614C2×#41—44no—
615C2×#41—42no—
616C2×#41—48no—
617C2×#41—48no—
618C2×#41—48no—
619C2×#41—48no—
620C22×Q8—28no—
621C22×Q8—28no—
622C22×Q8—48no—
623C22×Q8—48no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2411yescharacteristic
629C22×Q8C2411yescharacteristic
630C22×Q8C2414yes—
631C22×Q8C2414yes—
632C22×D4C2411yescharacteristic
633C22×D4C2412yes—
634C22×D4C2411yescharacteristic
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C22×D4C2411yescharacteristic
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2418yes—
649C22×D4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2414yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2411yescharacteristic
656C23×C4C2411yescharacteristic
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C23×C4C2414yes—
663C23×C4C2414yes—
664C23×C4C2412yes—
665C23×C4C2411yescharacteristic
666C4⋊Q8—28no—
667C4⋊Q8—28no—
668C4⋊Q8—24no—
669C4⋊Q8—216no—
670C4⋊Q8—28no—
671C4⋊Q8—28no—
672C4⋊Q8—24no—
673C4⋊Q8—24no—
674C4⋊Q8—28no—
675C4⋊Q8—24no—
676C4⋊Q8—28no—
677C4⋊Q8—216no—
678C4⋊Q8—48no—
679#127—28no—
680#127—216no—
681#127—24no—
682#127—28no—
683#127—42no—
684#127—44no—
685#126—216no—
686#126—216no—
687#126—216no—
688#126—216no—
689#126—28no—
690#126C2×D4116yes—
691#125—216no—
692#125—216no—
693#125—216no—
694#125—216no—
695#125—24no—
696#125—28no—
697#125—28no—
698#125C2×D418yes—
699#124—24no—
700#124—28no—
701#124—216no—
702#124—28no—
703#124—24no—
704#124—216no—
705#124—416no—
706#124—44no—
707#124—42no—
708#124—48no—
709#124C2×D418yes—
710#123—28no—
711#123—216no—
712#123—216no—
713#123—216no—
714#123—216no—
715#123—216no—
716#123—216no—
717#123—216no—
718#123—416no—
719#123—416no—
720#123—416no—
721#123—416no—
722#123C2×D4116yes—
723C22⋊Q8—24no—
724C22⋊Q8—28no—
725C22⋊Q8—28no—
726C22⋊Q8—216no—
727C22⋊Q8—28no—
728C22⋊Q8—28no—
729C22⋊Q8—216no—
730C22⋊Q8—216no—
731C22⋊Q8—216no—
732C22⋊Q8—216no—
733C22⋊Q8—216no—
734C22⋊Q8—416no—
735C22⋊Q8—416no—
736C22⋊Q8—416no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739C22⋊Q8—48no—
740C22⋊Q8C2×D418yes—
741#121—216no—
742#121—216no—
743#121—24no—
744#121—28no—
745#121—28no—
746#121—28no—
747#121—28no—
748#121—28no—
749#121—28no—
750#121—216no—
751#121—216no—
752#121—216no—
753#121—216no—
754#121—216no—
755#121—216no—
756#121—416no—
757#121—416no—
758#121—48no—
759#121C2×D418yes—
760C4×Q8—28no—
761C4×Q8—28no—
762C4×Q8—28no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—24no—
767C4×Q8—28no—
768C4×Q8—28no—
769C4×Q8C2×D418yes—
770C4×D4—216no—
771C4×D4—28no—
772C4×D4—28no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—216no—
776C4×D4—216no—
777C4×D4—216no—
778C4×D4—216no—
779C4×D4—216no—
780C4×D4—24no—
781C4×D4—24no—
782C4×D4—28no—
783C4×D4—28no—
784C4×D4—24no—
785C4×D4—28no—
786C4×D4—28no—
787C4×D4—28no—
788C4×D4—216no—
789C4×D4—416no—
790C4×D4C2×D418yes—
791C4×D4C2×D4116yes—
792#117—24no—
793#117—28no—
794#117—216no—
795#117—28no—
796#117—28no—
797#117—28no—
798#117—44no—
799#117—44no—
800#117C2×D4116yes—
801C2×C4⋊C4—28no—
802C2×C4⋊C4—28no—
803C2×C4⋊C4—28no—
804C2×C4⋊C4—28no—
805C2×C4⋊C4—216no—
806C2×C4⋊C4—416no—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2418yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2418yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2418yes—
845C2×C4⋊C4C2418yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2418yes—
849C2×C4⋊C4C2418yes—
850C2×C4⋊C4C2418yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2418yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2418yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2418yes—
888C2×C22⋊C4C2418yes—
889C2×C22⋊C4C2418yes—
890C2×C22⋊C4C2418yes—
