Finite Group Databasebeta

← #7646524

Subgroups — #7646524

Order 512.

6768 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#42985C212yesmaximal, complemented
4#42944C212yesmaximal, complemented
5#42913C212yesmaximal, complemented
6#42910C212yesmaximal, complemented
7#42393C214yesmaximal, complemented
8#42391C214yesmaximal, complemented
9#39725C212yesmaximal, complemented
10#39724C212yesmaximal, complemented
11#38909C212yesmaximal, complemented
12#38908C212yesmaximal, complemented
13#38033C214yesmaximal, complemented
14#38032C214yesmaximal, complemented
15#37559C212yesmaximal, complemented
16#37551C212yesmaximal, complemented
17#36746C218yesmaximal, complemented
18#35625C214yesmaximal, complemented
19#35292C211yesmaximal, characteristic, complemented
20#35247C211yesmaximal, characteristic, complemented
21#35234C212yesmaximal, complemented
22#35180C212yesmaximal, complemented
23#35169C214yesmaximal, complemented
24#34955C211yesmaximal, characteristic, complemented
25#34911C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27#3517—216no—
28C2×#557C2211yescharacteristic
29C2×#553C2214yes—
30C2×#553C2212yes—
31C2×#550C2211yescharacteristic
32C2×#550C2212yes—
33C2×#550C2212yes—
34C2×#550C2211yescharacteristic
35C2×#547C2212yes—
36C2×#547C2211yescharacteristic
37#3461—216no—
38C2×#544C2211yescharacteristic
39C2×#542C2212yes—
40C2×#542C2212yes—
41C2×#541C2212yes—
42C2×#541C2212yes—
43C2×#540C2212yes—
44C2×#540C2214yes—
45C2×#539C2214yes—
46C2×#537C2211yescharacteristic
47C2×#536C2211yescharacteristic
48C2×#536C2211yescharacteristic
49C2×#533C2212yes—
50C2×#533C2212yes—
51C2×#532C2212yes—
52C2×#532C2211yescharacteristic
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C2×#529C2214yes—
56C2×#529C2212yes—
57C2×#529C2212yes—
58C2×#520C2212yes—
59C2×C4×#41C2211yescharacteristic
60C2×C4×#41C2211yescharacteristic
61C22×C4×Q8C2211yescharacteristic
62#2857C2212yes—
63#2856C2212yes—
64#2855C2212yes—
65#2854C2218yes—
66#2854C2212yes—
67#2850C2218yes—
68#2821C2214yes—
69#2821C2214yes—
70#2816C2214yes—
71#2815C2214yes—
72#2719C2218yes—
73#2711C2218yes—
74#2709C2218yes—
75#2708C2218yes—
76#2706C2218yes—
77#2703C2218yes—
78#2695C2218yes—
79#2693C2218yes—
80#2691C2218yes—
81#2690C2218yes—
82#2688C2218yes—
83#2687C2218yes—
84#2676C2218yes—
85#2673C2218yes—
86#2672C2218yes—
87#2671C2218yes—
88#2664C2214yes—
89#2663C2218yes—
90#2662C2214yes—
91#2661C2218yes—
92#2639C2214yes—
93#2639C2214yes—
94#2638C2214yes—
95#2638C2214yes—
96#2637C2214yes—
97#2633C2214yes—
98#2631C2214yes—
99#2625C2214yes—
100#2624C2214yes—
101#2624C2212yes—
102#2621C2214yes—
103#2619C2214yes—
104#2615C2212yes—
105#2611C2218yes—
106#2604C2212yes—
107#2603C2218yes—
108#2603C2212yes—
109#2602C2214yes—
110#2601C2218yes—
111#2592C2211yescharacteristic
112#2592C2212yes—
113#2592C2212yes—
114#2592C2212yes—
115#2592C2212yes—
116#2591C2214yes—
117#2584C2211yescharacteristic
118#2584C2212yes—
119#2582C2212yes—
120#2581C2214yes—
121#2580C2214yes—
122#2580C2212yes—
123#2568C2214yes—
124#2568C2212yes—
125#2564C2214yes—
126#2563C2214yes—
127#2562C2218yes—
128#2562C2211yescharacteristic
129#2559C2218yes—
130#2557C2218yes—
131#2555C2218yes—
132#2553C2218yes—
133#2550C2214yes—
134#2548C2214yes—
135#2548C2212yes—
136#2547C2214yes—
137#2544C2214yes—
138#2543C2214yes—
139#2540C2214yes—
140#2540C2211yescharacteristic
141#2540C2212yes—
142#2538C2212yes—
143#2535C2214yes—
144#2535C2212yes—
145#2504C2212yes—
146#2491C2214yes—
147#2489C2214yes—
148#2486C2212yes—
149#2481C2218yes—
150#2473C2218yes—
151#2467C2218yes—
152#2460C2218yes—
153#2454C2214yes—
154#2446C2214yes—
155#2442C2214yes—
156#2436C2212yes—
157#2432C2214yes—
158#2428C2214yes—
159#2427C2214yes—
160#2427C2214yes—
161#2421C2214yes—
162#2417C2214yes—
163#2417C2214yes—
164#2416C2214yes—
165#2415C2212yes—
166#2414C2212yes—
167#2414C2214yes—
168#2413C2214yes—
