Finite Group Databasebeta

← #7732562

Subgroups — #7732562

Order 512.

7168 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C2×#3554C211yesmaximal, characteristic, complemented
3#48823C218yesmaximal, complemented
4#47692C218yesmaximal, complemented
5#45332C214yesmaximal, complemented
6#45248C214yesmaximal, complemented
7#39617C212yesmaximal, complemented
8#39616C211yesmaximal, characteristic, complemented
9#39616C211yesmaximal, characteristic, complemented
10#39611C212yesmaximal, complemented
11#39174C211yesmaximal, characteristic, complemented
12#39171C211yesmaximal, characteristic, complemented
13#39168C212yesmaximal, complemented
14#39161C212yesmaximal, complemented
15#37773C214yesmaximal, complemented
16#37675C214yesmaximal, complemented
17#37615C211yesmaximal, characteristic, complemented
18#37304C212yesmaximal, complemented
19#37303C212yesmaximal, complemented
20#36560C211yesmaximal, characteristic, complemented
21Q8×#127C211yesmaximal, characteristic, complemented
22#36538C211yesmaximal, characteristic, complemented
23#36465C211yesmaximal, characteristic, complemented
24#35535C212yesmaximal, complemented
25#35534C212yesmaximal, complemented
26#35317C211yesmaximal, characteristic, complemented
27#35190C211yesmaximal, characteristic, complemented
28#34910C211yesmaximal, characteristic, complemented
29#34085C211yesmaximal, characteristic, complemented
30#3554—216no—
31C2×#562C2214yes—
32#3503—216no—
33C2×#559C2212yes—
34C2×#559C2211yescharacteristic
35C2×Q82C2212yes—
36C2×#557C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#557C2211yescharacteristic
39C2×#554C2212yes—
40C2×#554C2214yes—
41C2×#554C2212yes—
42C2×#550C2211yescharacteristic
43C2×D4×Q8C2211yescharacteristic
44C2×D4×Q8C2212yes—
45C2×D4×Q8C2211yescharacteristic
46C2×D4×Q8C2211yescharacteristic
47C2×D4×Q8C2212yes—
48C2×D4×Q8C2214yes—
49C2×#548C2212yes—
50C2×#548C2214yes—
51C2×#547C2212yes—
52C2×#544C2214yes—
53C2×#544C2212yes—
54C2×#542C2212yes—
55C2×#542C2212yes—
56C2×#540C2212yes—
57C2×#539C2214yes—
58C2×#536C2212yes—
59C2×#536C2214yes—
60C2×#533C2212yes—
61C2×#533C2211yescharacteristic
62C2×#532C2211yescharacteristic
63C22×C4⋊Q8C2212yes—
64C22×C4⋊Q8C2211yescharacteristic
65C2×#529C2211yescharacteristic
66C2×#520C2212yes—
67C2×C4×#41C2211yescharacteristic
68#2868C2212yes—
69#2868C2211yescharacteristic
70#2868C2211yescharacteristic
71#2861C2212yes—
72#2859C2212yes—
73#2858C2212yes—
74#2858C2211yescharacteristic
75#2858C2211yescharacteristic
76#2850C2214yes—
77#2821C2214yes—
78#2732C2218yes—
79#2730C2218yes—
80#2721C2218yes—
81#2720C2218yes—
82#2720C2218yes—
83#2711C2218yes—
84#2696C2218yes—
85#2694C2218yes—
86#2683C2218yes—
87#2681C2218yes—
88#2681C2218yes—
89#2680C2218yes—
90#2677C2218yes—
91#2677C2218yes—
92#2677C2218yes—
93#2674C2218yes—
94#2674C2218yes—
95#2674C2218yes—
96#2674C2218yes—
97#2672C2218yes—
98#2660C2212yes—
99#2660C2212yes—
100#2660C2212yes—
101#2658C2214yes—
102#2641C2212yes—
103#2640C2212yes—
104#2640C2212yes—
105#2635C2214yes—
106#2623C2214yes—
107#2621C2214yes—
108#2602C2214yes—
109#2601C2214yes—
110#2598C2214yes—
111#2568C2211yescharacteristic
112#2568C2211yescharacteristic
