Finite Group Databasebeta

← #7732030

Subgroups — #7732030

Order 512.

6444 conjugacy classes of subgroups.

The subgroup lattice has 1247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C211yesmaximal, characteristic
2C2×#3538C211yesmaximal, characteristic
3#48829C218yesmaximal, complemented
4#47211C214yesmaximal, complemented
5#46818C214yesmaximal, complemented
6#43510C218yesmaximal, complemented
7#39484C212yesmaximal, complemented
8#38954C212yesmaximal, complemented
9#38081C212yesmaximal, complemented
10#38081C212yesmaximal, complemented
11#37868C212yesmaximal, complemented
12#37865C212yesmaximal, complemented
13#37763C214yesmaximal, complemented
14#37689C214yesmaximal, complemented
15#37453C211yesmaximal, characteristic, complemented
16#37392C212yesmaximal, complemented
17#37386C212yesmaximal, complemented
18#36276C212yesmaximal, complemented
19#36181C212yesmaximal, complemented
20#35670C212yesmaximal, complemented
21#35619C212yesmaximal, complemented
22#35311C211yesmaximal, characteristic, complemented
23#35011C211yesmaximal, characteristic, complemented
24C2×#2499C211yesmaximal, characteristic, complemented
25#34082C211yesmaximal, characteristic
26#3538—216no—
27C2×#563C2214yes—
28#3495—216no—
29C2×#556C2212yes—
30C2×#554C2212yes—
31C2×#552C2212yes—
32C2×#552C2212yes—
33C2×#552C2212yes—
34C2×#552C2212yes—
35C2×#552C2214yes—
36C2×#551C2214yes—
37C2×#551C2214yes—
38C2×D4×Q8C2212yes—
39C2×D4×Q8C2212yes—
40C2×#544C2212yes—
41C2×#544C2212yes—
42C2×#544C2211yescharacteristic
43C2×#542C2212yes—
44C2×#541C2212yes—
45C2×#541C2212yes—
46C2×#539C2212yes—
47C2×#539C2212yes—
48C2×#536C2212yes—
49C2×#536C2211yescharacteristic
50C2×#533C2212yes—
51C2×#529C2212yes—
52C2×#525C2211yescharacteristic
53C22×C22⋊Q8C2211yescharacteristic
54C22×C22⋊Q8C2211yescharacteristic
55C22×C22⋊Q8C2211yescharacteristic
56C2×#520C2211yescharacteristic
57C2×#519C2211yescharacteristic
58C22×#117C2211yescharacteristic
59#2862C2212yescomplemented
60#2859C2212yescomplemented
61#2857C2212yes—
62#2857C2212yes—
63#2857C2212yescomplemented
64#2857C2212yescomplemented
65#2855C2214yes—
66#2817C2214yes—
67#2734C2218yescomplemented
68#2726C2218yescomplemented
69#2724C2218yes—
70#2724C2218yes—
71#2722C2218yescomplemented
72#2719C2218yescomplemented
73#2719C2218yescomplemented
74#2717C2218yes—
75#2717C2218yes—
76#2717C2218yescomplemented
77#2713C2218yescomplemented
78#2713C2218yescomplemented
79#2713C2218yescomplemented
80#2698C2218yes—
81#2698C2218yes—
82#2698C2218yescomplemented
83#2698C2218yescomplemented
84#2689C2218yes—
85#2689C2218yes—
86#2689C2218yescomplemented
87#2660C2212yescomplemented
88#2659C2214yes—
89#2642C2212yescomplemented
90#2627C2214yes—
91#2627C2214yes—
92#2625C2214yes—
93#2621C2212yes—
94#2621C2212yes—
95#2621C2212yescomplemented
96#2621C2212yescomplemented
97#2583C2214yes—
98#2583C2214yes—
99#2568C2212yescomplemented
100#2567C2212yescomplemented
101#2565C2212yescomplemented
102#2565C2212yescomplemented
103#2565C2212yescomplemented
104#2565C2212yescomplemented
105#2550C2218yescomplemented
106#2549C2218yes—
107#2549C2218yescomplemented
108#2546C2212yescomplemented
109#2546C2212yescomplemented
110#2506C2218yescomplemented
111#2503C2212yes—
112#2503C2212yes—
113#2503C2212yes—
114#2503C2212yescomplemented
115#2502C2212yes—
116#2502C2212yes—
117#2502C2212yes—
118#2502C2212yescomplemented
119#2499C2212yes—
120#2499C2212yes—
121#2499C2212yes—
122#2499C2212yes—
123#2499C2212yes—
124#2499C2212yes—
