Finite Group Databasebeta

← #7679272

Subgroups — #7679272

Order 512.

6660 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic
2C22×#557C211yesmaximal, characteristic, complemented
3#59833C214yesmaximal, complemented
4#59667C214yesmaximal, complemented
5#59154C214yesmaximal, complemented
6#59152C214yesmaximal, complemented
7#45424C214yesmaximal, complemented
8#45277C214yesmaximal, complemented
9#45274C214yesmaximal, complemented
10#45272C214yesmaximal, complemented
11#39592C214yesmaximal, complemented
12#39589C214yesmaximal, complemented
13#39589C214yesmaximal, complemented
14#36547C214yesmaximal, complemented
15#35640C211yesmaximal, characteristic, complemented
16#35639C211yesmaximal, characteristic
17#35576C211yesmaximal, characteristic, complemented
18#35574C211yesmaximal, characteristic
19#35179C211yesmaximal, characteristic, complemented
20#35154C211yesmaximal, characteristic, complemented
21#35154C211yesmaximal, characteristic, complemented
22#34953C211yesmaximal, characteristic, complemented
23#34952C211yesmaximal, characteristic
24#34266C211yesmaximal, characteristic
25#34266C211yesmaximal, characteristic
26#34217C211yesmaximal, characteristic, complemented
27C4×#536C211yesmaximal, characteristic
28#3504—216no—
29C2×#557—216no—
30C2×#557C2214yes—
31C2×#557C2212yes—
32C2×#557C2214yes—
33C2×#557C2212yes—
34C2×#557C2214yes—
35C2×#557C2214yes—
36C2×#554C2212yes—
37C2×#554C2214yes—
38C2×#554C2214yes—
39C2×#554C2212yes—
40C2×#544C2211yescharacteristic
41C2×#544C2211yescharacteristic
42C2×#544C2212yes—
43C2×#544C2212yes—
44C2×#536C2211yescharacteristic
45C2×#533C2212yes—
46C2×#533C2211yescharacteristic
47C22×C4⋊Q8C2212yes—
48C22×C4⋊Q8C2211yescharacteristic
49C22×#125C2212yes—
50C22×#125C2211yescharacteristic
51C22×#125C2212yes—
52C22×#125C2212yes—
53C22×#125C2211yescharacteristic
54C2×#520C2211yescharacteristic
55C2×#520C2211yescharacteristic
56C2×C4×#41C2211yescharacteristic
57C22×C4×Q8C2211yescharacteristic
58C22×C4×Q8C2211yescharacteristic
59C22×C4×Q8C2211yescharacteristic
60C22×C4×Q8C2211yescharacteristic
61C22×C4×Q8C2212yes—
62#2855C2214yes—
63#2855C2214yes—
64#2855C2214yes—
65#2726C2218yes—
66#2726C2218yes—
67#2720C2218yes—
68#2720C2218yes—
69#2713C2218yes—
70#2713C2218yes—
71#2713C2218yes—
72#2713C2218yes—
73#2704C2218yes—
74#2704C2218yes—
75#2677C2218yes—
76#2677C2218yes—
77#2627C2214yes—
78#2627C2214yes—
79#2627C2214yes—
80#2584C2212yes—
81#2584C2212yes—
82#2583C2214yes—
83#2583C2212yes—
84#2583C2212yes—
85#2583C2214yes—
86#2582C2214yes—
87#2582C2212yes—
88#2581C2212yes—
89#2581C2214yes—
90#2580C2212yes—
91#2579C2214yes—
92#2579C2212yes—
93#2579C2212yes—
94#2579C2214yes—
95#2568C2212yes—
96#2567C2212yes—
97#2567C2212yes—
98#2565C2212yes—
99#2565C2212yes—
100#2556C2218yes—
101#2556C2218yes—
102#2552C2214yes—
103#2552C2214yes—
104#2551C2214yes—
105#2551C2214yes—
106#2551C2218yes—
107#2550C2214yes—
108#2550C2214yes—
109#2550C2214yes—
110#2550C2214yes—
111#2546C2212yes—
112#2538C2212yes—
113#2506C2218yes—
114#2506C2218yes—
115#2502C2214yes—
116#2502C2212yes—
117#2492C2218yes—
118#2487C2214yes—
119#2487C2212yes—
120#2473C2218yes—
121#2473C2218yes—
122#2465C2218yes—
123#2465C2218yes—
124#2462C2218yes—
125#2462C2218yes—
126#2462C2218yes—
127#2462C2218yes—
