Finite Group Databasebeta

← #7647343

Subgroups — #7647343

Order 512.

6910 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3483C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#42995C212yesmaximal, complemented
4#42968C212yesmaximal, complemented
5#42913C212yesmaximal, complemented
6#42909C212yesmaximal, complemented
7#42307C214yesmaximal, complemented
8#42303C214yesmaximal, complemented
9#39725C212yesmaximal, complemented
10#39597C212yesmaximal, complemented
11#38922C212yesmaximal, complemented
12#38909C212yesmaximal, complemented
13#38050C214yesmaximal, complemented
14#38033C214yesmaximal, complemented
15#37619C212yesmaximal, complemented
16#37554C212yesmaximal, complemented
17#37234C218yesmaximal, complemented
18#35607C214yesmaximal, complemented
19#35334C212yesmaximal, complemented
20#35292C211yesmaximal, characteristic, complemented
21#35249C211yesmaximal, characteristic, complemented
22#35210C212yesmaximal, complemented
23#35205C214yesmaximal, complemented
24#34952C211yesmaximal, characteristic, complemented
25#34909C211yesmaximal, characteristic, complemented
26#34191C211yesmaximal, characteristic, complemented
27#3483—216no—
28C2×Q82C2211yescharacteristic
29C2×#555C2211yescharacteristic
30C2×#555C2214yes—
31C2×#555C2212yes—
32C2×#555C2212yes—
33C2×#550C2211yescharacteristic
34C2×#550C2212yes—
35C2×#550C2212yes—
36C2×#550C2211yescharacteristic
37#3461—216no—
38C2×#544C2211yescharacteristic
39C2×#542C2212yes—
40C2×#542C2212yes—
41C2×#541C2212yes—
42C2×#541C2212yes—
43C2×#539C2214yes—
44C2×#537C2211yescharacteristic
45C2×#536C2211yescharacteristic
46C2×#536C2211yescharacteristic
47C2×#533C2212yes—
48C2×#533C2212yes—
49C2×#532C2212yes—
50C2×#532C2214yes—
51C2×#532C2211yescharacteristic
52C2×#532C2212yes—
53C2×#529C2212yes—
54C2×#529C2212yes—
55C2×#529C2214yes—
56C2×C4×#41C2212yes—
57C2×C4×#41C2211yescharacteristic
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2212yes—
60C2×C4×#41C2211yescharacteristic
61C22×C4×Q8C2211yescharacteristic
62#2857C2212yes—
63#2856C2212yes—
64#2854C2214yes—
65#2852C2218yes—
66#2851C2218yes—
67#2820C2214yes—
68#2819C2214yes—
69#2816C2214yes—
70#2816C2214yes—
71#2715C2218yes—
72#2713C2218yes—
73#2711C2218yes—
74#2710C2218yes—
75#2709C2218yes—
76#2708C2218yes—
77#2703C2218yes—
78#2691C2218yes—
79#2677C2218yes—
80#2676C2218yes—
81#2674C2218yes—
82#2673C2218yes—
83#2672C2218yes—
84#2672C2218yes—
85#2671C2218yes—
86#2671C2218yes—
87#2658C2214yes—
88#2656C2214yes—
89#2640C2214yes—
90#2639C2214yes—
91#2638C2214yes—
92#2636C2218yes—
93#2635C2214yes—
94#2633C2218yes—
95#2632C2214yes—
96#2628C2214yes—
97#2628C2214yes—
98#2628C2214yes—
99#2624C2214yes—
100#2624C2212yes—
101#2624C2214yes—
102#2619C2214yes—
103#2615C2212yes—
104#2611C2214yes—
105#2610C2214yes—
106#2602C2218yes—
107#2600C2214yes—
108#2599C2212yes—
109#2598C2212yes—
110#2592C2212yes—
111#2582C2212yes—
112#2581C2211yescharacteristic
113#2581C2212yes—
114#2581C2214yes—
115#2580C2214yes—
116#2580C2212yes—
117#2580C2212yes—
118#2580C2211yescharacteristic
119#2580C2212yes—
120#2580C2212yes—
121#2579C2214yes—
122#2567C2212yes—
123#2564C2218yes—
124#2564C2214yes—
125#2564C2214yes—
126#2559C2218yes—
127#2555C2218yes—
128#2551C2214yes—
129#2548C2214yes—
130#2548C2212yes—
131#2546C2214yes—
132#2544C2214yes—
133#2540C2214yes—
134#2540C2212yes—
135#2538C2212yes—