125#2499C2214yes—
126#2499C2214yes—
127#2499C2212yescomplemented
128#2499C2212yescomplemented
129#2499C2212yescomplemented
130#2499C2212yescomplemented
131#2496C2218yescomplemented
132#2486C2218yes—
133#2484C2214yes—
134#2483C2214yes—
135#2483C2214yes—
136#2478C2218yes—
137#2478C2218yes—
138#2478C2218yes—
139#2478C2218yes—
140#2478C2218yescomplemented
141#2462C2218yescomplemented
142#2462C2218yescomplemented
143#2462C2218yescomplemented
144#2451C2218yescomplemented
145#2447C2218yes—
146#2447C2218yes—
147#2446C2218yescomplemented
148#2438C2218yes—
149#2438C2218yes—
150#2438C2218yescomplemented
151#2434C2212yes—
152#2434C2212yes—
153#2434C2212yes—
154#2434C2212yes—
155#2434C2212yescomplemented
156#2434C2212yescomplemented
157#2419C2218yes—
158#2419C2218yes—
159#2419C2218yes—
160#2419C2218yes—
161#2419C2218yescomplemented
162C2×#397C2214yes—
163#2349C2218yes—
164#2344C2218yes—
165#2335C2214yes—
166#2333C2212yes—
167#2332C2212yes—
168#2329C2212yes—
169#2327C2212yescomplemented
170#2327C2212yescomplemented
171#2325C2212yes—
172#2321C2214yes—
173#2317C2211yescharacteristic
174#2317C2211yescharacteristic
175#2317C2212yescomplemented
176#2315C2214yes—
177#2310C2211yescharacteristic
178#2310C2211yescharacteristic
179#2310C2212yescomplemented
180C4×C4⋊Q8C2212yescomplemented
181C4×C4⋊Q8C2212yescomplemented
182#2298C2212yes—
183#2297C2212yes—
184C2×#391C2211yescharacteristic
185C2×#391C2211yescharacteristic
186C2×#391C2212yescomplemented
187#2293C2212yes—
188#2290C2212yes—
189#2290C2212yes—
190C2×#387C2214yes—
191#2285C2212yescomplemented
192C2×#384C2211yescharacteristic
193C2×#382C2211yescharacteristic
194#2280C2211yescharacteristic
195C42×D4C2212yes—
196C2×C4×C22⋊C4C2211yescharacteristic
197C22×#41C2311yescharacteristic
198C23×Q8C2311yescharacteristic
199C23×Q8C2312yes—
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C24×C4C2311yescharacteristic
203#563—232no—
204#556—216no—
205#554—216no—
206#552—232no—
207#552—216no—
208#552—216no—
209#552—216no—
210#552—216no—
211#551—232no—
212#551—232no—
213D4×Q8—216no—
214D4×Q8—216no—
215#544—216no—
216#544—216no—
217#544—28no—
218#542—216no—
219#541—216no—
220#541—216no—
221#539—216no—
222#539—216no—
223#536—28no—
224#536—216no—
225#533—216no—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237#529—216no—
238C2×#126C2314yes—
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#125C2314yes—
251C2×#125C2314yes—
252C2×#125C2314yes—
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#124C2312yes—
257C2×#124C2314yes—
258C2×#124C2314yes—
259#525D4116yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2312yes—
268C2×C22⋊Q8—28no—
269C2×C22⋊Q8—28no—
270C2×C22⋊Q8—28no—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2311yescharacteristic
296C2×#121C2311yescharacteristic
297C2×#121C2311yescharacteristic
298C2×#120C2312yes—
299#520—28no—
300#519—28no—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×#117—28no—
318C2×#117C2311yescharacteristic
319C2×#117C2311yescharacteristic
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2314yes—
324C2×#117C2312yes—
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2312yes—
328C2×#117C2314yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2312yes—
334C2×#117C2311yescharacteristic
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2311yescharacteristic
342C22×C4⋊C4C2311yescharacteristic
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2311yescharacteristic
345C22×C22⋊C4C2312yes—
346C22×C22⋊C4C2312yes—