169#2409C2212yes—
170#2407C2214yes—
171#2407C2214yes—
172#2407C2214yes—
173#2407C2214yes—
174#2398C2214yes—
175#2395C2212yes—
176#2388C2212yes—
177#2355C2212yes—
178#2352C2214yes—
179D4×C4⋊C4C2212yes—
180#2347C2212yes—
181#2343C2214yes—
182#2339C2212yes—
183#2324C2214yes—
184#2324C2214yes—
185#2323C2214yes—
186#2323C2214yes—
187#2311C2214yes—
188#2311C2214yes—
189C4×#124C2214yes—
190C4×C22⋊Q8C2212yes—
191C4×#121C2212yes—
192#2297C2214yes—
193#2295C2212yes—
194#2293C2214yes—
195#2290C2214yes—
196#2285C2211yescharacteristic
197#2283C2212yes—
198C42×D4C2212yes—
199C4×#117C2211yescharacteristic
200C2×C4×C4⋊C4C2212yes—
201C22×#41C2312yes—
202C22×#41C2312yes—
203C22×#41C2311yescharacteristic
204C22×#41C2312yes—
205C22×#41C2312yes—
206C22×#41C2311yescharacteristic
207C23×Q8C2311yescharacteristic
208#557—28no—
209#553—216no—
210#553—232no—
211#550—216no—
212#550—28no—
213#550—216no—
214#550—28no—
215#547—216no—
216#547—28no—
217#544—28no—
218#542—216no—
219#542—216no—
220#541—216no—
221#541—216no—
222#540—232no—
223#540—216no—
224#539—232no—
225#537—28no—
226#536—28no—
227#536—28no—
228#533—216no—
229#533—216no—
230#532—28no—
231#532—216no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×#127C2311yescharacteristic
239C2×#127C2312yes—
240C2×#127C2314yes—
241C2×#127C2312yes—
242#529—232no—
243#529—216no—
244#529—216no—
245#529—28no—
246#529—216no—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2312yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2314yes—
254C2×#125C2311yescharacteristic
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2312yes—
261C2×#124C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2318yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2312yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2311yescharacteristic
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C2×#121C2312yes—
311C2×#121C2318yes—
312C2×#121C2314yes—
313#520—216no—
314C4×#41—28no—
315C4×#41D4116yescomplemented
316C2×C4×Q8—28no—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×D4C2314yes—
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2311yescharacteristic
350C2×#117C2314yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2312yes—
354C2×#117C2314yes—
355C2×#117C2311yescharacteristic
356C2×#117C2312yes—
357C2×#117C2312yes—
358C2×#117C2312yes—
359C2×#117C2311yescharacteristic
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2311yescharacteristic
362C22×C4⋊C4C2312yes—
363C22×C4⋊C4C2314yes—
364C22×C4⋊C4C2314yes—
365C22×C42C2312yes—
366C22×C42C2312yes—
367C22×C42C2314yes—
368C22×C42C2311yescharacteristic
369C22×C42C2312yes—
370#400C2312yes—
371#400C2318yes—
372#400C2318yes—
373#400C2318yes—
374#400C2318yes—
375#400C2318yes—
376#399C2312yes—
377#399C2314yes—
378#399C2318yes—
379#399C2318yes—
380#398C2318yes—
381#398C2312yes—
382#398C2314yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#398C2318yes—
387#397C2314yes—
388#397C2314yes—
389#397C2318yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2318yes—
395#397C2318yes—
396#397C2318yes—
397#397C2318yes—
398#396C2318yes—
399#396C2318yes—
400#396C2318yes—
401#395C2314yes—
402#395C2312yes—
403#395C2318yes—
404#394C2318yes—
405#394C2318yes—
406#394C2318yes—
407#394C2312yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#394C2318yes—
412#394C2314yes—
413#394C2314yes—
414#394C2318yes—
415#394C2318yes—
416#394C2318yes—
417#394C2318yes—
418#393C2314yes—
419#393C2314yes—
420#393C2312yes—
421#393C2314yes—
422#393C2314yes—
423#393C2318yes—
424#392C2314yes—
425#392C2318yes—
426#392C2312yes—
427#392C2314yes—
428#392C2318yes—
429#392C2318yes—
430#392C2318yes—
431#392C2318yes—
432#391C2312yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2318yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#390C2318yes—
442#390C2312yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2318yes—
