Finite Group Databasebeta

← #7657583

Subgroups — #7657583

Order 512.

6762 conjugacy classes of subgroups.

The subgroup lattice has 1303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42888C212yesmaximal, complemented
4#42885C212yesmaximal, complemented
5#42796C214yesmaximal, complemented
6#42170C214yesmaximal, complemented
7#41992C214yesmaximal, complemented
8#40522C218yesmaximal, complemented
9#39136C212yesmaximal, complemented
10#39130C214yesmaximal, complemented
11#39126C212yesmaximal, complemented
12#39119C214yesmaximal, complemented
13#37639C211yesmaximal, characteristic, complemented
14#37634C211yesmaximal, characteristic, complemented
15#37621C212yesmaximal, complemented
16#37550C212yesmaximal, complemented
17#36504C212yesmaximal, complemented
18#36492C212yesmaximal, complemented
19#36065C212yesmaximal, complemented
20#35853C212yesmaximal, complemented
21#35752C214yesmaximal, complemented
22#35342C212yesmaximal, complemented
23#35297C211yesmaximal, characteristic, complemented
24#34614C212yesmaximal, complemented
25#34609C211yesmaximal, characteristic, complemented
26#34196C211yesmaximal, characteristic, complemented
27#3507—216no—
28#3480—216no—
29C2×#559C2212yes—
30C2×#559C2211yescharacteristic
31C2×#559C2212yes—
32C2×#557C2212yes—
33C2×#557C2211yescharacteristic
34C2×#556C2214yes—
35C2×#556C2211yescharacteristic
36C2×#556C2211yescharacteristic
37C2×#556C2212yes—
38C2×#556C2211yescharacteristic
39C2×#554C2211yescharacteristic
40C2×#554C2211yescharacteristic
41C2×#553C2214yes—
42C2×#553C2212yes—
43C2×#552C2212yes—
44C2×#552C2212yes—
45C2×#550C2211yescharacteristic
46C2×#548C2212yes—
47C2×#539C2214yes—
48C2×#536C2212yes—
49C2×#533C2211yescharacteristic
50C2×#532C2211yescharacteristic
51C2×#532C2211yescharacteristic
52C2×#532C2212yes—
53C2×#529C2212yes—
54C2×#529C2212yes—
55C2×#529C2214yes—
56C2×#529C2212yes—
57C2×#520C2212yes—
58C2×C4×#41C2212yes—
59C2×C4×#41C2211yescharacteristic
60C2×C4×#41C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2857C2212yes—
63#2857C2212yes—
64#2851C2214yes—
65#2850C2214yes—
66#2821C2214yes—
67#2819C2214yes—
68#2818C2214yes—
69#2816C2214yes—
70#2813C2218yes—
71#2733C2218yes—
72#2731C2218yes—
73#2730C2218yes—
74#2729C2218yes—
75#2727C2218yes—
76#2719C2218yes—
77#2711C2218yes—
78#2705C2218yes—
79#2702C2218yes—
80#2694C2218yes—
81#2681C2218yes—
82#2673C2218yes—
83#2662C2214yes—
84#2662C2214yes—
85#2661C2218yes—
86#2660C2212yes—
87#2641C2212yes—
88#2637C2214yes—
89#2636C2214yes—
90#2635C2214yes—
91#2635C2218yes—
92#2632C2214yes—
93#2632C2212yes—
94#2631C2212yes—
95#2630C2218yes—
96#2629C2214yes—
97#2628C2212yes—
98#2628C2214yes—
99#2625C2212yes—
100#2624C2211yescharacteristic
101#2624C2211yescharacteristic
102#2620C2214yes—
103#2619C2214yes—
104#2619C2214yes—
105#2619C2212yes—
106#2616C2212yes—
107#2616C2212yes—
108#2616C2212yes—
109#2615C2212yes—
110#2615C2214yes—
111#2615C2212yes—
112#2615C2211yescharacteristic
113#2615C2211yescharacteristic
114#2610C2214yes—
115#2610C2214yes—
116#2604C2214yes—
117#2603C2214yes—
118#2602C2218yes—
119#2600C2218yes—
120#2599C2214yes—
121#2598C2214yes—
122#2584C2212yes—
123#2581C2212yes—
124#2563C2212yes—
125#2563C2212yes—
126#2563C2212yes—
127#2562C2212yes—
128#2562C2214yes—
129#2562C2214yes—
130#2558C2218yes—
131#2554C2218yes—
132#2542C2212yes—
133#2541C2212yes—
134#2541C2212yes—
135#2540C2214yes—
136#2540C2214yes—
137#2538C2214yes—
138#2538C2214yes—
139#2537C2212yes—
140#2537C2212yes—
141#2537C2214yes—
142#2536C2214yes—
143#2536C2212yes—
144#2536C2214yes—
145#2536C2214yes—
146#2535C2214yes—
147#2519C2218yes—
148#2500C2214yes—
149#2485C2214yes—
150#2479C2218yes—
151#2477C2218yes—
152#2469C2218yes—
153#2467C2218yes—
154#2467C2218yes—
155#2463C2218yes—
156#2458C2218yes—
157#2456C2218yes—