136#2537C2214yes—
137#2536C2211yescharacteristic
138#2535C2211yescharacteristic
139#2535C2212yes—
140#2521C2218yes—
141#2501C2212yes—
142#2492C2214yes—
143#2491C2214yes—
144#2491C2218yes—
145#2487C2212yes—
146#2485C2214yes—
147#2485C2212yes—
148#2479C2218yes—
149#2475C2218yes—
150#2467C2218yes—
151#2460C2218yes—
152#2454C2214yes—
153#2446C2214yes—
154#2441C2214yes—
155#2436C2212yes—
156#2432C2218yes—
157#2432C2214yes—
158#2430C2218yes—
159#2428C2214yes—
160#2427C2214yes—
161#2427C2214yes—
162#2423C2214yes—
163#2416C2214yes—
164#2416C2214yes—
165#2415C2214yes—
166#2414C2214yes—
167#2409C2212yes—
168#2407C2214yes—
169#2407C2212yes—
170#2407C2214yes—
171#2407C2214yes—
172#2406C2214yes—
173#2396C2214yes—
174#2395C2212yes—
175#2388C2212yes—
176#2355C2212yes—
177#2352C2214yes—
178D4×C4⋊C4C2212yes—
179#2346C2212yes—
180#2343C2214yes—
181#2339C2212yes—
182#2326C2214yes—
183#2324C2214yes—
184#2324C2214yes—
185#2323C2214yes—
186#2320C2212yes—
187#2318C2214yes—
188#2316C2214yes—
189#2311C2214yes—
190C4×C22⋊Q8C2214yes—
191C4×C22⋊Q8C2212yes—
192C4×#121C2212yes—
193#2297C2212yes—
194#2296C2212yes—
195#2290C2214yes—
196#2285C2211yescharacteristic
197#2283C2211yescharacteristic
198#2283C2212yes—
199C2×#382C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2312yes—
205C22×#41C2312yes—
206C22×#41C2314yes—
207C22×#41C2311yescharacteristic
208C23×Q8C2311yescharacteristic
209Q82—28no—
210#555—28no—
211#555—216no—
212#555—216no—
213#555—232no—
214#550—216no—
215#550—28no—
216#550—216no—
217#550—28no—
218#544—28no—
219#542—216no—
220#542—216no—
221#541—216no—
222#541—216no—
223#539—232no—
224#537—28no—
225#536—28no—
226#536—28no—
227#533—216no—
228#533—216no—
229#532—232no—
230#532—216no—
231#532—28no—
232#532—216no—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2318yes—
242C2×#127C2311yescharacteristic
243C2×#127C2312yes—
244C2×#127C2314yes—
245C2×#127C2312yes—
246#529—232no—
247#529—216no—
248#529—216no—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2314yes—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2318yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2318yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×#121C2314yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2318yes—
305C2×#121C2318yes—
306C4×#41—216no—
307C4×#41—28no—
308C4×#41—28no—
309C4×#41—216no—
310C4×#41D4116yescomplemented
311C2×C4×Q8—28no—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2314yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×C4×D4C2311yescharacteristic
348C2×#117C2314yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2312yes—
352C2×#117C2312yes—
353C2×#117C2314yes—
354C2×#117C2311yescharacteristic
355C2×#117C2312yes—
356C2×#117C2314yes—
357C2×#117C2311yescharacteristic
358C2×#117C2312yes—
359C2×#117C2312yes—
360C2×#117C2311yescharacteristic
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2311yescharacteristic
363C22×C4⋊C4C2314yes—
364C22×C42C2314yes—
365C22×C42C2312yes—
366C22×C42C2312yes—
367C22×C42C2312yes—
368C22×C42C2311yescharacteristic
369C22×C42C2312yes—
370#400C2312yes—
371#400C2314yes—
372#400C2318yes—
373#400C2318yes—
374#399C2312yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2318yes—
380#399C2318yes—
381#399C2318yes—
382#399C2318yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#398C2312yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2318yes—