347C22×C22⋊C4C2312yes—
348C22×C22⋊C4C2312yes—
349C22×C22⋊C4C2312yes—
350C22×C42C2312yes—
351C22×C42C2311yescharacteristic
352C22×C42C2311yescharacteristic
353C22×C42C2312yes—
354#400C2318yes—
355#400C2318yes—
356#400C2318yes—
357#400C2318yes—
358#400C2318yes—
359#400C2318yes—
360#400C2318yes—
361#398C2318yes—
362#398C2318yes—
363#398C2318yes—
364#398C2318yes—
365#398C2318yes—
366#398C2318yes—
367#398C2318yes—
368#398C2318yes—
369#398C2318yes—
370#398C2318yes—
371#398C2318yes—
372#398C2318yes—
373#398C2318yes—
374#398C2318yes—
375#398C2318yes—
376#397C2318yes—
377#397C2318yes—
378#397C2318yes—
379#397C2318yes—
380#397C2318yes—
381#397C2318yes—
382#397C2318yes—
383#397C2318yes—
384#397C2318yes—
385#397C2318yes—
386#397C2318yes—
387#397C2318yes—
388#397C2318yes—
389#397C2318yes—
390#395C2318yes—
391#395C2318yes—
392#395C2318yes—
393#395C2318yes—
394#395C2318yes—
395#395C2318yes—
396#395C2318yes—
397#395C2318yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2314yes—
411#391C2314yes—
412#391C2312yes—
413#391C2312yes—
414#391C2318yes—
415#391C2312yes—
416#391C2312yes—
417#391C2318yes—
418#391C2314yes—
419#391C2318yes—
420#391C2318yes—
421#391C2314yes—
422#391C2314yes—
423#390C2314yes—
424#390C2314yes—
425#389C2318yes—
426#389C2318yes—
427#389C2318yes—
428#389C2314yes—
429#389C2314yes—
430#389C2318yes—
431#389C2318yes—
432#389C2318yes—
433#389C2314yes—
434#389C2318yes—
435#389C2318yes—
436#389C2318yes—
437#389C2318yes—
438#389C2318yes—
439#389C2318yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2314yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#387C2318yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2318yes—
459#387C2318yes—
460#387C2318yes—
461#387C2318yes—
462#387C2318yes—
463#387C2318yes—
464#387C2318yes—
465#387C2318yes—
466#387C2318yes—
467#387C2318yes—
468#386C2314yes—
469#386C2314yes—
470#386C2314yes—
471#386C2314yes—
472#385C2318yes—
473#385C2318yes—
474#385C2318yes—
475#385C2318yes—
476#385C2314yes—
477#385C2314yes—
478#385C2318yes—
479#385C2314yes—
480#385C2314yes—
481#385C2318yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2318yes—
486#385C2318yes—
487#384C2312yes—
488#384C2312yes—
489#384C2312yes—
490#384C2312yes—
491#384C2312yes—
492#384C2312yes—
493#384C2314yes—
494#382C2312yes—
495#382C2312yes—
496#382C2312yes—
497#382C2312yes—
498#382C2312yes—
499#382C2312yes—
500#382C2318yes—
501#382C2314yes—
502#381C2312yes—
503#381C2314yes—
504#381C2314yes—
505#381C2318yes—
506#381C2318yes—
507#381C2318yes—
508#381C2318yes—
509#381C2318yes—
510#380C2318yes—
511#380C2318yes—
512#380C2312yes—
513#380C2312yes—
514#380C2318yes—
515#380C2318yes—
516#380C2318yes—
517#379C2312yes—
518C4×C4⋊C4C2318yes—
519C4×C4⋊C4C2318yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2314yes—
523C4×C4⋊C4C2318yes—
524C4×C22⋊C4C2314yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2312yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2312yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2312yes—
534#376C2312yes—
535C2×#95C2312yes—
536C2×#95C2314yes—
537C2×#95C2318yes—
538C2×#95C2314yes—
539C2×#95C2314yes—
540C43C2312yes—
541C25C2411yescharacteristic
542C2×#41—42no—
543C2×#41—42no—
544C2×#41C2×D418yes—
545C22×Q8—24no—
546C22×Q8—24no—
547C22×Q8—24no—
548C22×Q8—28no—
549C22×Q8—42no—
550C22×Q8—42no—
551C22×Q8—42no—
552C22×Q8—42no—
553C22×Q8—44no—
554C22×Q8—42no—
555C22×Q8—42no—
556C22×Q8—44no—
557C22×Q8C2412yes—
558C22×Q8C2412yes—
559C22×Q8C2412yes—
560C22×Q8C2412yes—
