Finite Group Databasebeta

← #7720853

Subgroups — #7720853

Order 512.

7126 conjugacy classes of subgroups.

The subgroup lattice has 1221 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3544C211yesmaximal, characteristic, complemented
2C2×#3559C211yesmaximal, characteristic, complemented
3#51546C214yesmaximal, complemented
4#51543C214yesmaximal, complemented
5#50651C218yesmaximal, complemented
6#44758C218yesmaximal, complemented
7#44447C214yesmaximal, complemented
8#43497C214yesmaximal, complemented
9#39617C212yesmaximal, complemented
10#39611C212yesmaximal, complemented
11#37869C212yesmaximal, complemented
12#37864C212yesmaximal, complemented
13#37863C212yesmaximal, complemented
14#37862C212yesmaximal, complemented
15#37304C212yesmaximal, complemented
16#37303C212yesmaximal, complemented
17#36184C212yesmaximal, complemented
18#36179C212yesmaximal, complemented
19#35317C211yesmaximal, characteristic, complemented
20#35303C211yesmaximal, characteristic, complemented
21#35276C212yesmaximal, complemented
22#35275C212yesmaximal, complemented
23#35139C211yesmaximal, characteristic, complemented
24C2×#2660C211yesmaximal, characteristic, complemented
25#34149C211yesmaximal, characteristic, complemented
26#3559—216no—
27#3544—216no—
28C2×#563C2212yes—
29C2×#563C2214yes—
30C2×#562C2212yes—
31C2×Q82C2211yescharacteristic
32C2×#555C2211yescharacteristic
33C2×#554C2212yes—
34C2×#554C2211yescharacteristic
35C2×#554C2211yescharacteristic
36C2×#553C2212yes—
37C2×#553C2212yes—
38C2×#552C2212yes—
39C2×#552C2212yes—
40C2×#547C2212yes—
41C2×#547C2214yes—
42C2×#547C2212yes—
43C2×#547C2212yes—
44C2×#547C2218yes—
45C2×#544C2212yes—
46C2×#544C2212yes—
47C2×#544C2212yes—
48C2×#542C2212yes—
49C2×#542C2212yes—
50C2×#540C2212yes—
51C2×#539C2214yes—
52C2×#539C2212yes—
53C2×#537C2212yes—
54C2×#536C2214yes—
55C2×#536C2214yes—
56C2×#532C2211yescharacteristic
57C22×C4⋊Q8C2211yescharacteristic
58C2×#529C2211yescharacteristic
59C2×#529C2211yescharacteristic
60C22×#125C2211yescharacteristic
61#2868C2212yes—
62#2868C2212yes—
63#2861C2212yes—
64#2859C2212yes—
65#2859C2212yes—
66#2858C2212yes—
67#2856C2212yes—
68#2856C2212yes—
69#2850C2212yes—
70#2850C2212yes—
71#2732C2218yes—
72#2723C2218yes—
73#2721C2218yes—
74#2721C2218yes—
75#2720C2218yes—
76#2718C2218yes—
77#2706C2218yes—
78#2694C2218yes—
79#2683C2218yes—
80#2681C2218yes—
81#2680C2218yes—
82#2680C2218yes—
83#2677C2218yes—
84#2677C2218yes—
85#2677C2218yes—
86#2674C2218yes—
87#2674C2218yes—
88#2672C2218yes—
89#2672C2218yes—
90#2671C2218yes—
91#2664C2214yes—
92#2660C2214yes—
93#2660C2212yes—
94#2660C2212yes—
95#2660C2212yes—
96#2660C2212yes—
97#2660C2214yes—
98#2660C2212yes—
99#2660C2212yes—
100#2660C2211yescharacteristic
101#2658C2214yes—
102#2657C2211yescharacteristic
103#2641C2211yescharacteristic
104#2640C2211yescharacteristic
105#2620C2212yes—
106#2619C2212yes—
107#2611C2214yes—
108#2610C2214yes—
109#2603C2214yes—
110#2567C2212yes—
111#2566C2212yes—
112#2566C2212yes—
113#2566C2212yes—
114#2566C2212yes—
115#2565C2212yes—
116#2565C2212yes—
117#2563C2212yes—
118#2555C2218yes—
119#2554C2218yes—
120#2553C2218yes—
121#2552C2218yes—
122#2551C2218yes—
123#2543C2214yes—
124#2542C2218yes—
125#2542C2212yes—
126#2542C2212yes—
127#2542C2212yes—
128#2542C2212yes—