128#2454C2214yes—
129#2453C2214yes—
130#2453C2214yes—
131#2453C2214yes—
132#2453C2214yes—
133#2453C2214yes—
134#2452C2214yes—
135#2451C2214yes—
136#2451C2214yes—
137#2451C2218yes—
138#2451C2214yes—
139#2451C2214yes—
140#2451C2214yes—
141#2451C2218yes—
142#2442C2214yes—
143#2441C2214yes—
144#2440C2218yes—
145#2440C2214yes—
146#2439C2214yes—
147#2434C2212yes—
148#2434C2214yes—
149#2429C2218yes—
150#2409C2212yes—
151#2409C2214yes—
152#2399C2214yes—
153#2396C2214yes—
154#2370C2214yes—
155#2370C2214yes—
156#2367C2214yes—
157#2367C2214yes—
158#2365C2218yes—
159#2365C2214yes—
160#2365C2214yes—
161#2362C2214yes—
162#2362C2214yes—
163#2360C2218yes—
164#2360C2214yes—
165#2360C2214yes—
166#2345C2214yes—
167#2345C2214yes—
168#2330C2214yes—
169#2327C2212yes—
170#2326C2212yes—
171#2323C2214yes—
172#2322C2214yes—
173#2322C2214yes—
174#2322C2214yes—
175#2317C2211yescharacteristic
176#2317C2211yescharacteristic
177#2317C2211yescharacteristic
178#2316C2211yescharacteristic
179#2316C2211yescharacteristic
180#2311C2211yescharacteristic
181#2310C2211yescharacteristic
182#2310C2211yescharacteristic
183#2310C2211yescharacteristic
184C4×C4⋊Q8C2212yes—
185C4×C4⋊Q8C2214yes—
186C4×#125C2214yes—
187C4×#124C2212yes—
188C4×C22⋊Q8C2214yes—
189C4×C22⋊Q8C2214yes—
190C4×#123C2214yes—
191C4×#123C2214yes—
192C4×#123C2214yes—
193#2297C2211yescharacteristic
194#2297C2211yescharacteristic
195#2296C2211yescharacteristic
196#2296C2211yescharacteristic
197#2296C2211yescharacteristic
198#2296C2211yescharacteristic
199#2296C2211yescharacteristic
200#2296C2211yescharacteristic
201#2285C2211yescharacteristic
202#2274C2211yescharacteristic
203#2274C2211yescharacteristic
204C4×#117C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C23×Q8C2311yescharacteristic
207C23×Q8C2311yescharacteristic
208C23×Q8C2312yes—
209#557—232no—
210#557—232no—
211#557—232no—
212#557—232no—
213#557—216no—
214#557—216no—
215#554—216no—
216#554—216no—
217#554—232no—
218#554—232no—
219#544—216no—
220#544—216no—
221#544—28no—
222#544—28no—
223#536Q8116yescomplemented
224#533—216no—
225#533—28no—
226C2×C4⋊Q8—216no—
227C2×C4⋊Q8—28no—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2318yes—
231C2×C4⋊Q8C2318yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2318yes—
242C2×C4⋊Q8C2312yes—
243C2×#125—216no—
244C2×#125—216no—
245C2×#125—28no—
246C2×#125—216no—
247C2×#125D4116yes—
248C2×#125C2311yescharacteristic
249C2×#125C2311yescharacteristic
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2314yes—
253C2×#125C2318yes—
254C2×#125C2318yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2318yes—
259C2×#125C2318yes—
260C2×#125C2312yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#124C2312yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2318yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283#520—28no—
284#520—28no—
285C4×#41—28no—
286C2×C4×Q8—28no—
287C2×C4×Q8—216no—
288C2×C4×Q8—28no—
289C2×C4×Q8—28no—
290C2×C4×Q8—28no—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2318yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2314yes—
311C2×C4×Q8C2318yes—
312C2×C4×Q8C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×#117C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2311yescharacteristic