561C22×Q8C2414yes—
562C22×Q8C2412yes—
563C22×Q8C2412yes—
564C22×Q8C2414yes—
565C22×Q8C2411yescharacteristic
566C22×D4C2412yes—
567C22×D4C2412yes—
568C22×D4C2412yes—
569C22×D4C2411yescharacteristic
570C23×C4—42no—
571C23×C4—42no—
572C23×C4C2×D418yes—
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2412yes—
578C23×C4C2411yescharacteristic
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2412yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2411yescharacteristic
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2412yes—
593C4⋊Q8—28no—
594C4⋊Q8—216no—
595C4⋊Q8—28no—
596C4⋊Q8—216no—
597C4⋊Q8—216no—
598C4⋊Q8—28no—
599C4⋊Q8—28no—
600C4⋊Q8—44no—
601C4⋊Q8—44no—
602C4⋊Q8—44no—
603C4⋊Q8—44no—
604#126—216no—
605#126—216no—
606#126—216no—
607#126—216no—
608#126—216no—
609#126—216no—
610#126—216no—
611#126—216no—
612#125—28no—
613#125—216no—
614#125—216no—
615#125—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—216no—
620#125—28no—
621#125—28no—
622#124—28no—
623#124—216no—
624#124—216no—
625#123—216no—
626#123—216no—
627#123—216no—
628#123—216no—
629#123—216no—
630#123—216no—
631#123—216no—
632#123C2×D4116yes—
633C22⋊Q8—28no—
634C22⋊Q8—28no—
635C22⋊Q8—28no—
636C22⋊Q8—28no—
637C22⋊Q8—28no—
638C22⋊Q8—28no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8C2×D418yes—
657C22⋊Q8C2×D418yes—
658#121C2×D418yes—
659#121C2×D418yes—
660#120C2×D4116yes—
661C4×Q8—28no—
662C4×Q8—28no—
663C4×Q8—28no—
664C4×Q8—216no—
665C4×Q8—28no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×D4—28no—
670C4×D4—216no—
671C4×D4—216no—
672C4×D4—216no—
673C4×D4—216no—
674C4×D4—216no—
675C4×D4C2×D4116yes—
676C4×D4C2×D4116yes—
677#117—24no—
678#117—24no—
679#117—28no—
680#117—24no—
681#117—28no—
682#117—24no—
683#117—28no—
684#117—28no—
685#117—216no—
686#117—216no—
687#117—216no—
688#117—216no—
689#117—216no—
690#117—42no—
691#117—44no—
692#117—42no—
693#117C2×D418yes—
694C2×C4⋊C4—24no—
695C2×C4⋊C4—24no—
696C2×C4⋊C4—24no—
697C2×C4⋊C4—28no—
698C2×C4⋊C4—28no—
699C2×C4⋊C4—28no—
700C2×C4⋊C4—24no—
701C2×C4⋊C4—24no—
702C2×C4⋊C4—28no—
703C2×C4⋊C4—216no—
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2418yes—
724C2×C4⋊C4C2418yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2418yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2418yes—
752C2×C4⋊C4C2418yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C22⋊C4—28no—
758C2×C22⋊C4—28no—
759C2×C22⋊C4—28no—
760C2×C22⋊C4—28no—
761C2×C22⋊C4—28no—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2412yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C42—28no—
793C2×C42—42no—
794C2×C42—44no—
795C2×C42—42no—
796C2×C42C2412yes—
797C2×C42C2414yes—
798C2×C42C2412yes—
799C2×C42C2414yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2412yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2412yes—
816#95C2418yes—
817#95C2414yes—
818#95C2414yes—
819#95C2418yes—
820#95C2418yes—
821#95C2418yes—
822#95C2418yes—
823#95C2418yes—
824#95C2418yes—
825#95C2418yes—
826#95C2418yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2414yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844#95C2418yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848C24—24no—
849C24—41no—
850C24—41no—
851C24—42no—
852C24C22×D414yes—
853C24C2511yescharacteristic
854C24C2511yescharacteristic
855C24C2512yes—
856C24C2511yescharacteristic
857#41—416no—
858C2×Q8—24no—
859C2×Q8—24no—
860C2×Q8—24no—
861C2×Q8—24no—
862C2×Q8—28no—
863C2×Q8—24no—
864C2×Q8—24no—
865C2×Q8—28no—