129#2542C2214yes—
130#2519C2218yes—
131#2504C2211yescharacteristic
132#2504C2212yes—
133#2503C2211yescharacteristic
134#2502C2211yescharacteristic
135#2502C2212yes—
136#2501C2211yescharacteristic
137#2501C2212yes—
138#2501C2218yes—
139#2501C2212yes—
140#2501C2212yes—
141#2501C2218yes—
142#2501C2214yes—
143#2501C2212yes—
144#2500C2212yes—
145#2500C2212yes—
146#2500C2212yes—
147#2499C2212yes—
148#2479C2218yes—
149#2464C2218yes—
150#2461C2218yes—
151#2461C2218yes—
152#2449C2218yes—
153#2449C2218yes—
154#2449C2218yes—
155#2443C2218yes—
156#2440C2218yes—
157#2440C2218yes—
158#2440C2218yes—
159#2430C2218yes—
160#2430C2214yes—
161#2425C2218yes—
162#2425C2218yes—
163#2423C2218yes—
164#2413C2214yes—
165#2413C2218yes—
166#2406C2218yes—
167C2×#398C2214yes—
168C2×#395C2214yes—
169#2373C2214yes—
170#2372C2212yes—
171#2371C2212yes—
172#2368C2212yes—
173#2364C2212yes—
174#2359C2218yes—
175#2359C2214yes—
176#2328C2212yes—
177#2328C2212yes—
178#2326C2212yes—
179#2326C2212yes—
180#2322C2214yes—
181#2317C2212yes—
182#2317C2212yes—
183C4×#127C2212yes—
184C4×#124C2212yes—
185#2298C2212yes—
186#2295C2212yes—
187#2290C2212yes—
188#2290C2212yes—
189#2285C2212yes—
190C2×#384C2212yes—
191C2×#384C2212yes—
192C2×#382C2212yes—
193C42×D4C2212yes—
194C4×#117C2211yescharacteristic
195C4×#117C2212yes—
196C2×#376C2211yescharacteristic
197C22×#41C2314yes—
198C22×#41C2312yes—
199C22×#41C2314yes—
200C23×Q8C2312yes—
201#563—232no—
202#563—216no—
203#562—216no—
204Q82—28no—
205#555—28no—
206#554—28no—
207#554—216no—
208#554—28no—
209#553—216no—
210#553—216no—
211#552—216no—
212#552—216no—
213#547—232no—
214#547—216no—
215#547—216no—
216#547—216no—
217#547—432no—
218#544—216no—
219#544—216no—
220#544—216no—
221#542—216no—
222#542—216no—
223#540—216no—
224#539—232no—
225#539—216no—
226#537—216no—
227#536—232no—
228#536—416no—
229#532—28no—
230C2×C4⋊Q8—28no—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2318yes—
244C2×C4⋊Q8C2318yes—
245C2×#127C2312yes—
246C2×#127C2311yescharacteristic
247#529—28no—
248#529D4116yescomplemented
249C2×#126C2312yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2312yes—
255C2×#125—28no—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2311yescharacteristic
260C2×#125C2312yes—
261C2×#125C2312yes—
262C2×#125C2312yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2312yes—
266C2×#125C2314yes—
267C2×#125C2311yescharacteristic
268C2×#124C2312yes—
269C2×#124C2311yescharacteristic
270C2×#124C2312yes—
271C2×#124C2314yes—
272C2×#124C2314yes—
273C2×#124C2318yes—
274C2×#124C2311yescharacteristic
275C2×#123C2314yes—
276C2×#123C2318yes—
277C2×#123C2314yes—
278C2×#123C2312yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2318yes—
289C2×#123C2318yes—
290C2×#123C2318yes—
291C2×#123C2312yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2318yes—
308C2×C22⋊Q8C2318yes—
309C2×C22⋊Q8C2318yes—
310C2×C22⋊Q8C2318yes—
311C2×C22⋊Q8C2311yescharacteristic
312C2×#121C2312yes—
313C2×#121C2312yes—
314C2×#121C2311yescharacteristic
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2318yes—
324C2×#121C2318yes—
325C2×#121C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2318yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2311yescharacteristic