113#2568C2211yescharacteristic
114#2567C2212yes—
115#2567C2212yes—
116#2566C2212yes—
117#2566C2211yescharacteristic
118#2566C2212yes—
119#2566C2212yes—
120#2566C2212yes—
121#2565C2211yescharacteristic
122#2565C2212yes—
123#2565C2212yes—
124#2563C2212yes—
125#2558C2218yes—
126#2548C2212yes—
127#2548C2211yescharacteristic
128#2546C2214yes—
129#2545C2211yescharacteristic
130#2545C2212yes—
131#2545C2214yes—
132#2544C2212yes—
133#2544C2211yescharacteristic
134#2542C2212yes—
135#2542C2212yes—
136#2542C2211yescharacteristic
137#2542C2214yes—
138#2542C2214yes—
139#2542C2218yes—
140#2542C2212yes—
141#2542C2211yescharacteristic
142#2542C2211yescharacteristic
143#2542C2212yes—
144#2542C2212yes—
145#2541C2211yescharacteristic
146#2541C2212yes—
147#2540C2218yes—
148#2540C2214yes—
149#2506C2218yes—
150#2504C2212yes—
151#2502C2212yes—
152#2501C2212yes—
153#2501C2214yes—
154#2501C2212yes—
155#2500C2211yescharacteristic
156#2500C2212yes—
157#2499C2211yescharacteristic
158#2479C2218yes—
159#2471C2218yes—
160#2464C2218yes—
161#2463C2218yes—
162#2461C2218yes—
163#2456C2218yes—
164#2455C2218yes—
165#2452C2218yes—
166#2449C2218yes—
167#2449C2218yes—
168#2449C2218yes—
169#2448C2218yes—
170#2443C2218yes—
171#2443C2218yes—
172#2440C2218yes—
173#2436C2214yes—
174#2434C2214yes—
175#2434C2214yes—
176#2432C2214yes—
177#2432C2211yescharacteristic
178#2431C2211yescharacteristic
179#2431C2212yes—
180#2429C2214yes—
181#2429C2214yes—
182#2427C2214yes—
183#2426C2214yes—
184#2423C2218yes—
185#2409C2214yes—
186#2407C2214yes—
187#2392C2214yes—
188#2367C2214yes—
189#2365C2214yes—
190#2336C2214yes—
191#2332C2214yes—
192#2331C2212yes—
193#2328C2212yes—
194#2328C2212yes—
195#2327C2212yes—
196#2326C2212yes—
197#2326C2212yes—
198#2326C2212yes—
199#2326C2212yes—
200#2323C2212yes—
201#2323C2212yes—
202C4×C4⋊Q8C2212yes—
203C4×C4⋊Q8C2211yescharacteristic
204C4×#127C2211yescharacteristic
205C4×#127C2212yes—
206C4×#127C2212yes—
207C4×#124C2211yescharacteristic
208C4×#124C2211yescharacteristic
209C4×#124C2212yes—
210#2298C2212yes—
211#2298C2212yes—
212#2295C2212yes—
213#2295C2211yescharacteristic
214#2295C2211yescharacteristic
215#2295C2212yes—
216#2290C2214yes—
217#2283C2211yescharacteristic
218C42×Q8C2211yescharacteristic
219C42×Q8C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C22×#41C2312yes—
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226C23×Q8C2312yes—
227C23×Q8C2312yes—
228#562—232no—
229#559—216no—
230#559—28no—
231Q82—216no—
232#557—28no—
233#557—28no—
234#557—28no—
235#554—232no—
236#554—216no—
237#554—216no—
238#550—28no—
239D4×Q8—216no—
240D4×Q8—216no—
241D4×Q8—28no—
242D4×Q8—28no—
243D4×Q8—28no—
244D4×Q8—416no—
245#548—216no—
246#548—416no—
247#547—216no—
248#544—232no—
249#544—216no—
250#542—216no—
251#542—216no—
252#540—216no—
253#539—232no—
254#536—216no—
255#536—416no—
256#533—216no—
257#533D4116yescomplemented
258#532—28no—
259C2×C4⋊Q8—216no—
260C2×C4⋊Q8—28no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2318yes—
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2311yescharacteristic
283C2×#127C2311yescharacteristic
284C2×#127C2312yes—
285C2×#127C2311yescharacteristic