891C2×C22⋊C4C2418yes—
892C2×C22⋊C4C2418yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2418yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2418yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C42—28no—
905C2×C42—44no—
906C2×C42C2×D418yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2418yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2418yes—
950#95C2414yes—
951#95C2414yes—
952#95C2418yes—
953#95C2414yes—
954#95C2418yes—
955#95C2418yes—
956#95C2418yes—
957C24C2512yes—
958C24C2514yes—
959C24C2512yes—
960C24C2511yescharacteristic
961C24C2512yes—
962#41—416no—
963#41—432no—
964#41—816no—
965#41—816no—
966#41—816no—
967#41—816no—
968C2×Q8—22no—
969C2×Q8—22no—
970C2×Q8—24no—
971C2×Q8—24no—
972C2×Q8—24no—
973C2×Q8—28no—
974C2×Q8—28no—
975C2×Q8—24no—
976C2×Q8—28no—
977C2×Q8—28no—
978C2×Q8—28no—
979C2×Q8—22no—
980C2×Q8—22no—
981C2×Q8—22no—
982C2×Q8—48no—
983C2×Q8—48no—
984C2×Q8—816no—
985C2×Q8—816no—
986C2×Q8C22×D414yes—
987C2×Q82−1+414yes—
988C2×D4—24no—
989C2×D4—28no—
990C2×D4—24no—
991C2×D4—28no—
992C2×D4—28no—
993C2×D4—28no—
994C2×D4—28no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—24no—
1003C2×D4—28no—
1004C2×D4—28no—
1005C2×D4—22no—
1006C2×D4—24no—
1007C2×D4—28no—
1008C2×D4—24no—
1009C2×D4—22no—
1010C2×D4—24no—
1011C2×D4—22no—
1012C2×D4—22no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—42no—
1016C2×D4—44no—
1017C2×D4—48no—
1018C2×D4—48no—
1019C2×D4—48no—
1020C2×D4—48no—
1021C2×D4—48no—
1022C2×D4—44no—
1023C2×D4—48no—
1024C2×D4—44no—
1025C2×D4—48no—
1026C2×D4—44no—
1027C2×D4—48no—
1028C2×D4—48no—
1029C2×D4C22×D414yes—
1030C2×D4C22×D418yes—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—22no—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—28no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—24no—
1043C22×C4—28no—
1044C22×C4—28no—
1045C22×C4—28no—
1046C22×C4—28no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—28no—
1051C22×C4—28no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—48no—
1058C22×C4—48no—
1059C22×C4—48no—
1060C22×C4—48no—
1061C22×C4—48no—
1062C22×C4—48no—
1063C22×C4—44no—
1064C22×C4C22×D414yes—
1065C22×C4C22×D414yes—
1066C22×C4C22×D418yes—
1067C22×C4C22×D414yes—
1068C22×C4C2512yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—28no—
1095C4⋊C4—22no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—22no—
1106C4⋊C4—24no—
1107C4⋊C4—22no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—216no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—216no—
1128C4⋊C4—28no—
1129C4⋊C4—48no—
1130C4⋊C4—48no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—48no—
1137C4⋊C4—48no—
1138C4⋊C4—48no—
1139C4⋊C4C22×D418yes—
1140C4⋊C4C22×D418yes—
1141C4⋊C4C22×D414yes—
1142C4⋊C4C22×D418yes—
1143C4⋊C4C22×D414yes—
1144C4⋊C4C22×D418yes—
1145C22⋊C4—24no—
1146C22⋊C4—28no—
1147C22⋊C4—24no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—24no—
1154C22⋊C4—24no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—216no—
1168C22⋊C4—216no—
1169C22⋊C4—28no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—48no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—48no—
1177C22⋊C4—48no—
1178C22⋊C4—48no—
1179C22⋊C4—48no—
1180C22⋊C4—48no—
1181C22⋊C4—48no—
1182C22⋊C4—48no—
1183C22⋊C4—44no—
1184C22⋊C4C22×D418yes—
1185C22⋊C4C22×D418yes—
1186C22⋊C4C22×D418yes—
1187C22⋊C4C22×D418yes—
1188C22⋊C4C22×D418yes—
1189C42—24no—
1190C42—24no—
1191C42—24no—
1192C42—28no—
1193C42—24no—
1194C42—28no—
1195C42—28no—
1196C42—24no—
1197C42—28no—
1198C42—22no—
1199C42—22no—
1200C42—22no—
1201C42—24no—
1202C42—22no—
1203C42—24no—
1204C42—44no—
1205C42—42no—
1206C42—44no—
1207C42—42no—
1208C42C22×D414yes—