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2314yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2311yescharacteristic
358C22×C4⋊C4C2311yescharacteristic
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2314yes—
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2318yes—
363C22×C4⋊C4C2318yes—
364C22×C42C2312yes—
365C22×C42C2312yes—
366C22×C42C2311yescharacteristic
367#400C2314yes—
368#399C2314yes—
369#399C2318yes—
370#399C2318yes—
371#399C2318yes—
372#399C2318yes—
373#399C2318yes—
374#399C2318yes—
375#399C2318yes—
376#399C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2314yes—
380#398C2314yes—
381#398C2318yes—
382#398C2318yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#398C2318yes—
387#398C2318yes—
388#397C2314yes—
389#397C2314yes—
390#397C2318yes—
391#397C2318yes—
392#396C2318yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#395C2318yes—
398#395C2314yes—
399#395C2318yes—
400#395C2318yes—
401#395C2318yes—
402#395C2318yes—
403#395C2318yes—
404#395C2318yes—
405#394C2314yes—
406#394C2314yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#394C2318yes—
412#393C2318yes—
413#393C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2318yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#390C2312yes—
422#390C2312yes—
423#390C2318yes—
424#390C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2318yes—
432#390C2318yes—
433#390C2318yes—
434#389C2318yes—
435#389C2318yes—
436#389C2318yes—
437#389C2318yes—
438#389C2318yes—
439#389C2318yes—
440#389C2318yes—
441#389C2314yes—
442#388C2318yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2314yes—
449#388C2314yes—
450#388C2318yes—
451#388C2314yes—
452#388C2314yes—
453#388C2318yes—
454#388C2318yes—
455#388C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2314yes—
459#387C2314yes—
460#387C2318yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#386C2314yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2318yes—
470#386C2318yes—
471#386C2318yes—
472#386C2314yes—
473#386C2314yes—
474#386C2318yes—
475#385C2318yes—
476#385C2318yes—
477#385C2318yes—
478#385C2318yes—
479#385C2318yes—
480#385C2318yes—
481#385C2314yes—
482#385C2318yes—
483#385C2318yes—
484#385C2314yes—
485#385C2314yes—
486#385C2318yes—
487#384C2312yes—
488#384C2312yes—
489#384C2312yes—
490#384C2312yes—
491#384C2312yes—
492#384C2312yes—
493#384C2312yes—
494#384C2312yes—
495#384C2312yes—
496#384C2312yes—
497#384C2312yes—
498#384C2318yes—
499#384C2318yes—
500#384C2318yes—
501#384C2318yes—
502#382C2312yes—
503#382C2312yes—
504#382C2312yes—
505#382C2312yes—
506#382C2312yes—
507#382C2312yes—
508#382C2312yes—
509#382C2318yes—
510#381C2314yes—
511#380C2318yes—
512#380C2318yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2318yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2318yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2312yes—
529C4×C22⋊C4C2311yescharacteristic
530C4×C22⋊C4C2311yescharacteristic
531#376C2312yes—
532#376C2312yes—
533#376C2312yes—
534#376C2312yes—
535#376C2312yes—
536#376C2311yescharacteristic
537#376C2311yescharacteristic
538C2×#95C2312yes—
539C2×#95C2318yes—
540C2×#95C2312yes—
541C43C2312yes—
542C43C2312yes—
543C2×#41—216no—
544C2×#41—216no—
545C2×#41—28no—
546C2×#41—48no—
547C2×#41—416no—
548C2×#41—416no—
549C22×Q8—28no—
550C22×Q8—48no—
551C22×Q8C2411yescharacteristic