286C2×#127C2312yes—
287#529—28no—
288C2×#126C2312yes—
289C2×#126C2314yes—
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2311yescharacteristic
293C2×#125C2312yes—
294C2×#125C2314yes—
295C2×#125C2314yes—
296C2×#125C2314yes—
297C2×#125C2314yes—
298C2×#125C2312yes—
299C2×#124C2312yes—
300C2×#124C2311yescharacteristic
301C2×#124C2311yescharacteristic
302C2×#124C2312yes—
303C2×#124C2314yes—
304C2×#124C2312yes—
305C2×#124C2311yescharacteristic
306C2×#124C2314yes—
307C2×#124C2312yes—
308C2×#124C2314yes—
309C2×#124C2314yes—
310C2×#124C2318yes—
311C2×#123C2312yes—
312C2×#123C2314yes—
313C2×#123C2314yes—
314C2×#123C2314yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2318yes—
319C2×#123C2318yes—
320C2×C22⋊Q8C2311yescharacteristic
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2318yes—
340C2×C22⋊Q8C2318yes—
341C2×C22⋊Q8C2318yes—
342C2×C22⋊Q8C2318yes—
343C2×C22⋊Q8C2318yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2312yes—
347C2×#121C2312yes—
348C2×#121C2311yescharacteristic
349C2×#121C2314yes—
350C2×#121C2312yes—
351C2×#121C2314yes—
352C2×#121C2312yes—
353C2×#121C2314yes—
354C2×#121C2314yes—
355C2×#121C2318yes—
356#520—216no—
357C4×#41—28no—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2311yescharacteristic
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2314yes—
370C2×C4×Q8C2311yescharacteristic
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2312yes—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2314yes—
389C2×C4×D4C2314yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2318yes—
392C2×C4×D4C2318yes—
393C2×#117C2312yes—
394C2×#117C2312yes—
395C2×#117C2312yes—
396C2×#117C2311yescharacteristic
397C2×#117C2314yes—
398C2×#117C2312yes—
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2314yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2314yes—
403C22×C4⋊C4C2314yes—
404C22×C42C2312yes—
405C22×C42C2311yescharacteristic
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#399C2314yes—
410#399C2314yes—
411#399C2314yes—
412#399C2318yes—
413#399C2318yes—
414#399C2318yes—
415#399C2318yes—
416#399C2318yes—
417#399C2318yes—
418#399C2318yes—
419#398C2314yes—
420#398C2318yes—
421#398C2318yes—
422#398C2318yes—
423#398C2318yes—
424#398C2318yes—
425#398C2318yes—
426#397C2318yes—
427#397C2314yes—
428#397C2318yes—
429#397C2318yes—
430#396C2314yes—
431#396C2318yes—
432#396C2318yes—
433#396C2318yes—
434#396C2318yes—
435#396C2314yes—
436#396C2318yes—
437#395C2318yes—
438#395C2318yes—
439#395C2318yes—
440#395C2318yes—
441#395C2318yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2318yes—
447#394C2318yes—
448#394C2318yes—
449#394C2318yes—
450#394C2318yes—
451#393C2318yes—
452#393C2318yes—
453#393C2318yes—
454#392C2314yes—
455#392C2314yes—
456#392C2318yes—
457#392C2318yes—
458#391C2311yescharacteristic
459#391C2311yescharacteristic
460#391C2312yes—
461#391C2312yes—
462#391C2311yescharacteristic
463#391C2311yescharacteristic
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#390C2311yescharacteristic
473#390C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2311yescharacteristic
477#390C2312yes—
478#390C2318yes—
479#390C2318yes—
480#390C2312yes—