1209C42C22×D414yes—
1210C42C22×D414yes—
1211C42C22×D414yes—
1212C42C22×D418yes—
1213C42H(5,𝔽2)18yes—
1214C23—22no—
1215C23—24no—
1216C23—21no—
1217C23—22no—
1218C23—21no—
1219C23—22no—
1220C23—24no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—24no—
1225C23—28no—
1226C23—24no—
1227C23—24no—
1228C23—22no—
1229C23—24no—
1230C23—22no—
1231C23—22no—
1232C23—24no—
1233C23—22no—
1234C23—24no—
1235C23—24no—
1236C23—28no—
1237C23C23×D414yes—
1238C23C23×D412yes—
1239C23C2611yescharacteristic
1240Q8—28no—
1241Q8—28no—
1242Q8—44no—
1243Q8—48no—
1244Q8—48no—
1245Q8—48no—
1246Q8—88no—
1247Q8—88no—
1248D4—28no—
1249D4—48no—
1250D4—48no—
1251D4—416no—
1252D4—48no—
1253D4—44no—
1254D4—44no—
1255D4—48no—
1256D4—48no—
1257D4—84no—
1258D4—88no—
1259D4—88no—
1260D4—88no—
1261D4—88no—
1262D4—88no—
1263D4—88no—
1264D4—88no—
1265D4—816no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—216no—
1282C2×C4—28no—
1283C2×C4—28no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—28no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—28no—
1300C2×C4—28no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—44no—
1314C2×C4—48no—
1315C2×C4—416no—
1316C2×C4—416no—
1317C2×C4—48no—
1318C2×C4—48no—
1319C2×C4—84no—
1320C2×C4—88no—
1321C2×C4—88no—
1322C2×C4—88no—
1323C2×C4—88no—
1324C2×C4—88no—
1325C2×C4—88no—
1326C2×C4C23×D414yes—
1327C2×C4C23×D412yes—
1328C2×C4C23×D412yes—
1329C2×C4C23×D414yes—
1330C2×C4C23×D412yes—
1331C2×C4C23×D412yes—
1332C2×C4C23×D414yes—
1333C2×C4C23×D412yes—
1334C2×C4C23×D412yes—
1335C2×C4C2×H(5,𝔽2)14yes—
1336C2×C4C2×H(5,𝔽2)14yes—
1337C2×C4C2×H(5,𝔽2)14yes—
1338C2×C4C2×2−1+414yes—
1339C2×C4C2×2−1+412yes—
1340C2×C4#58512yes—
1341C22—22no—
1342C22—24no—
1343C22—22no—
1344C22—24no—
1345C22—22no—
1346C22—24no—
1347C22—44no—
1348C22—42no—
1349C22—42no—
1350C22—44no—
1351C22—42no—
1352C22—42no—
1353C22—44no—
1354C22—42no—
1355C22—44no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—48no—
1363C22—48no—
1364C22—44no—
1365C22—44no—
1366C22C24×D411yescharacteristic
1367C22C22×H(5,𝔽2)12yes—
1368C22C22×2−1+411yescharacteristic
1369C22C2×#58511yescharacteristic
1370C222−1+612yes—
1371C4—22no—
1372C4—24no—
1373C4—24no—
1374C4—22no—
1375C4—24no—
1376C4—22no—
1377C4—22no—
1378C4—24no—
1379C4—24no—
1380C4—24no—
1381C4—42no—
1382C4—42no—
1383C4—44no—
1384C4—44no—
1385C4—44no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—44no—
1391C4—44no—
1392C4—42no—
1393C4#348914yes—
1394C4#349814yes—
1395C2—42no—
1396C2—44no—
1397C2—82no—
1398C2—82no—
1399C2—84no—
1400C2C2×#349811yescharacteristic
1401C2C2×#348911yescharacteristic
1402C2#6285911yescharacteristic
1403C2#6292512yes—
1404C2#6294612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3517C2semidirect
2. C2×#3552C2semidirect
3. #51202C2semidirect
4. #47207C2semidirect
5. #45332C2semidirect
6. #45241C2semidirect
7. #39616C2semidirect
8. #39488C2semidirect
9. #39483C2semidirect
10. #39174C2semidirect
11. #38956C2semidirect
12. #38952C2semidirect
13. #38089C2semidirect
14. #37862C2semidirect
15. #37774C2semidirect
16. #37680C2semidirect
17. #37616C2semidirect
18. #37304C2semidirect
19. #37301C2semidirect
20. #36560C2semidirect
21. #36465C2semidirect
22. #36419C2semidirect
23. #36179C2semidirect
24. #35535C2semidirect
25. #35532C2semidirect
26. #35317C2semidirect
27. #35279C2semidirect
28. #34910C2semidirect
29. #34084C2semidirect
281. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#35522
#512022
#472072
#453322
#452412
#396162
#394882
#394832
#391742
#389562
#389522
#380892
#378622
#377742
#376802
#376162
#373042
#373012
#365602
#364652
#364192
#361792
#355352
#355322
#353172
#352792
#349102
#340842