447#390C2318yes—
448#390C2314yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2318yes—
457#389C2318yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#388C2314yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2314yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2314yes—
477#388C2318yes—
478#388C2314yes—
479#388C2314yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2314yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2314yes—
498#386C2318yes—
499#386C2314yes—
500#386C2318yes—
501#386C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2314yes—
508#385C2314yes—
509#385C2318yes—
510#385C2318yes—
511#384C2312yes—
512#383C2314yes—
513#382C2318yes—
514#382C2314yes—
515#382C2314yes—
516#382C2312yes—
517#381C2314yes—
518#381C2314yes—
519#380C2318yes—
520#380C2318yes—
521#380C2318yes—
522#380C2318yes—
523#380C2312yes—
524#380C2312yes—
525#380C2318yes—
526#380C2314yes—
527#380C2314yes—
528#380C2312yes—
529#380C2312yes—
530#380C2314yes—
531#380C2314yes—
532C4×C4⋊C4C2314yes—
533C4×C4⋊C4C2311yescharacteristic
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2311yescharacteristic
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2312yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2318yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2318yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550#376C2312yes—
551#376C2314yes—
552C2×#95C2314yes—
553C43C2312yes—
554C2×#41—28no—
555C2×#41—24no—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—44no—
560C2×#41—44no—
561C2×#41—48no—
562C2×#41—48no—
563C2×#41—48no—
564C2×#41—48no—
565C2×#41C2×D418yes—
566C22×Q8—24no—
567C22×Q8—44no—
568C22×Q8C2412yes—
569C22×Q8C2412yes—
570C22×Q8C2411yescharacteristic
571C22×Q8C2411yescharacteristic
572C22×Q8C2412yes—
573C22×Q8C2411yescharacteristic
574C22×Q8C2414yes—
575C22×D4C2412yes—
576C22×D4C2412yes—
577C22×D4C2411yescharacteristic
578C22×D4C2411yescharacteristic
579C22×D4C2412yes—
580C22×D4C2411yescharacteristic
581C22×D4C2414yes—
582C22×D4C2412yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2414yes—
586C22×D4C2412yes—
587C22×D4C2414yes—
588C22×D4C2414yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2418yes—
592C22×D4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2412yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2412yes—
605C23×C4C2412yes—
606C23×C4C2418yes—
607C23×C4C2411yescharacteristic
608C23×C4C2412yes—
609C23×C4C2412yes—
610C4⋊Q8—28no—
611C4⋊Q8—28no—
612C4⋊Q8—24no—
613C4⋊Q8—28no—
614C4⋊Q8—28no—
615C4⋊Q8—28no—
616#127—28no—
617#127—216no—
618#127—24no—
619#127—28no—
620#126—216no—
621#126—216no—
622#126—216no—
623#126—216no—
624#126—28no—
625#126—216no—
626#125—216no—
627#125—28no—
628#125—216no—
629#125—216no—
630#125—28no—
631#125—24no—
632#125—28no—
633#125—216no—
634#124—28no—
635#124—216no—
636#124—24no—
637#124—28no—
638#124—28no—
639#124—48no—
640#124—88no—
641#123—216no—
642#123—216no—
643#123—28no—
644#123—216no—
645#123—216no—
646#123—216no—
647#123—216no—
648#123—216no—
649#123—216no—
650#123—84no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—24no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—216no—
658C22⋊Q8—28no—
659C22⋊Q8—28no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—48no—
663C22⋊Q8—44no—
664C22⋊Q8—48no—
665#121—216no—
666#121—28no—
667#121—28no—
668#121—216no—
669#121—28no—
670#121—24no—
671#121—28no—
672#121—28no—
673#121—216no—
674#121—28no—
675#121—216no—
676#121—216no—
677#121—28no—
678#121—216no—
679#121—216no—
680#121—216no—
681#121—48no—
682#121—44no—
683#121—48no—
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—216no—
694C4×Q8—24no—
695C4×Q8—28no—
696C4×Q8C2×D418yes—
697C4×Q8C2×D418yes—
698C4×D4—28no—
699C4×D4—28no—
700C4×D4—216no—
701C4×D4—28no—
702C4×D4—216no—
703C4×D4—28no—
704C4×D4—216no—
705C4×D4—24no—
706C4×D4—24no—
707C4×D4—28no—
708C4×D4—216no—