481#390C2312yes—
482#390C2311yescharacteristic
483#390C2312yes—
484#390C2311yescharacteristic
485#390C2312yes—
486#390C2312yes—
487#390C2314yes—
488#390C2312yes—
489#390C2318yes—
490#390C2314yes—
491#390C2314yes—
492#390C2318yes—
493#389C2314yes—
494#389C2318yes—
495#389C2318yes—
496#389C2318yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2318yes—
502#389C2318yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2318yes—
508#388C2318yes—
509#388C2318yes—
510#388C2318yes—
511#388C2318yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2318yes—
517#388C2318yes—
518#388C2318yes—
519#388C2318yes—
520#387C2314yes—
521#387C2318yes—
522#387C2318yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#386C2318yes—
535#386C2318yes—
536#386C2318yes—
537#386C2318yes—
538#386C2318yes—
539#386C2314yes—
540#386C2314yes—
541#386C2318yes—
542#386C2318yes—
543#385C2314yes—
544#385C2318yes—
545#385C2318yes—
546#385C2318yes—
547#385C2318yes—
548#385C2318yes—
549#385C2318yes—
550#385C2318yes—
551#385C2318yes—
552#385C2314yes—
553#385C2318yes—
554#384C2312yes—
555#384C2311yescharacteristic
556#384C2312yes—
557#384C2311yescharacteristic
558#384C2312yes—
559#384C2312yes—
560#384C2312yes—
561#384C2312yes—
562#384C2312yes—
563#384C2318yes—
564#384C2314yes—
565#384C2314yes—
566#383C2312yes—
567#382C2311yescharacteristic
568#382C2312yes—
569#382C2312yes—
570#382C2311yescharacteristic
571#382C2312yes—
572#382C2312yes—
573#381C2312yes—
574#380C2318yes—
575#380C2312yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2318yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2311yescharacteristic
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2311yescharacteristic
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2311yescharacteristic
585C4×C4⋊C4C2311yescharacteristic
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2312yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2318yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2311yescharacteristic
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2311yescharacteristic
598#376C2312yes—
599#376C2312yes—
600#376C2312yes—
601#376C2312yes—
602C43C2312yes—
603C43C2311yescharacteristic
604C43C2312yes—
605C43C2311yescharacteristic
606C2×#41—28no—
607C2×#41—24no—
608C2×#41—24no—
609C2×#41—24no—
610C2×#41—28no—
611C2×#41—48no—
612C2×#41—48no—
613C22×Q8—28no—
614C22×Q8—28no—
615C22×Q8—28no—
616C22×Q8—28no—
617C22×Q8—48no—
618C22×Q8—48no—
619C22×Q8—48no—
620C22×Q8—48no—
621C22×Q8C2411yescharacteristic
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C22×Q8C2411yescharacteristic
626C22×Q8C2411yescharacteristic
627C22×Q8C2411yescharacteristic
628C22×Q8C2414yes—
629C22×Q8C2414yes—
630C22×Q8C2414yes—
631C22×Q8C2414yes—
632C22×Q8C2412yes—
633C22×D4C2412yes—
634C22×D4C2411yescharacteristic
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C22×D4C2411yescharacteristic
639C22×D4C2412yes—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2418yes—
643C22×D4C2414yes—
644C22×D4C2414yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2412yes—
648C23×C4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2414yes—
651C23×C4C2414yes—