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2312yes—
328C2×#117C2312yes—
329C2×#117C2312yes—
330C2×#117C2311yescharacteristic
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2312yes—
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2314yes—
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2314yes—
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2311yescharacteristic
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2312yes—
349C22×C42C2312yes—
350C22×C42C2312yes—
351C22×C42C2312yes—
352C22×C42C2311yescharacteristic
353C22×C42C2311yescharacteristic
354C22×C42C2312yes—
355C22×C42C2311yescharacteristic
356#400C2318yes—
357#400C2314yes—
358#400C2318yes—
359#400C2318yes—
360#400C2318yes—
361#399C2314yes—
362#399C2318yes—
363#398C2318yes—
364#398C2318yes—
365#398C2314yes—
366#398C2314yes—
367#398C2318yes—
368#398C2318yes—
369#398C2314yes—
370#398C2314yes—
371#398C2318yes—
372#398C2318yes—
373#398C2314yes—
374#398C2314yes—
375#398C2318yes—
376#398C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2318yes—
381#396C2314yes—
382#396C2314yes—
383#396C2318yes—
384#396C2318yes—
385#395C2318yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2318yes—
390#395C2318yes—
391#395C2314yes—
392#395C2314yes—
393#395C2318yes—
394#395C2318yes—
395#395C2318yes—
396#395C2318yes—
397#395C2318yes—
398#393C2314yes—
399#393C2318yes—
400#391C2312yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2318yes—
413#391C2312yes—
414#391C2312yes—
415#391C2314yes—
416#391C2318yes—
417#391C2318yes—
418#391C2318yes—
419#391C2318yes—
420#391C2318yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#389C2314yes—
425#389C2314yes—
426#389C2318yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2318yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2318yes—
442#389C2318yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2318yes—
449#389C2318yes—
450#389C2318yes—
451#389C2318yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2318yes—
457#389C2318yes—
458#389C2318yes—
459#389C2318yes—
460#389C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#387C2318yes—
468#387C2318yes—
469#387C2318yes—
470#387C2318yes—
471#387C2318yes—
472#387C2318yes—
473#387C2318yes—
474#387C2318yes—
475#387C2314yes—
476#387C2314yes—
477#387C2318yes—
478#387C2318yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#386C2314yes—
488#386C2312yes—
489#386C2312yes—
490#386C2312yes—
491#386C2312yes—
492#385C2314yes—
493#385C2314yes—
494#385C2314yes—
495#385C2312yes—
496#385C2312yes—
497#385C2318yes—
498#385C2318yes—
499#385C2318yes—
500#385C2312yes—
501#385C2312yes—
502#385C2314yes—
503#385C2314yes—
504#385C2312yes—
505#385C2312yes—
506#385C2312yes—
507#385C2318yes—
508#385C2312yes—
509#385C2318yes—
510#385C2312yes—
511#385C2312yes—
512#385C2312yes—
513#385C2312yes—
514#384C2314yes—
515#384C2312yes—
516#384C2312yes—
517#384C2312yes—
518#384C2312yes—
519#384C2318yes—
520#382C2312yes—
521#382C2312yes—
522#382C2312yes—
523#382C2312yes—
524#381C2314yes—
525#381C2314yes—
526#381C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2312yes—
531#380C2312yes—
532#380C2318yes—
533#380C2314yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2318yes—