158#2445C2218yes—
159#2442C2214yes—
160#2441C2214yes—
161#2426C2214yes—
162#2426C2214yes—
163#2423C2214yes—
164#2421C2214yes—
165#2416C2214yes—
166#2415C2214yes—
167#2414C2218yes—
168#2414C2214yes—
169#2407C2214yes—
170#2407C2214yes—
171#2398C2212yes—
172#2397C2212yes—
173#2396C2214yes—
174#2392C2214yes—
175#2392C2218yes—
176#2388C2214yes—
177#2363C2214yes—
178#2361C2214yes—
179#2355C2212yes—
180#2355C2214yes—
181#2354C2214yes—
182#2352C2214yes—
183Q8×C4⋊C4C2212yes—
184#2344C2214yes—
185#2344C2212yes—
186Q8×C22⋊C4C2212yes—
187#2324C2214yes—
188#2323C2214yes—
189#2323C2214yes—
190#2320C2214yes—
191#2320C2212yes—
192C4×C22⋊Q8C2214yes—
193C4×#121C2212yes—
194C4×#121C2212yes—
195C4×#121C2214yes—
196#2285C2211yescharacteristic
197#2285C2212yes—
198#2283C2211yescharacteristic
199#2283C2212yes—
200#2276C2212yes—
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C22×#41C2312yes—
204C22×#41C2312yes—
205C23×Q8C2311yescharacteristic
206#559—28no—
207#559—216no—
208#559—216no—
209#557—28no—
210#557—216no—
211#556—28no—
212#556—216no—
213#556—28no—
214#556—28no—
215#556—232no—
216#554—28no—
217#554—28no—
218#553—216no—
219#553—232no—
220#552—216no—
221#552—216no—
222#550—28no—
223#548—216no—
224#539—232no—
225#536—216no—
226#533—28no—
227#532—216no—
228#532—28no—
229#532—28no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2314yes—
236C2×#127C2312yes—
237C2×#127C2311yescharacteristic
238C2×#127C2311yescharacteristic
239C2×#127C2314yes—
240#529—216no—
241#529—232no—
242#529—216no—
243#529—216no—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2312yes—
289C2×#121C2311yescharacteristic
290C2×#121C2311yescharacteristic
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2318yes—
304#520—216no—
305C4×#41—216no—
306C4×#41—216no—
307C4×#41—28no—
308C2×C4×Q8D4116yescomplemented
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2311yescharacteristic
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2314yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2314yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2318yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2314yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2314yes—
357C2×#117C2311yescharacteristic
358C2×#117C2314yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2312yes—
362C2×#117C2314yes—
363C22×C4⋊C4C2312yes—
364C22×C4⋊C4C2312yes—
365C22×C4⋊C4C2311yescharacteristic
366C22×C4⋊C4C2312yes—
367C22×C42C2314yes—
368C22×C42C2312yes—
369C22×C42C2312yes—
370C22×C42C2311yescharacteristic
371#400C2318yes—
372#400C2314yes—
373#400C2318yes—
374#400C2314yes—
375#399C2318yes—
376#399C2318yes—
377#399C2312yes—
378#399C2312yes—
379#399C2314yes—
380#399C2318yes—
381#398C2318yes—
382#398C2318yes—
383#398C2314yes—
384#398C2318yes—
385#398C2318yes—
386#397C2318yes—
387#397C2312yes—
388#397C2318yes—
389#397C2312yes—
390#396C2318yes—
391#396C2318yes—
392#396C2318yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#394C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2314yes—
404#394C2318yes—
405#394C2318yes—
406#394C2314yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2314yes—
411#394C2314yes—
412#394C2318yes—
413#394C2314yes—
414#394C2314yes—
415#394C2318yes—
416#394C2318yes—
417#394C2314yes—
418#394C2318yes—
419#394C2318yes—
420#393C2318yes—
421#393C2314yes—
422#393C2314yes—
423#393C2318yes—
424#393C2312yes—
425#393C2312yes—
426#393C2314yes—
427#392C2312yes—
428#392C2314yes—
429#392C2318yes—
430#392C2318yes—
431#392C2314yes—
432#392C2318yes—
433#392C2318yes—
434#392C2318yes—
435#392C2312yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2318yes—
441#391C2314yes—
442#391C2318yes—
443#391C2314yes—
444#391C2314yes—
445#390C2314yes—
446#390C2314yes—
447#390C2314yes—
448#390C2312yes—
449#390C2318yes—
450#390C2318yes—