552C22×Q8C2412yes—
553C22×Q8C2414yes—
554C22×Q8C2412yes—
555C22×Q8C2414yes—
556C22×Q8C2414yes—
557C22×Q8C2412yes—
558C22×Q8C2411yescharacteristic
559C22×D4C2411yescharacteristic
560C22×D4C2412yes—
561C22×D4C2414yes—
562C22×D4C2412yes—
563C22×D4C2412yes—
564C22×D4C2414yes—
565C22×D4C2412yes—
566C22×D4C2418yes—
567C22×D4C2414yes—
568C22×D4C2414yes—
569C22×D4C2412yes—
570C22×D4C2411yescharacteristic
571C23×C4C2412yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2411yescharacteristic
576C23×C4C2412yes—
577C23×C4C2411yescharacteristic
578C23×C4C2412yes—
579C23×C4C2414yes—
580C23×C4C2414yes—
581C23×C4C2412yes—
582C23×C4C2414yes—
583C23×C4C2414yes—
584C23×C4C2414yes—
585C23×C4C2414yes—
586C23×C4C2411yescharacteristic
587C4⋊Q8—216no—
588C4⋊Q8—216no—
589C4⋊Q8—28no—
590C4⋊Q8—216no—
591C4⋊Q8—28no—
592C4⋊Q8—28no—
593C4⋊Q8—24no—
594C4⋊Q8—24no—
595C4⋊Q8—28no—
596C4⋊Q8—24no—
597C4⋊Q8—28no—
598C4⋊Q8—28no—
599C4⋊Q8—416no—
600C4⋊Q8—416no—
601#127—24no—
602#127—28no—
603#126—216no—
604#126—216no—
605#126—216no—
606#126—216no—
607#126—28no—
608#126C2×D4116yes—
609#125—216no—
610#125—28no—
611#125—216no—
612#125—216no—
613#125—28no—
614#125—28no—
615#125—28no—
616#125—28no—
617#125—24no—
618#125—28no—
619#125—28no—
620#125C2×D418yes—
621#124—216no—
622#124—216no—
623#124—24no—
624#124—28no—
625#124—28no—
626#124—416no—
627#124C2×D418yes—
628#123—216no—
629#123—28no—
630#123—216no—
631#123—216no—
632#123—216no—
633#123—216no—
634#123—216no—
635#123—216no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—232no—
640#123—216no—
641#123—416no—
642#123—416no—
643#123—416no—
644#123C2×D4116yes—
645C22⋊Q8—216no—
646C22⋊Q8—28no—
647C22⋊Q8—24no—
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⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—216no—
659C22⋊Q8—216no—
660C22⋊Q8—416no—
661C22⋊Q8—416no—
662C22⋊Q8—416no—
663C22⋊Q8—416no—
664C22⋊Q8C2×D418yes—
665#121—216no—
666#121—216no—
667#121—28no—
668#121—24no—
669#121—28no—
670#121—28no—
671#121—28no—
672#121—28no—
673#121—28no—
674#121—216no—
675#121—216no—
676#121—416no—
677#121—416no—
678#121C2×D418yes—
679C4×Q8—28no—
680C4×Q8—24no—
681C4×Q8—28no—
682C4×Q8C2×D418yes—
683C4×D4—28no—
684C4×D4—28no—
685C4×D4—216no—
686C4×D4—216no—
687C4×D4—216no—
688C4×D4—24no—
689C4×D4—28no—
690C4×D4—28no—
691C4×D4—28no—
692C4×D4—28no—
693C4×D4—28no—
694C4×D4—416no—
695C4×D4C2×D4116yes—
696C4×D4C2×D418yes—
697#117—28no—
698#117—28no—
699#117—28no—
700#117—216no—
701#117—28no—
702#117—28no—
703#117—28no—
704#117C2×D4116yes—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—28no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—216no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4—416no—
716C2×C4⋊C4—416no—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2418yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2418yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2418yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2412yes—
806C2×C42—28no—
807C2×C42—28no—
808C2×C42C2×D418yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2411yescharacteristic
823C2×C42C2411yescharacteristic
824C2×C42C2412yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2412yes—
828#95C2412yes—
829#95C2412yes—
830#95C2414yes—
831#95C2414yes—
832#95C2412yes—