652C23×C4C2414yes—
653C23×C4C2412yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2411yescharacteristic
659C4⋊Q8—28no—
660C4⋊Q8—28no—
661C4⋊Q8—28no—
662C4⋊Q8—24no—
663C4⋊Q8—216no—
664C4⋊Q8—216no—
665C4⋊Q8—216no—
666C4⋊Q8—216no—
667C4⋊Q8—28no—
668C4⋊Q8—28no—
669C4⋊Q8—24no—
670C4⋊Q8—24no—
671C4⋊Q8—28no—
672C4⋊Q8—24no—
673C4⋊Q8—28no—
674C4⋊Q8—28no—
675C4⋊Q8—28no—
676C4⋊Q8—216no—
677C4⋊Q8—416no—
678C4⋊Q8—48no—
679C4⋊Q8C2×D418yes—
680C4⋊Q8C2×D418yes—
681#127—24no—
682#127—28no—
683#127—24no—
684#127—28no—
685#126—216no—
686#126—28no—
687#125—216no—
688#125—216no—
689#125—216no—
690#125—216no—
691#125—24no—
692#125—28no—
693#125—28no—
694#125—28no—
695#125C2×D4116yes—
696#124—28no—
697#124—216no—
698#124—28no—
699#124—24no—
700#124—24no—
701#124—216no—
702#124—24no—
703#124—28no—
704#124—28no—
705#124—216no—
706#124—416no—
707#124—48no—
708#123—28no—
709#123—216no—
710#123—216no—
711#123—216no—
712#123—216no—
713#123—216no—
714#123—216no—
715#123—416no—
716#123—416no—
717C22⋊Q8—216no—
718C22⋊Q8—216no—
719C22⋊Q8—24no—
720C22⋊Q8—28no—
721C22⋊Q8—28no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—216no—
726C22⋊Q8—28no—
727C22⋊Q8—216no—
728C22⋊Q8—216no—
729C22⋊Q8—216no—
730C22⋊Q8—216no—
731C22⋊Q8—216no—
732C22⋊Q8—216no—
733C22⋊Q8—416no—
734C22⋊Q8—416no—
735C22⋊Q8—416no—
736C22⋊Q8—416no—
737C22⋊Q8—416no—
738C22⋊Q8—48no—
739C22⋊Q8—48no—
740C22⋊Q8—48no—
741C22⋊Q8C2×D418yes—
742C22⋊Q8C2×D418yes—
743C22⋊Q8C2×D4116yes—
744#121—24no—
745#121—28no—
746#121—28no—
747#121—216no—
748#121—28no—
749#121—216no—
750#121—216no—
751#121—416no—
752#121—48no—
753C4×Q8—216no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—28no—
757C4×Q8—24no—
758C4×Q8—24no—
759C4×Q8—28no—
760C4×Q8—28no—
761C4×Q8—24no—
762C4×Q8—28no—
763C4×Q8—28no—
764C4×Q8—28no—
765C4×Q8C2×D418yes—
766C4×Q8C2×D418yes—
767C4×Q8C2×D4116yes—
768C4×D4—28no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—216no—
772C4×D4—28no—
773C4×D4—216no—
774C4×D4—216no—
775C4×D4—24no—
776C4×D4—24no—
777C4×D4—28no—
778C4×D4—28no—
779C4×D4—24no—
780C4×D4—28no—
781C4×D4—28no—
782C4×D4—28no—
783C4×D4—28no—
784C4×D4—28no—
785C4×D4—216no—
786C4×D4—416no—
787C4×D4—416no—
788#117—24no—
789#117—216no—
790#117—28no—
791#117—28no—
792#117—28no—
793#117C2×D4116yes—
794C2×C4⋊C4—28no—
795C2×C4⋊C4—28no—
796C2×C4⋊C4—216no—
797C2×C4⋊C4—216no—
798C2×C4⋊C4—216no—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2418yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2418yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2418yes—
840C2×C4⋊C4C2418yes—
841C2×C4⋊C4C2418yes—
842C2×C4⋊C4C2418yes—
843C2×C4⋊C4C2418yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2418yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2418yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2418yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2418yes—
883C2×C22⋊C4C2418yes—
884C2×C22⋊C4C2418yes—
885C2×C22⋊C4C2418yes—
886C2×C22⋊C4C2418yes—
887C2×C22⋊C4C2418yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2418yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C42—28no—
895C2×C42C2×D418yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2418yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2418yes—