451#390C2318yes—
452#390C2318yes—
453#390C2314yes—
454#390C2318yes—
455#390C2312yes—
456#390C2318yes—
457#389C2314yes—
458#389C2318yes—
459#389C2312yes—
460#389C2314yes—
461#389C2318yes—
462#389C2318yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2314yes—
483#388C2314yes—
484#388C2318yes—
485#388C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2314yes—
501#386C2314yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#384C2312yes—
507#384C2314yes—
508#384C2314yes—
509#383C2314yes—
510#383C2312yes—
511#382C2314yes—
512#382C2314yes—
513#382C2312yes—
514#382C2314yes—
515#382C2314yes—
516#382C2312yes—
517#381C2312yes—
518#381C2314yes—
519#380C2314yes—
520#380C2312yes—
521#380C2312yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2312yes—
531#380C2314yes—
532#380C2314yes—
533#380C2312yes—
534#380C2311yescharacteristic
535#380C2311yescharacteristic
536#380C2318yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2318yes—
545C4×C4⋊C4C2318yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552#376C2314yes—
553#376C2312yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—24no—
557C2×#41—28no—
558C2×#41—48no—
559C2×#41—44no—
560C2×#41—48no—
561C2×#41—44no—
562C2×#41—44no—
563C22×Q8—44no—
564C22×Q8C2×D418yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2411yescharacteristic
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×Q8C2412yes—
572C22×Q8C2412yes—
573C22×D4C2411yescharacteristic
574C22×D4C2411yescharacteristic
575C22×D4C2412yes—
576C22×D4C2414yes—
577C22×D4C2412yes—
578C22×D4C2412yes—
579C22×D4C2412yes—
580C22×D4C2414yes—
581C22×D4C2412yes—
582C22×D4C2411yescharacteristic
583C22×D4C2412yes—
584C22×D4C2414yes—
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2414yes—
588C22×D4C2418yes—
589C22×D4C2414yes—
590C22×D4C2418yes—
591C23×C4C2412yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2414yes—
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2412yes—
603C23×C4C2412yes—
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C4⋊Q8—216no—
607C4⋊Q8—28no—
608C4⋊Q8—24no—
609C4⋊Q8—24no—
610C4⋊Q8—24no—
611C4⋊Q8—24no—
612#127—28no—
613#127—24no—
614#127—24no—
615#127—84no—
616#126—216no—
617#126—216no—
618#126—216no—
619#126—216no—
620#126—216no—
621#126—216no—
622#126—216no—
623#125—28no—
624#125—216no—
625#125—216no—
626#125—216no—
627#125—28no—
628#125—28no—
629#125—28no—
630#124—28no—
631#124—216no—
632#124—216no—
633#124—28no—
634#124—28no—
635#124—28no—
636#124—28no—
637#124—28no—
638#124—28no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—216no—
643#123—216no—
644#123—216no—
645#123—216no—
646C22⋊Q8—28no—
647C22⋊Q8—216no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—28no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—48no—
657C22⋊Q8—48no—
658C22⋊Q8—48no—
659C22⋊Q8—84no—
660#121—24no—
661#121—24no—
662#121—28no—
663#121—28no—
664#121—216no—
665#121—216no—
666#121—28no—
667#121—28no—
668#121—216no—
669#121—48no—
670#121—48no—
671#121—48no—
672#121—48no—
673#121—44no—
674#121—44no—
675#121—88no—
676C4×Q8—28no—
677C4×Q8—216no—
678C4×Q8—28no—
679C4×Q8—24no—
680C4×Q8—28no—
681C4×Q8—24no—
682C4×Q8—28no—
683C4×Q8—28no—
684C4×Q8—28no—
685C4×Q8—28no—
686C4×Q8—48no—
687C4×Q8C2×D418yes—
688C4×Q8C2×D418yes—
689C4×Q8C2×D4116yes—
690C4×Q8C2×D418yes—
691C4×Q8C2×D418yes—
692C4×Q8C2×D4116yes—
693C4×D4—28no—
694C4×D4—216no—
695C4×D4—216no—
696C4×D4—28no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—28no—
700C4×D4—216no—
701C4×D4—216no—
702C4×D4—28no—
703C4×D4—216no—
704C4×D4—28no—
705C4×D4—24no—
706C4×D4—28no—
707C4×D4—24no—
708C4×D4—216no—
709C4×D4—28no—
710C4×D4—28no—
711C4×D4—28no—
712C4×D4—28no—
713C4×D4—24no—
714C4×D4—24no—
715C4×D4—48no—
716C4×D4—48no—
717C4×D4—88no—
718#117—24no—
719#117—28no—
720#117—28no—
721#117—216no—
722#117—28no—