537C4×C4⋊C4C2318yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2318yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2312yes—
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2314yes—
549C4×C4⋊C4C2318yes—
550C4×C4⋊C4C2318yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C22⋊C4C2312yes—
554C4×C22⋊C4C2314yes—
555C4×C22⋊C4C2314yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2318yes—
558C4×C22⋊C4C2318yes—
559C4×C22⋊C4C2314yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2318yes—
562#376C2312yes—
563C43C2312yes—
564C2×#41—24no—
565C2×#41—24no—
566C2×#41C2×Q818yes—
567C22×Q8—24no—
568C22×Q8—28no—
569C22×Q8—24no—
570C22×Q8—24no—
571C22×Q8—44no—
572C22×Q8—48no—
573C22×Q8C2×Q818yes—
574C22×Q8C2412yes—
575C22×Q8C2418yes—
576C22×Q8C2412yes—
577C22×Q8C2412yes—
578C22×Q8C2412yes—
579C22×Q8C2411yescharacteristic
580C22×Q8C2414yes—
581C22×Q8C2412yes—
582C22×Q8C2414yes—
583C22×Q8C2412yes—
584C22×D4C2412yes—
585C22×D4C2411yescharacteristic
586C23×C4C2411yescharacteristic
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2411yescharacteristic
590C23×C4C2412yes—
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2414yes—
594C23×C4C2414yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2411yescharacteristic
600C23×C4C2411yescharacteristic
601C23×C4C2411yescharacteristic
602C4⋊Q8—232no—
603C4⋊Q8—232no—
604C4⋊Q8—216no—
605C4⋊Q8—216no—
606C4⋊Q8—28no—
607C4⋊Q8—28no—
608C4⋊Q8—216no—
609C4⋊Q8—216no—
610C4⋊Q8—28no—
611C4⋊Q8—28no—
612C4⋊Q8—24no—
613C4⋊Q8—24no—
614C4⋊Q8—48no—
615C4⋊Q8—416no—
616C4⋊Q8C2×Q8116yescomplemented
617#125—28no—
618#125—28no—
619#125—216no—
620#125—216no—
621#125—232no—
622#125—232no—
623#125—216no—
624#125—232no—
625#125—216no—
626#125—232no—
627#125—216no—
628#125—216no—
629#125—28no—
630#125—28no—
631#125—24no—
632#125—24no—
633#125C2×D4116yes—
634#125C2×D4116yes—
635#125C2×D4116yes—
636#125C2×D4116yes—
637#124C2×Q8116yescomplemented
638#123C2×Q8132yes—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—216no—
642C22⋊Q8—216no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—216no—
647C22⋊Q8—216no—
648C22⋊Q8—216no—
649C22⋊Q8—416no—
650C22⋊Q8—48no—
651C22⋊Q8C2×Q8132yescomplemented
652C4×Q8—216no—
653C4×Q8—216no—
654C4×Q8—232no—
655C4×Q8—232no—
656C4×Q8—216no—
657C4×Q8—216no—
658C4×Q8—28no—
659C4×Q8—28no—
660C4×Q8—216no—
661C4×Q8—216no—
662C4×Q8—28no—
663C4×Q8—28no—
664C4×Q8—28no—
665C4×Q8—28no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×D4—28no—
675C4×D4—28no—
676C4×D4—216no—
677C4×D4—216no—
678C4×D4—28no—
679C4×D4—28no—
680C4×D4—24no—
681C4×D4—24no—
682#117—24no—
683#117—24no—
684#117—24no—
685#117—24no—
686#117—24no—
687#117—24no—
688#117—28no—
689#117—28no—
690#117—28no—
691#117C2×Q818yes—
692C2×C4⋊C4—24no—
693C2×C4⋊C4—28no—
694C2×C4⋊C4—24no—
695C2×C4⋊C4—28no—
696C2×C4⋊C4—24no—
697C2×C4⋊C4—28no—
698C2×C4⋊C4—28no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—28no—
701C2×C4⋊C4—28no—
702C2×C4⋊C4—28no—
703C2×C4⋊C4—28no—
704C2×C4⋊C4—216no—
705C2×C4⋊C4—216no—
706C2×C4⋊C4C2×D418yes—
707C2×C4⋊C4C2×D418yes—
708C2×C4⋊C4C2×D4116yes—
709C2×C4⋊C4C2×D4116yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2418yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2418yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2418yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2418yes—