391#397C2318yes—
392#397C2318yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#395C2312yes—
397#395C2314yes—
398#395C2318yes—
399#395C2318yes—
400#395C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2318yes—
405#394C2318yes—
406#394C2318yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2312yes—
411#394C2314yes—
412#394C2314yes—
413#394C2318yes—
414#394C2318yes—
415#394C2318yes—
416#394C2318yes—
417#394C2318yes—
418#393C2312yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2318yes—
424#393C2318yes—
425#392C2312yes—
426#392C2314yes—
427#392C2318yes—
428#392C2314yes—
429#392C2318yes—
430#392C2318yes—
431#392C2318yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2318yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2318yes—
444#390C2318yes—
445#390C2314yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2318yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2318yes—
456#389C2318yes—
457#389C2314yes—
458#389C2318yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2314yes—
471#388C2318yes—
472#388C2314yes—
473#388C2314yes—
474#387C2314yes—
475#387C2318yes—
476#387C2318yes—
477#387C2318yes—
478#387C2318yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2314yes—
483#387C2314yes—
484#386C2318yes—
485#386C2318yes—
486#386C2318yes—
487#386C2314yes—
488#386C2314yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2314yes—
493#386C2314yes—
494#386C2318yes—
495#386C2314yes—
496#386C2318yes—
497#386C2318yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2314yes—
505#385C2314yes—
506#385C2318yes—
507#385C2318yes—
508#385C2314yes—
509#385C2318yes—
510#385C2314yes—
511#385C2314yes—
512#384C2314yes—
513#384C2312yes—
514#383C2314yes—
515#383C2312yes—
516#382C2314yes—
517#382C2314yes—
518#382C2311yescharacteristic
519#382C2311yescharacteristic
520#382C2312yes—
521#382C2314yes—
522#381C2314yes—
523#381C2312yes—
524#380C2318yes—
525#380C2318yes—
526#380C2318yes—
527#380C2318yes—
528#380C2312yes—
529#380C2314yes—
530#380C2312yes—
531#380C2314yes—
532#380C2312yes—
533#380C2312yes—
534#380C2314yes—
535#380C2312yes—
536#380C2314yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2318yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2318yes—
550#376C2312yes—
551#376C2314yes—
552C2×#95C2314yes—
553C2×#95C2314yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—24no—
557C2×#41—24no—
558C2×#41—24no—
559C2×#41—28no—
560C2×#41—28no—
561C2×#41—216no—
562C2×#41—44no—
563C2×#41—44no—
564C2×#41—42no—
565C2×#41—44no—
566C2×#41—48no—
567C2×#41—88no—
568C2×#41—84no—
569C2×#41C2×D418yes—
570C22×Q8—24no—
571C22×Q8—44no—
572C22×Q8C2412yes—
573C22×Q8C2411yescharacteristic
574C22×Q8C2411yescharacteristic
575C22×Q8C2412yes—
576C22×Q8C2411yescharacteristic
577C22×Q8C2414yes—
578C22×Q8C2412yes—
579C22×Q8C2414yes—
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2411yescharacteristic
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2411yescharacteristic
586C22×D4C2412yes—
587C22×D4C2411yescharacteristic
588C22×D4C2414yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2412yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C22×D4C2414yes—
596C22×D4C2418yes—
597C22×D4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2414yes—
603C23×C4C2412yes—
604C23×C4C2411yescharacteristic
605C23×C4C2411yescharacteristic