866C2×Q8—24no—
867C2×Q8—24no—
868C2×Q8—24no—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—42no—
873C2×Q8—42no—
874C2×Q8—41no—
875C2×Q8—41no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—44no—
879C2×Q8—42no—
880C2×Q8—42no—
881C2×Q8—44no—
882C2×Q8—48no—
883C2×Q8—416no—
884C2×Q8—88no—
885C2×Q8—88no—
886C2×Q8—816no—
887C2×Q8C22×D414yes—
888C2×D4—28no—
889C2×D4—44no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—41no—
893C2×D4—41no—
894C2×D4C22×D418yes—
895C2×D4C22×D418yes—
896C2×D4C22×D418yes—
897C2×D4C22×D414yes—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—24no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—24no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—28no—
911C22×C4—28no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—28no—
917C22×C4—28no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—416no—
921C22×C4—42no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—42no—
929C22×C4—44no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—44no—
933C22×C4—42no—
934C22×C4—44no—
935C22×C4—42no—
936C22×C4—48no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4C22×D414yes—
946C22×C4C22×D414yes—
947C22×C4C22×D414yes—
948C22×C4C22×D418yes—
949C22×C4C22×D414yes—
950C22×C4C22×D414yes—
951C22×C4C22×D414yes—
952C22×C42−1+418yes—
953C22×C4C2514yes—
954C22×C4C2514yes—
955C22×C4C2514yes—
956C22×C4C2512yes—
957C22×C4C2512yes—
958C22×C4C2514yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2514yes—
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2514yes—
973C22×C4C2511yescharacteristic
974C4⋊C4—22no—
975C4⋊C4—24no—
976C4⋊C4—22no—
977C4⋊C4—24no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—24no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—216no—
1009C4⋊C4—216no—
1010C4⋊C4—28no—
1011C4⋊C4—48no—
1012C4⋊C4—44no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4—48no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—44no—
1019C4⋊C4—48no—
1020C4⋊C4—48no—
1021C4⋊C4—48no—
1022C4⋊C4—48no—
1023C4⋊C4C22×D414yes—
1024C4⋊C4C22×D414yes—
1025C4⋊C4C22×D418yes—
1026C4⋊C4C22×D418yes—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—42no—
1050C22⋊C4—44no—
1051C22⋊C4—42no—
1052C22⋊C4C22×D418yes—
1053C22⋊C4C22×D418yes—
1054C22⋊C4C22×D418yes—
1055C22⋊C4C22×D418yes—
1056C22⋊C4C22×D418yes—
1057C42—24no—
1058C42—24no—
1059C42—24no—
1060C42—24no—
1061C42—28no—
1062C42—28no—
1063C42—28no—
1064C42—28no—
1065C42—28no—
1066C42—28no—
1067C42—28no—
1068C42—24no—
1069C42—24no—
1070C42—24no—
1071C42—24no—
1072C42—42no—
1073C42—44no—
1074C42—42no—
1075C42—44no—
1076C42C22×D418yes—
1077C23—21no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—24no—
1083C23—21no—
1084C23—21no—
1085C23—22no—
1086C23—22no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—24no—
1091C23—22no—
1092C23—28no—
1093C23—44no—
1094C23—44no—
1095C23—84no—
1096C23—84no—
1097C23C23×D412yes—
1098C23C23×D412yes—
1099C23C23×D414yes—
1100C23C23×D412yes—
1101C23C2×2−1+414yes—
1102C23C2611yescharacteristic
1103Q8—44no—
1104Q8—48no—
1105Q8—48no—
1106Q8—48no—
1107Q8—48no—
1108Q8—88no—
1109Q8—84no—
1110Q8—84no—
1111Q8—88no—
1112D4—216no—
1113D4—48no—
1114D4—44no—
1115D4—48no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—28no—
1131C2×C4—216no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—28no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—28no—
1161C2×C4—24no—
1162C2×C4—28no—
1163C2×C4—24no—
1164C2×C4—44no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—48no—