723#117—28no—
724#117—216no—
725#117—28no—
726#117—216no—
727#117—216no—
728#117—84no—
729#117—82no—
730C2×C4⋊C4—28no—
731C2×C4⋊C4—28no—
732C2×C4⋊C4C2×D418yes—
733C2×C4⋊C4C2×D4116yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2418yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2418yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2418yes—
822C2×C42—28no—
823C2×C42—216no—
824C2×C42C2×D4116yes—
825C2×C42C2×D418yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2412yes—
831C2×C42C2414yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2418yes—
836C2×C42C2414yes—
837C2×C42C2418yes—
838C2×C42C2412yes—
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2411yescharacteristic
845C2×C42C2411yescharacteristic
846#95C2412yes—
847#95C2414yes—
848#95C2412yes—
849#95C2418yes—
850#95C2414yes—
851#95C2414yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2414yes—
859#95C2414yes—
860#95C2418yes—
861#95C2418yes—
862#95C2414yes—
863#95C2418yes—
864#95C2418yes—
865#95C2414yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869C24C2512yes—
870C24C2512yes—
871C24C2512yes—
872C24C2514yes—
873C24C2511yescharacteristic
874#41—432no—
875#41—416no—
876#41—432no—
877#41—432no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—22no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—24no—
885C2×Q8—28no—
886C2×Q8—44no—
887C2×Q8—42no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—416no—
893C2×Q8C22×D414yes—
894C2×Q8C22×D414yes—
895C2×Q8C22×D418yes—
896C2×D4—24no—
897C2×D4—28no—
898C2×D4—24no—
899C2×D4—24no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—28no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—22no—
907C2×D4—28no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—24no—
914C2×D4—42no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—42no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—48no—
928C2×D4—48no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—48no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—44no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—44no—
940C2×D4—48no—
941C2×D4—48no—
942C2×D4—48no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—28no—
947C22×C4—28no—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—28no—
954C22×C4—28no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—28no—
958C22×C4—24no—
959C22×C4—28no—
960C22×C4—24no—
961C22×C4—28no—
962C22×C4—28no—
963C22×C4—42no—
964C22×C4—41no—
965C22×C4—42no—
966C22×C4—41no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—42no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—42no—
978C22×C4C22×D414yes—
979C22×C4C22×D414yes—
980C22×C4C22×D418yes—
981C22×C4C22×D414yes—
982C22×C4C22×D418yes—
983C22×C4C2514yes—
984C22×C4C2518yes—
985C22×C4C2514yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2514yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2511yescharacteristic
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—24no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—24no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—48no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—48no—
1038C4⋊C4—48no—
1039C4⋊C4—48no—
1040C4⋊C4—48no—
1041C4⋊C4—48no—
1042C4⋊C4C22×D414yes—
1043C4⋊C4C22×D414yes—
1044C4⋊C4C22×D418yes—
1045C4⋊C4C22×D418yes—
1046C4⋊C4C22×D418yes—
1047C4⋊C4C22×D418yes—
1048C4⋊C4C22×D418yes—
1049C22⋊C4—24no—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—28no—
1054C22⋊C4—24no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—24no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—42no—
1072C22⋊C4—44no—
1073C22⋊C4—48no—
1074C22⋊C4—42no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—48no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—48no—
1087C22⋊C4—48no—
1088C22⋊C4—48no—
1089C22⋊C4—48no—