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2414yes—
609C23×C4C2414yes—
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2418yes—
613C23×C4C2411yescharacteristic
614C23×C4C2412yes—
615C23×C4C2412yes—
616C4⋊Q8—28no—
617C4⋊Q8—216no—
618C4⋊Q8—28no—
619C4⋊Q8—28no—
620C4⋊Q8—24no—
621C4⋊Q8—28no—
622C4⋊Q8—28no—
623C4⋊Q8—28no—
624C4⋊Q8—88no—
625#127—28no—
626#127—216no—
627#127—24no—
628#127—28no—
629#126—216no—
630#126—216no—
631#126—216no—
632#126—216no—
633#125—216no—
634#125—28no—
635#125—216no—
636#125—28no—
637#125—216no—
638#124—28no—
639#124—216no—
640#124—216no—
641#124—216no—
642#124—216no—
643#124—28no—
644#124—28no—
645#124—216no—
646#124—48no—
647#124—88no—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—216no—
652#123—88no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—216no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—48no—
664C22⋊Q8—84no—
665#121—216no—
666#121—28no—
667#121—28no—
668#121—216no—
669#121—28no—
670#121—28no—
671#121—28no—
672#121—28no—
673#121—28no—
674#121—216no—
675#121—216no—
676#121—28no—
677#121—216no—
678#121—216no—
679#121—216no—
680#121—44no—
681#121—48no—
682#121—48no—
683#121—88no—
684#121—88no—
685#121—84no—
686C4×Q8—28no—
687C4×Q8—28no—
688C4×Q8—28no—
689C4×Q8—28no—
690C4×Q8—28no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—28no—
696C4×Q8—216no—
697C4×Q8C2×D418yes—
698C4×Q8C2×D418yes—
699C4×D4—28no—
700C4×D4—28no—
701C4×D4—216no—
702C4×D4—28no—
703C4×D4—28no—
704C4×D4—216no—
705C4×D4—216no—
706C4×D4—28no—
707C4×D4—216no—
708C4×D4—24no—
709C4×D4—28no—
710C4×D4—216no—
711C4×D4—28no—
712C4×D4—24no—
713C4×D4—24no—
714C4×D4—24no—
715C4×D4—28no—
716C4×D4—48no—
717C4×D4—48no—
718C4×D4C2×D418yes—
719C4×D4C2×D4116yes—
720C4×D4C2×D4116yes—
721C4×D4C2×D418yes—
722#117—24no—
723#117—24no—
724#117—28no—
725#117—216no—
726#117—28no—
727#117—216no—
728#117—28no—
729#117—28no—
730#117—216no—
731#117—216no—
732#117—44no—
733#117C2×D418yes—
734#117C2×D4116yes—
735C2×C4⋊C4—24no—
736C2×C4⋊C4—28no—
737C2×C4⋊C4—48no—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2418yes—
773C2×C4⋊C4C2418yes—
774C2×C4⋊C4C2418yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C42—28no—
821C2×C42—28no—
822C2×C42—216no—
823C2×C42—28no—
824C2×C42C2×D418yes—
825C2×C42C2×D4116yes—
826C2×C42C2412yes—
827C2×C42C2414yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2414yes—
834C2×C42C2414yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2414yes—
838C2×C42C2418yes—
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2411yescharacteristic
844C2×C42C2412yes—
845C2×C42C2411yescharacteristic
846#95C2412yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2418yes—
851#95C2418yes—
852#95C2412yes—
853#95C2414yes—
854#95C2412yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2418yes—
860#95C2418yes—
861#95C2414yes—
862#95C2418yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869#95C2418yes—
870#95C2418yes—
871#95C2418yes—
872C24C2512yes—
873C24C2512yes—
874C24C2514yes—
875C24C2511yescharacteristic
876C24C2512yes—
877#41—416no—
878#41—432no—
879#41—416no—
880#41—416no—
881#41—432no—
882#41—816no—
883#41—832no—
884C2×Q8—22no—
885C2×Q8—24no—
886C2×Q8—24no—
887C2×Q8—22no—
888C2×Q8—28no—
889C2×Q8—24no—
890C2×Q8—28no—
891C2×Q8—24no—
892C2×Q8—22no—
893C2×Q8—24no—
894C2×Q8—24no—
895C2×Q8—44no—
896C2×Q8—42no—
897C2×Q8—44no—
898C2×Q8—44no—