1168C2×C4—48no—
1169C2×C4—48no—
1170C2×C4—48no—
1171C2×C4—48no—
1172C2×C4—88no—
1173C2×C4—88no—
1174C2×C4—84no—
1175C2×C4—84no—
1176C2×C4—84no—
1177C2×C4—84no—
1178C2×C4—84no—
1179C2×C4—88no—
1180C2×C4C23×D414yes—
1181C2×C4C23×D414yes—
1182C2×C4C23×D412yes—
1183C2×C4C23×D414yes—
1184C2×C4C23×D412yes—
1185C2×C4C23×D412yes—
1186C2×C4C23×D412yes—
1187C2×C4C2×2−1+418yes—
1188C2×C4#58512yes—
1189C2×C4#58512yes—
1190C22—22no—
1191C22—22no—
1192C22—24no—
1193C22—24no—
1194C22—22no—
1195C22—22no—
1196C22—24no—
1197C22—24no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—24no—
1202C22—22no—
1203C22—44no—
1204C22—42no—
1205C22—42no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—88no—
1210C22#349914yes—
1211C22C24×D411yescharacteristic
1212C22C22×2−1+412yes—
1213C22C2×#58511yescharacteristic
1214C22C2×#58511yescharacteristic
1215C222−1+612yes—
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—24no—
1220C4—24no—
1221C4—24no—
1222C4—28no—
1223C4—44no—
1224C4—44no—
1225C4—44no—
1226C4—42no—
1227C4—42no—
1228C4—44no—
1229C4—44no—
1230C4—42no—
1231C4—44no—
1232C4—42no—
1233C4—44no—
1234C4—44no—
1235C4—44no—
1236C4#348514yes—
1237C2—24no—
1238C2—44no—
1239C2—42no—
1240C2—42no—
1241C2C2×#348511yescharacteristic
1242C2C2×#349911yescharacteristic
1243C2#6285911yescharacteristic
1244C2#6290412yes—
1245C2#6293212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #48829C2semidirect
4. #47211C2semidirect
5. #46818C2semidirect
6. #43510C2semidirect
7. #39484C2semidirect
8. #38954C2semidirect
9. #38081C2semidirect
10. #38081C2semidirect
11. #37868C2semidirect
12. #37865C2semidirect
13. #37763C2semidirect
14. #37689C2semidirect
15. #37453C2semidirect
16. #37392C2semidirect
17. #37386C2semidirect
18. #36276C2semidirect
19. #36181C2semidirect
20. #35670C2semidirect
21. #35619C2semidirect
22. #35311C2semidirect
23. #35011C2semidirect
24. C2×#2499C2semidirect
59. #2862C22semidirect
60. #2859C22semidirect
63. #2857C22semidirect
64. #2857C22semidirect
67. #2734C22semidirect
68. #2726C22semidirect
71. #2722C22semidirect
72. #2719C22semidirect
73. #2719C22semidirect
76. #2717C22semidirect
77. #2713C22semidirect
78. #2713C22semidirect
79. #2713C22semidirect
82. #2698C22semidirect
83. #2698C22semidirect
86. #2689C22semidirect
87. #2660C22semidirect
89. #2642C22semidirect
95. #2621C22semidirect
96. #2621C22semidirect
99. #2568C22semidirect
100. #2567C22semidirect
101. #2565C22semidirect
102. #2565C22semidirect
103. #2565C22semidirect
104. #2565C22semidirect
105. #2550C22semidirect
107. #2549C22semidirect
108. #2546C22semidirect
109. #2546C22semidirect
110. #2506C22semidirect
114. #2503C22semidirect
118. #2502C22semidirect
127. #2499C22semidirect
128. #2499C22semidirect
129. #2499C22semidirect
130. #2499C22semidirect
131. #2496C22semidirect
140. #2478C22semidirect
141. #2462C22semidirect
142. #2462C22semidirect
143. #2462C22semidirect
144. #2451C22semidirect
147. #2446C22semidirect
150. #2438C22semidirect
155. #2434C22semidirect
156. #2434C22semidirect
161. #2419C22semidirect
169. #2327C22semidirect
170. #2327C22semidirect
175. #2317C22semidirect
179. #2310C22semidirect
180. C4×C4⋊Q8C22semidirect
181. C4×C4⋊Q8C22semidirect
186. C2×#391C22semidirect
191. #2285C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
C2×#35382
#488292
#472112
#468182
#435102
#394842
#389542
#380812
#378682
#378652
#377632
#376892
#374532
#373922
#373862
#362762
#361812
#356702
#356192
#353112
#350112
C2×#24992
#340822