1090C22⋊C4—48no—
1091C22⋊C4—48no—
1092C42—24no—
1093C42—28no—
1094C42—24no—
1095C42—28no—
1096C42—24no—
1097C42—28no—
1098C42—28no—
1099C42—28no—
1100C42—28no—
1101C42—48no—
1102C42—44no—
1103C42—48no—
1104C42C22×D414yes—
1105C42C22×D418yes—
1106C42C22×D418yes—
1107C42C22×D414yes—
1108C42C22×D418yes—
1109C42C22×D418yes—
1110C42C22×D414yes—
1111C42C22×D414yes—
1112C23—22no—
1113C23—22no—
1114C23—21no—
1115C23—21no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—24no—
1120C23—22no—
1121C23—24no—
1122C23—24no—
1123C23—24no—
1124C23—24no—
1125C23—22no—
1126C23—22no—
1127C23—24no—
1128C23—24no—
1129C23—24no—
1130C23—24no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—24no—
1135C23—22no—
1136C23—22no—
1137C23—24no—
1138C23—22no—
1139C23—22no—
1140C23C23×D412yes—
1141C23C2611yescharacteristic
1142Q8—28no—
1143Q8—28no—
1144Q8—48no—
1145Q8—44no—
1146Q8—48no—
1147Q8—48no—
1148Q8—48no—
1149Q8—84no—
1150D4—44no—
1151D4—48no—
1152D4—48no—
1153D4—416no—
1154D4—48no—
1155D4—416no—
1156D4—48no—
1157D4—48no—
1158D4—48no—
1159D4—44no—
1160D4—44no—
1161D4—88no—
1162D4—84no—
1163D4—84no—
1164D4—88no—
1165D4—816no—
1166D4—88no—
1167D4—168no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—28no—
1181C2×C4—28no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—28no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—28no—
1197C2×C4—28no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—28no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—48no—
1213C2×C4—44no—
1214C2×C4—48no—
1215C2×C4—416no—
1216C2×C4—48no—
1217C2×C4—48no—
1218C2×C4—48no—
1219C2×C4—48no—
1220C2×C4—416no—
1221C2×C4—88no—
1222C2×C4—88no—
1223C2×C4—88no—
1224C2×C4—84no—
1225C2×C4C23×D414yes—
1226C2×C4C23×D412yes—
1227C2×C4C23×D412yes—
1228C2×C4C23×D414yes—
1229C2×C4C23×D414yes—
1230C2×C4C23×D412yes—
1231C2×C4C23×D414yes—
1232C2×C4C23×D412yes—
1233C2×C4C23×D412yes—
1234C2×C4C23×D412yes—
1235C2×C4#58514yes—
1236C2×C4#58514yes—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—44no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—42no—
1253C22—44no—
1254C22—44no—
1255C22—42no—
1256C22—44no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—44no—
1262C22—42no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22C24×D411yescharacteristic
1267C22C2×#58512yes—
1268C22C2×#58512yes—
1269C22H(7,𝔽2)11yescharacteristic
1270C222−1+611yescharacteristic
1271C4—22no—
1272C4—24no—
1273C4—24no—
1274C4—22no—
1275C4—22no—
1276C4—22no—
1277C4—24no—
1278C4—24no—
1279C4—42no—
1280C4—44no—
1281C4—44no—
1282C4—42no—
1283C4—44no—
1284C4—44no—
1285C4—48no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—44no—
1290C4#344914yes—
1291C4#348714yes—
1292C2—42no—
1293C2—84no—
1294C2—82no—
1295C2—82no—
1296C2—82no—
1297C2C2×#344911yescharacteristic
1298C2C2×#348711yescharacteristic
1299C2#6285311yescharacteristic
1300C2#6293812yes—
1301C2#6293912yes—
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×#3507C2semidirect
2. C2×#3480C2semidirect
3. #42888C2semidirect
4. #42885C2semidirect
5. #42796C2semidirect
6. #42170C2semidirect
7. #41992C2semidirect
8. #40522C2semidirect
9. #39136C2semidirect
10. #39130C2semidirect
11. #39126C2semidirect
12. #39119C2semidirect
13. #37639C2semidirect
14. #37634C2semidirect
15. #37621C2semidirect
16. #37550C2semidirect
17. #36504C2semidirect
18. #36492C2semidirect
19. #36065C2semidirect
20. #35853C2semidirect
21. #35752C2semidirect
22. #35342C2semidirect
23. #35297C2semidirect
24. #34614C2semidirect
25. #34609C2semidirect
26. #34196C2semidirect
308. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C2×#34802
#428882
#428852
#427962
#421702
#419922
#405222
#391362
#391302
#391262
#391192
#376392
#376342
#376212
#375502
#365042
#364922
#360652
#358532
#357522
#353422
#352972
#346142
#346092
#341962