833#95C2412yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2412yes—
839#95C2414yes—
840#95C2414yes—
841#95C2414yes—
842#95C2412yes—
843#95C2414yes—
844#95C2414yes—
845#95C2418yes—
846#95C2414yes—
847#95C2418yes—
848#95C2414yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853C24C2512yes—
854C24C2514yes—
855C24C2512yes—
856C24C2511yescharacteristic
857#41—816no—
858#41—832no—
859#41—832no—
860C2×Q8—22no—
861C2×Q8—24no—
862C2×Q8—28no—
863C2×Q8—28no—
864C2×Q8—24no—
865C2×Q8—28no—
866C2×Q8—24no—
867C2×Q8—24no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—48no—
872C2×Q8—48no—
873C2×Q8—48no—
874C2×Q8—44no—
875C2×Q8—816no—
876C2×Q8C22×D414yes—
877C2×D4—28no—
878C2×D4—28no—
879C2×D4—24no—
880C2×D4—28no—
881C2×D4—216no—
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—22no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—24no—
891C2×D4—24no—
892C2×D4—216no—
893C2×D4—42no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—48no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—48no—
900C2×D4—48no—
901C2×D4C22×D418yes—
902C2×D4C22×D414yes—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—28no—
909C22×C4—28no—
910C22×C4—28no—
911C22×C4—216no—
912C22×C4—24no—
913C22×C4—28no—
914C22×C4—28no—
915C22×C4—24no—
916C22×C4—28no—
917C22×C4—28no—
918C22×C4—28no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—28no—
923C22×C4—44no—
924C22×C4—42no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—48no—
930C22×C4—48no—
931C22×C4—48no—
932C22×C4—48no—
933C22×C4—44no—
934C22×C4C22×D414yes—
935C22×C4C22×D414yes—
936C22×C4C22×D418yes—
937C22×C4C22×D414yes—
938C22×C4C2514yes—
939C22×C4C2514yes—
940C22×C4C2512yes—
941C22×C4C2514yes—
942C22×C4C2512yes—
943C22×C4C2514yes—
944C22×C4C2514yes—
945C22×C4C2512yes—
946C22×C4C2514yes—
947C22×C4C2514yes—
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2512yes—
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2511yescharacteristic
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2511yescharacteristic
959C4⋊C4—24no—
960C4⋊C4—28no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—22no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—24no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—24no—
980C4⋊C4—22no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—28no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—216no—
992C4⋊C4—216no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—216no—
996C4⋊C4—28no—
997C4⋊C4—48no—
998C4⋊C4—48no—
999C4⋊C4—48no—
1000C4⋊C4—48no—
1001C4⋊C4—48no—
1002C4⋊C4—48no—
1003C4⋊C4—44no—
1004C4⋊C4—48no—
1005C4⋊C4—48no—
1006C4⋊C4C22×D414yes—
1007C4⋊C4C22×D418yes—
1008C4⋊C4C22×D414yes—
1009C4⋊C4C22×D418yes—
1010C4⋊C4C22×D418yes—
1011C4⋊C4C22×D418yes—
1012C22⋊C4—24no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—28no—
1019C22⋊C4—24no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—28no—
1030C22⋊C4—216no—
1031C22⋊C4—216no—
1032C22⋊C4—216no—
1033C22⋊C4—28no—
1034C22⋊C4—216no—
1035C22⋊C4—44no—
1036C22⋊C4—48no—
1037C22⋊C4—48no—
1038C22⋊C4—48no—
1039C22⋊C4—48no—
1040C22⋊C4—48no—
1041C22⋊C4—48no—
1042C22⋊C4C22×D418yes—
1043C22⋊C4C22×D418yes—
1044C22⋊C4C22×D418yes—
1045C22⋊C4C22×D418yes—
1046C22⋊C4C22×D418yes—
1047C22⋊C4H(5,𝔽2)18yes—
1048C42—28no—
1049C42—24no—
1050C42—28no—
1051C42—28no—
1052C42—28no—