796C2×C42—28no—
797C2×C42—28no—
798C2×C42—24no—
799C2×C42—28no—
800C2×C42—24no—
801C2×C42—28no—
802C2×C42C2×D418yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2412yes—
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2418yes—
816C2×C42C2412yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2418yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2418yes—
823C2×C42C2414yes—
824C2×C42C2418yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828C2×C42C2411yescharacteristic
829C2×C42C2412yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2418yes—
835#95C2418yes—
836#95C2414yes—
837#95C2414yes—
838#95C2418yes—
839#95C2418yes—
840#95C2418yes—
841#95C2418yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2418yes—
848#95C2418yes—
849#95C2414yes—
850#95C2414yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2418yes—
863#95C2418yes—
864C24C2512yes—
865C24C2511yescharacteristic
866#41—232no—
867C2×Q8—232no—
868C2×Q8—24no—
869C2×Q8—24no—
870C2×Q8—22no—
871C2×Q8—216no—
872C2×Q8—24no—
873C2×Q8—24no—
874C2×Q8—28no—
875C2×Q8—28no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—22no—
881C2×Q8—24no—
882C2×Q8—216no—
883C2×Q8—24no—
884C2×Q8—42no—
885C2×Q8—48no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×Q8—48no—
889C2×Q8—48no—
890C2×Q8—44no—
891C2×Q8—416no—
892C2×Q8—432no—
893C2×Q8C22×Q818yes—
894C2×Q8C22×Q818yes—
895C2×Q8C22×Q814yes—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4C22×Q818yes—
901C2×D4C22×Q814yes—
902C22×C4—24no—
903C22×C4—22no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—24no—
911C22×C4—22no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—28no—
915C22×C4—28no—
916C22×C4—42no—
917C22×C4—44no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—44no—
922C22×C4—42no—
923C22×C4—44no—
924C22×C4—48no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—48no—
928C22×C4C22×D414yes—
929C22×C4C22×D418yes—
930C22×C4C22×D418yes—
931C22×C4C22×D414yes—
932C22×C4C22×D414yes—
933C22×C4C22×Q818yes—
934C22×C4C22×Q818yes—
935C22×C4C22×Q814yes—
936C22×C42−1+414yes—
937C22×C4C2514yes—
938C22×C4C2514yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2512yes—
942C22×C4C2512yes—
943C22×C4C2512yes—
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2512yes—
947C22×C4C2512yes—
948C22×C4C2514yes—
949C22×C4C2512yes—
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2511yescharacteristic
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—216no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—216no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—216no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—216no—
986C4⋊C4—216no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—48no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—48no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4—44no—
1019C4⋊C4—48no—
1020C4⋊C4—44no—
1021C4⋊C4C22×D418yes—
1022C4⋊C4C22×D418yes—
1023C4⋊C4C22×D4116yes—
1024C4⋊C4C22×D4116yes—
1025C4⋊C4C22×D418yes—
1026C4⋊C4C22×D418yes—
1027C4⋊C4C22×D4116yes—
1028C4⋊C4C22×D4116yes—
1029C4⋊C4C22×Q818yes—
1030C4⋊C4C22×Q8132yes—
1031C22⋊C4—24no—
1032C22⋊C4—24no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—24no—
1040C22⋊C4—24no—
1041C22⋊C4—28no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—44no—