947#95C2418yes—
948#95C2414yes—
949#95C2418yes—
950#95C2418yes—
951#95C2418yes—
952C24C2514yes—
953C24C2512yes—
954C24C2511yescharacteristic
955C24C2512yes—
956#41—232no—
957#41—816no—
958#41—816no—
959C2×Q8—22no—
960C2×Q8—22no—
961C2×Q8—24no—
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—28no—
965C2×Q8—28no—
966C2×Q8—28no—
967C2×Q8—28no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—28no—
971C2×Q8—28no—
972C2×Q8—28no—
973C2×Q8—22no—
974C2×Q8—22no—
975C2×Q8—22no—
976C2×Q8—44no—
977C2×Q8—48no—
978C2×Q8—48no—
979C2×Q8—48no—
980C2×Q8—48no—
981C2×Q8—816no—
982C2×Q8—816no—
983C2×Q8—816no—
984C2×Q8—816no—
985C2×Q8C22×D414yes—
986C2×Q8C22×D414yes—
987C2×Q8C22×D418yes—
988C2×Q82−1+414yes—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—28no—
992C2×D4—24no—
993C2×D4—28no—
994C2×D4—216no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—28no—
1003C2×D4—28no—
1004C2×D4—24no—
1005C2×D4—22no—
1006C2×D4—22no—
1007C2×D4—24no—
1008C2×D4—22no—
1009C2×D4—24no—
1010C2×D4—44no—
1011C2×D4—48no—
1012C2×D4—48no—
1013C2×D4—48no—
1014C2×D4—44no—
1015C2×D4—48no—
1016C2×D4—48no—
1017C2×D4—44no—
1018C2×D42−1+414yes—
1019C22×C4—24no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—28no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—28no—
1036C22×C4—28no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4—48no—
1040C22×C4—48no—
1041C22×C4—48no—
1042C22×C4—48no—
1043C22×C4—48no—
1044C22×C4—48no—
1045C22×C4—48no—
1046C22×C4C22×D414yes—
1047C22×C4C22×D414yes—
1048C22×C4C22×D414yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—216no—
1108C4⋊C4—28no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—216no—
1113C4⋊C4—28no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—48no—
1118C4⋊C4—48no—
1119C4⋊C4—48no—
1120C4⋊C4—48no—
1121C4⋊C4—48no—
1122C4⋊C4C22×D418yes—
1123C4⋊C4C22×D418yes—
1124C4⋊C4C22×D418yes—
1125C4⋊C4C22×D418yes—
1126C4⋊C4C22×D414yes—
1127C4⋊C4C22×D418yes—
1128C4⋊C4C22×D414yes—
1129C4⋊C4C22×D418yes—
1130C4⋊C4C22×D418yes—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—28no—
1134C22⋊C4—24no—
1135C22⋊C4—24no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—216no—
1154C22⋊C4—216no—
1155C22⋊C4—216no—
1156C22⋊C4—28no—
1157C22⋊C4—44no—
1158C22⋊C4—48no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—48no—
1162C22⋊C4—48no—
1163C22⋊C4—48no—
1164C22⋊C4—48no—
1165C22⋊C4—48no—
1166C22⋊C4—48no—
1167C22⋊C4C22×D418yes—
1168C22⋊C4C22×D418yes—
1169C42—24no—
1170C42—24no—
1171C42—24no—
1172C42—24no—
1173C42—28no—
1174C42—28no—
1175C42—28no—
1176C42—24no—
1177C42—28no—
1178C42—28no—
1179C42—24no—
1180C42—22no—
1181C42—22no—
1182C42—22no—
1183C42—24no—
1184C42—22no—
1185C42—42no—
1186C42—44no—
1187C42—44no—
1188C42—42no—
1189C42C22×D414yes—
1190C42C22×D414yes—
1191C42C22×D414yes—
1192C42C22×D414yes—
1193C42C22×D418yes—
1194C42C22×D418yes—
1195C42H(5,𝔽2)18yes—
1196C23—22no—
1197C23—22no—
1198C23—24no—
1199C23—21no—
1200C23—21no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—22no—
1205C23—24no—
1206C23—28no—
1207C23—24no—
1208C23—24no—
1209C23—22no—
1210C23—22no—
1211C23—24no—
1212C23—28no—