1053C42—28no—
1054C42—28no—
1055C42—24no—
1056C42—28no—
1057C42—24no—
1058C42—24no—
1059C42—44no—
1060C42—44no—
1061C42C22×D414yes—
1062C42C22×D414yes—
1063C42C22×D414yes—
1064C42C22×D414yes—
1065C42C22×D418yes—
1066C422−1+418yes—
1067C23—22no—
1068C23—22no—
1069C23—24no—
1070C23—22no—
1071C23—22no—
1072C23—24no—
1073C23—22no—
1074C23—24no—
1075C23—28no—
1076C23—24no—
1077C23—24no—
1078C23—24no—
1079C23—24no—
1080C23—24no—
1081C23—28no—
1082C23C23×D414yes—
1083C23C23×D412yes—
1084C23C2×H(5,𝔽2)14yes—
1085C23C2611yescharacteristic
1086Q8—44no—
1087Q8—44no—
1088Q8—84no—
1089Q8—84no—
1090Q8—88no—
1091Q8—84no—
1092Q8—88no—
1093Q8—88no—
1094D4—216no—
1095D4—44no—
1096D4—416no—
1097D4—48no—
1098D4—44no—
1099D4—48no—
1100D4—84no—
1101D4—816no—
1102D4—84no—
1103D4—88no—
1104D4—88no—
1105D4—88no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—28no—
1120C2×C4—28no—
1121C2×C4—216no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—28no—
1133C2×C4—28no—
1134C2×C4—28no—
1135C2×C4—24no—
1136C2×C4—28no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—28no—
1144C2×C4—44no—
1145C2×C4—416no—
1146C2×C4—416no—
1147C2×C4—48no—
1148C2×C4—416no—
1149C2×C4—48no—
1150C2×C4—88no—
1151C2×C4—88no—
1152C2×C4—88no—
1153C2×C4—88no—
1154C2×C4—84no—
1155C2×C4—88no—
1156C2×C4—88no—
1157C2×C4C23×D414yes—
1158C2×C4C23×D412yes—
1159C2×C4C23×D414yes—
1160C2×C4C23×D412yes—
1161C2×C4C23×D412yes—
1162C2×C4C23×D412yes—
1163C2×C4C23×D412yes—
1164C2×C4C23×D414yes—
1165C2×C4C23×D412yes—
1166C2×C4C2×H(5,𝔽2)18yes—
1167C2×C4C2×2−1+418yes—
1168C2×C4C2×2−1+414yes—
1169C22—22no—
1170C22—22no—
1171C22—28no—
1172C22—24no—
1173C22—24no—
1174C22—24no—
1175C22—44no—
1176C22—44no—
1177C22—44no—
1178C22—42no—
1179C22—42no—
1180C22—44no—
1181C22—42no—
1182C22—44no—
1183C22—48no—
1184C22—48no—
1185C22—48no—
1186C22#349814yes—
1187C22C24×D411yescharacteristic
1188C22C22×H(5,𝔽2)12yes—
1189C22C22×2−1+412yes—
1190C222−1+612yes—
1191C4—22no—
1192C4—22no—
1193C4—24no—
1194C4—22no—
1195C4—24no—
1196C4—22no—
1197C4—22no—
1198C4—24no—
1199C4—28no—
1200C4—28no—
1201C4—44no—
1202C4—44no—
1203C4—44no—
1204C4—44no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—44no—
1209C4—44no—
1210C4—44no—
1211C4#349914yes—
1212C2—24no—
1213C2—44no—
1214C2—82no—
1215C2—84no—
1216C2C2×#349811yescharacteristic
1217C2C2×#349911yescharacteristic
1218C2#6285911yescharacteristic
1219C2#6291514yes—
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×#3544C2semidirect
2. C2×#3559C2semidirect
3. #51546C2semidirect
4. #51543C2semidirect
5. #50651C2semidirect
6. #44758C2semidirect
7. #44447C2semidirect
8. #43497C2semidirect
9. #39617C2semidirect
10. #39611C2semidirect
11. #37869C2semidirect
12. #37864C2semidirect
13. #37863C2semidirect
14. #37862C2semidirect
15. #37304C2semidirect
16. #37303C2semidirect
17. #36184C2semidirect
18. #36179C2semidirect
19. #35317C2semidirect
20. #35303C2semidirect
21. #35276C2semidirect
22. #35275C2semidirect
23. #35139C2semidirect
24. C2×#2660C2semidirect
25. #34149C2semidirect
248. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35442
C2×#35592
#515462
#515432
#506512
#447582
#444472
#434972
#396172
#396112
#378692
#378642
#378632
#378622
#373042
#373032
#361842
#361792
#353172
#353032
#352762
#352752
#351392
C2×#26602
#341492