1045C22⋊C4—48no—
1046C22⋊C4C22×Q818yes—
1047C22⋊C4C22×Q8132yes—
1048C42—24no—
1049C42—24no—
1050C42—24no—
1051C42—216no—
1052C42—28no—
1053C42—28no—
1054C42—24no—
1055C42—24no—
1056C42—216no—
1057C42—24no—
1058C42—24no—
1059C42—28no—
1060C42—28no—
1061C42—24no—
1062C42—24no—
1063C42—24no—
1064C42—24no—
1065C42—24no—
1066C42—44no—
1067C42—48no—
1068C42—44no—
1069C42—48no—
1070C42C22×D414yes—
1071C42C22×D414yes—
1072C42C22×D414yes—
1073C42C22×D414yes—
1074C42C22×Q818yes—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—24no—
1080C23—24no—
1081C23C23×D412yes—
1082C23C23×Q814yes—
1083C23C23×Q812yes—
1084C23C2×2−1+412yes—
1085C23C2611yescharacteristic
1086Q8—216no—
1087Q8—216no—
1088Q8—28no—
1089Q8—48no—
1090Q8—432no—
1091Q8—48no—
1092Q8—88no—
1093Q8—84no—
1094Q8—88no—
1095Q8—84no—
1096D4—216no—
1097D4—28no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—28no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—28no—
1112C2×C4—22no—
1113C2×C4—216no—
1114C2×C4—216no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—28no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—44no—
1148C2×C4—48no—
1149C2×C4—44no—
1150C2×C4—48no—
1151C2×C4—44no—
1152C2×C4—44no—
1153C2×C4—44no—
1154C2×C4—48no—
1155C2×C4—84no—
1156C2×C4—88no—
1157C2×C4—84no—
1158C2×C4—88no—
1159C2×C4D4×Q8116yes—
1160C2×C4C23×D412yes—
1161C2×C4C23×D412yes—
1162C2×C4C23×D418yes—
1163C2×C4C23×D418yes—
1164C2×C4C23×D412yes—
1165C2×C4C23×D412yes—
1166C2×C4C23×D412yes—
1167C2×C4C23×D412yes—
1168C2×C4C23×Q818yes—
1169C2×C4C23×Q818yes—
1170C2×C4C23×Q814yes—
1171C2×C4C23×Q812yes—
1172C2×C4C23×Q812yes—
1173C2×C4C2×2−1+412yes—
1174C2×C4C2×2−1+412yes—
1175C2×C4#58514yes—
1176C22—24no—
1177C22—22no—
1178C22—22no—
1179C22—24no—
1180C22—28no—
1181C22—24no—
1182C22—42no—
1183C22—42no—
1184C22—44no—
1185C22C2×D4×Q814yes—
1186C22C24×D411yescharacteristic
1187C22C24×Q811yescharacteristic
1188C22C22×2−1+411yescharacteristic
1189C22C2×#58512yes—
1190C222−1+612yes—
1191C4—28no—
1192C4—24no—
1193C4—22no—
1194C4—28no—
1195C4—22no—
1196C4—22no—
1197C4—28no—
1198C4—22no—
1199C4—24no—
1200C4—28no—
1201C4—42no—
1202C4—44no—
1203C4—42no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—42no—
1210C4—42no—
1211C4—44no—
1212C4—44no—
1213C4—44no—
1214C4C2×D4×Q814yes—
1215C4C2×D4×Q814yes—
1216C2—24no—
1217C2—44no—
1218C2C22×D4×Q811yescharacteristic
1219C2#6281111yescharacteristic
1220C2#6285911yescharacteristic
1221C2#6295612yes—
1222C2#6300412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#557C2semidirect
3. #59833C2semidirect
4. #59667C2semidirect
5. #59154C2semidirect
6. #59152C2semidirect
7. #45424C2semidirect
8. #45277C2semidirect
9. #45274C2semidirect
10. #45272C2semidirect
11. #39592C2semidirect
12. #39589C2semidirect
13. #39589C2semidirect
14. #36547C2semidirect
15. #35640C2semidirect
17. #35576C2semidirect
19. #35179C2semidirect
20. #35154C2semidirect
21. #35154C2semidirect
22. #34953C2semidirect
26. #34217C2semidirect
223. #536Q8semidirect
616. C4⋊Q8C2×Q8semidirect
637. #124C2×Q8semidirect
651. C22⋊Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C22×#5572
#598332
#596672
#591542
#591522
#454242
#452772
#452742
#452722
#395922
#395892
#365472
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