1213C23—24no—
1214C23C23×D412yes—
1215C23C2×2−1+414yes—
1216C23C2611yescharacteristic
1217Q8—28no—
1218Q8—28no—
1219Q8—28no—
1220Q8—48no—
1221Q8—44no—
1222Q8—48no—
1223Q8—48no—
1224Q8—48no—
1225Q8—88no—
1226Q8—88no—
1227Q8—88no—
1228Q8—88no—
1229D4—216no—
1230D4—28no—
1231D4—416no—
1232D4—44no—
1233D4—48no—
1234D4—48no—
1235D4—84no—
1236D4—88no—
1237D4—88no—
1238D4—84no—
1239D4—816no—
1240D4—88no—
1241C2×C4—216no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—28no—
1258C2×C4—28no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—28no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—28no—
1275C2×C4—28no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—44no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—48no—
1292C2×C4—88no—
1293C2×C4—88no—
1294C2×C4—88no—
1295C2×C4—88no—
1296C2×C4—88no—
1297C2×C4—88no—
1298C2×C4—88no—
1299C2×C4C23×D414yes—
1300C2×C4C23×D412yes—
1301C2×C4C23×D412yes—
1302C2×C4C23×D414yes—
1303C2×C4C23×D412yes—
1304C2×C4C23×D412yes—
1305C2×C4C23×D414yes—
1306C2×C4C23×D414yes—
1307C2×C4C23×D412yes—
1308C2×C4C23×D412yes—
1309C2×C4C2×H(5,𝔽2)14yes—
1310C2×C4C2×H(5,𝔽2)14yes—
1311C2×C4C2×H(5,𝔽2)14yes—
1312C2×C4C2×2−1+414yes—
1313C2×C4C2×2−1+412yes—
1314C2×C4C2×2−1+412yes—
1315C22—22no—
1316C22—24no—
1317C22—22no—
1318C22—22no—
1319C22—28no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—44no—
1325C22—42no—
1326C22—44no—
1327C22—42no—
1328C22—44no—
1329C22—44no—
1330C22—42no—
1331C22—44no—
1332C22—48no—
1333C22—48no—
1334C22—44no—
1335C22C24×D411yescharacteristic
1336C22C22×H(5,𝔽2)12yes—
1337C22C22×2−1+411yescharacteristic
1338C22C22×2−1+411yescharacteristic
1339C222−1+612yes—
1340C4—22no—
1341C4—24no—
1342C4—22no—
1343C4—24no—
1344C4—24no—
1345C4—22no—
1346C4—22no—
1347C4—24no—
1348C4—24no—
1349C4—24no—
1350C4—24no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—44no—
1355C4—44no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—42no—
1362C4—44no—
1363C4#348614yes—
1364C4#349814yes—
1365C2—42no—
1366C2—44no—
1367C2—82no—
1368C2—84no—
1369C2C2×#348611yescharacteristic
1370C2C2×#349811yescharacteristic
1371C2#6285911yescharacteristic
1372C2#6294212yes—
1373C2#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×#3503C2semidirect
2. C2×#3554C2semidirect
3. #48823C2semidirect
4. #47692C2semidirect
5. #45332C2semidirect
6. #45248C2semidirect
7. #39617C2semidirect
8. #39616C2semidirect
9. #39616C2semidirect
10. #39611C2semidirect
11. #39174C2semidirect
12. #39171C2semidirect
13. #39168C2semidirect
14. #39161C2semidirect
15. #37773C2semidirect
16. #37675C2semidirect
17. #37615C2semidirect
18. #37304C2semidirect
19. #37303C2semidirect
20. #36560C2semidirect
21. Q8×#127C2semidirect
22. #36538C2semidirect
23. #36465C2semidirect
24. #35535C2semidirect
25. #35534C2semidirect
26. #35317C2semidirect
27. #35190C2semidirect
28. #34910C2semidirect
29. #34085C2semidirect
257. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C2×#35542
#488232
#476922
#453322
#452482
#396172
#396162
#396112
#391742
#391712
#391682
#391612
#377732
#376752
#376152
#373042
#373032
#365602
Q8×#1272
#365382
#364652
#355352
#355342
#353172
#351902
#349102
#340852