899C2×Q8—44no—
900C2×Q8—48no—
901C2×Q8—416no—
902C2×Q8C22×D414yes—
903C2×Q82−1+414yes—
904C2×D4—24no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—22no—
912C2×D4—28no—
913C2×D4—24no—
914C2×D4—22no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—28no—
918C2×D4—28no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—22no—
922C2×D4—24no—
923C2×D4—22no—
924C2×D4—24no—
925C2×D4—28no—
926C2×D4—42no—
927C2×D4—44no—
928C2×D4—42no—
929C2×D4—44no—
930C2×D4—48no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—48no—
940C2×D4—48no—
941C2×D4—48no—
942C2×D4—48no—
943C2×D4—48no—
944C2×D4—48no—
945C2×D4—48no—
946C2×D4C22×D414yes—
947C2×D4C22×D418yes—
948C22×C4—24no—
949C22×C4—22no—
950C22×C4—24no—
951C22×C4—22no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—28no—
958C22×C4—28no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—28no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—28no—
966C22×C4—24no—
967C22×C4—28no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—44no—
972C22×C4—42no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—48no—
976C22×C4—44no—
977C22×C4—42no—
978C22×C4—44no—
979C22×C4—48no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—44no—
983C22×C4—48no—
984C22×C4—48no—
985C22×C4—48no—
986C22×C4C22×D414yes—
987C22×C4C22×D414yes—
988C22×C4C22×D418yes—
989C22×C4C22×D414yes—
990C22×C4C22×D418yes—
991C22×C4C22×D418yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2518yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2514yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2514yes—
1001C22×C4C2512yes—
1002C22×C4C2514yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2512yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2512yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—22no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—24no—
1027C4⋊C4—22no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—24no—
1038C4⋊C4—28no—
1039C4⋊C4—24no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—48no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—48no—
1046C4⋊C4—48no—
1047C4⋊C4—48no—
1048C4⋊C4—48no—
1049C4⋊C4—48no—
1050C4⋊C4—44no—
1051C4⋊C4C22×D414yes—
1052C4⋊C4C22×D418yes—
1053C4⋊C4C22×D418yes—
1054C4⋊C4C22×D414yes—
1055C22⋊C4—28no—
1056C22⋊C4—24no—
1057C22⋊C4—24no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—24no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—24no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—44no—
1075C22⋊C4—48no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—48no—
1079C22⋊C4—44no—
1080C22⋊C4—48no—
1081C22⋊C4—44no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—48no—
1087C22⋊C4—44no—
1088C22⋊C4—48no—
1089C22⋊C4—48no—
1090C22⋊C4—48no—
1091C22⋊C4—44no—
1092C22⋊C4C22×D418yes—
1093C22⋊C4C22×D418yes—
1094C22⋊C4C22×D418yes—
1095C42—24no—
1096C42—24no—
1097C42—28no—
1098C42—28no—
1099C42—24no—
1100C42—24no—
1101C42—28no—
1102C42—24no—
1103C42—24no—
1104C42—28no—
1105C42—28no—
1106C42—44no—
1107C42—48no—
1108C42C22×D414yes—
1109C42C22×D418yes—
1110C42C22×D414yes—
1111C42C22×D414yes—
1112C42C22×D414yes—
1113C42C22×D418yes—
1114C42C22×D418yes—
1115C23—21no—
1116C23—22no—
1117C23—21no—
1118C23—24no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—24no—
1123C23—22no—
1124C23—24no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—24no—
1129C23—24no—
1130C23—28no—
1131C23—22no—
1132C23—22no—
1133C23—24no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—24no—
1138C23—28no—
1139C23—22no—
1140C23C23×D414yes—
1141C23C23×D412yes—
1142C23C2611yescharacteristic
1143Q8—28no—
1144Q8—28no—
1145Q8—48no—
1146Q8—44no—
1147Q8—48no—
1148Q8—88no—
1149Q8—84no—
1150Q8—88no—
1151D4—28no—
1152D4—48no—
1153D4—48no—
1154D4—416no—
1155D4—44no—
1156D4—416no—
1157D4—48no—
1158D4—48no—
1159D4—44no—
1160D4—48no—
1161D4—84no—
1162D4—88no—
1163D4—88no—
1164D4—88no—
1165D4—88no—
1166D4—88no—
1167D4—88no—
1168D4—168no—
1169C2×C4—22no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—28no—
1181C2×C4—216no—
1182C2×C4—28no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—28no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—28no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—28no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—28no—
1212C2×C4—22no—
1213C2×C4—48no—
1214C2×C4—44no—
1215C2×C4—48no—
1216C2×C4—48no—
1217C2×C4—416no—
1218C2×C4—416no—
1219C2×C4—48no—
1220C2×C4—416no—
1221C2×C4—48no—
1222C2×C4—48no—
1223C2×C4—48no—
1224C2×C4—48no—
1225C2×C4—84no—
1226C2×C4—84no—
1227C2×C4—168no—
1228C2×C4C23×D412yes—
1229C2×C4C23×D412yes—
1230C2×C4C23×D414yes—
1231C2×C4C23×D412yes—
1232C2×C4C23×D414yes—
1233C2×C4C23×D412yes—
1234C2×C4C23×D414yes—
1235C2×C4C23×D412yes—
1236C2×C4C23×D412yes—
1237C2×C4C2×2−1+414yes—
1238C2×C4C2×2−1+412yes—
1239C2×C4#58514yes—
1240C2×C4#58512yes—
1241C22—22no—
1242C22—24no—
1243C22—22no—
1244C22—24no—
1245C22—22no—
1246C22—24no—
1247C22—44no—
1248C22—42no—
1249C22—44no—
1250C22—42no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—42no—
1257C22—44no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—44no—
1263C22—48no—
1264C22—42no—
1265C22—44no—
1266C22—42no—
1267C22—48no—
1268C22C24×D411yescharacteristic
1269C22C22×2−1+411yescharacteristic
1270C22C2×#58511yescharacteristic
1271C22C2×#58512yes—
1272C22H(7,𝔽2)12yes—
1273C4—22no—
1274C4—24no—
1275C4—24no—
1276C4—22no—
1277C4—22no—
1278C4—24no—
1279C4—22no—
1280C4—24no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—44no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—44no—
1289C4—44no—
1290C4—44no—
1291C4—48no—
1292C4#344914yes—
1293C4#348914yes—
1294C2—42no—
1295C2—44no—
1296C2—82no—
1297C2—84no—
1298C2—82no—
1299C2C2×#344911yescharacteristic
1300C2C2×#348911yescharacteristic
1301C2#6285211yescharacteristic
1302C2#6295212yes—
1303C2#6296612yes—
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×#3483C2semidirect
2. C2×#3461C2semidirect
3. #42995C2semidirect
4. #42968C2semidirect
5. #42913C2semidirect
6. #42909C2semidirect
7. #42307C2semidirect
8. #42303C2semidirect
9. #39725C2semidirect
10. #39597C2semidirect
11. #38922C2semidirect
12. #38909C2semidirect
13. #38050C2semidirect
14. #38033C2semidirect
15. #37619C2semidirect
16. #37554C2semidirect
17. #37234C2semidirect
18. #35607C2semidirect
19. #35334C2semidirect
20. #35292C2semidirect
21. #35249C2semidirect
22. #35210C2semidirect
23. #35205C2semidirect
24. #34952C2semidirect
25. #34909C2semidirect
26. #34191C2semidirect
310. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34832
C2×#34612
#429952
#429682
#429132
#429092
#423072
#423032
#397252
#395972
#389222
#389092
#380502
#380332
#376192
#375542
#372342
#356072
#353342
#352922
#352492
#352102
#352052
#349522
#349092
#341912