709C4×D4—24no—
710C4×D4—28no—
711C4×D4—28no—
712C4×D4—216no—
713C4×D4—48no—
714C4×D4—48no—
715C4×D4C2×D418yes—
716C4×D4C2×D4116yes—
717C4×D4C2×D4116yes—
718C4×D4C2×D418yes—
719#117—24no—
720#117—216no—
721#117—28no—
722#117—28no—
723#117—216no—
724#117—216no—
725#117—44no—
726#117—82no—
727#117C2×D418yes—
728#117C2×D4116yes—
729C2×C4⋊C4—24no—
730C2×C4⋊C4—28no—
731C2×C4⋊C4—28no—
732C2×C4⋊C4—216no—
733C2×C4⋊C4—48no—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2418yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C42—28no—
820C2×C42—28no—
821C2×C42—84no—
822C2×C42C2×D418yes—
823C2×C42C2×D4116yes—
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2412yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2412yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2418yes—
835C2×C42C2412yes—
836C2×C42C2412yes—
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839C2×C42C2412yes—
840C2×C42C2412yes—
841C2×C42C2412yes—
842C2×C42C2411yescharacteristic
843C2×C42C2411yescharacteristic
844#95C2412yes—
845#95C2414yes—
846#95C2418yes—
847#95C2412yes—
848#95C2414yes—
849#95C2418yes—
850#95C2418yes—
851#95C2414yes—
852#95C2418yes—
853#95C2414yes—
854#95C2414yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2414yes—
859#95C2418yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869C24C2512yes—
870C24C2512yes—
871C24C2514yes—
872C24C2511yescharacteristic
873C24C2512yes—
874#41—416no—
875#41—416no—
876#41—432no—
877#41—816no—
878#41—816no—
879#41—816no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—22no—
883C2×Q8—22no—
884C2×Q8—24no—
885C2×Q8—28no—
886C2×Q8—24no—
887C2×Q8—24no—
888C2×Q8—28no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—416no—
896C2×Q8C22×D414yes—
897C2×D4—24no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—24no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—22no—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—22no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—28no—
911C2×D4—24no—
912C2×D4—28no—
913C2×D4—24no—
914C2×D4—28no—
915C2×D4—42no—
916C2×D4—44no—
917C2×D4—48no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—42no—
932C2×D4—44no—
933C2×D4—48no—
934C2×D4—48no—
935C2×D4—48no—
936C2×D4—48no—
937C2×D4—48no—
938C2×D4—48no—
939C2×D4C22×D414yes—
940C2×D4C22×D418yes—
941C22×C4—28no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—28no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—28no—
957C22×C4—28no—
958C22×C4—28no—
959C22×C4—42no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—42no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—48no—
966C22×C4—48no—
967C22×C4—48no—
968C22×C4—48no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—48no—
974C22×C4—48no—
975C22×C4—48no—
976C22×C4C22×D414yes—
977C22×C4C22×D414yes—
978C22×C4C22×D418yes—
979C22×C4C22×D414yes—
980C22×C4C22×D418yes—
981C22×C4C22×D418yes—
982C22×C4C2514yes—
983C22×C4C2514yes—
984C22×C4C2518yes—
985C22×C4C2512yes—
986C22×C4C2514yes—
987C22×C4C2512yes—
988C22×C4C2514yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2514yes—
992C22×C4C2512yes—
993C22×C4C2512yes—
994C22×C4C2511yescharacteristic
995C22×C4C2512yes—
996C22×C4C2511yescharacteristic
997C22×C4C2512yes—
998C22×C4C2511yescharacteristic
999C22×C4C2512yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2511yescharacteristic
1003C4⋊C4—24no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—24no—
1014C4⋊C4—22no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—22no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—22no—
1026C4⋊C4—24no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—24no—
1032C4⋊C4—28no—
1033C4⋊C4—24no—
1034C4⋊C4—28no—
1035C4⋊C4—48no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—48no—
1040C4⋊C4—44no—
1041C4⋊C4—48no—
1042C4⋊C4—48no—
1043C4⋊C4C22×D414yes—
1044C4⋊C4C22×D418yes—
1045C4⋊C4C22×D418yes—
1046C4⋊C4C22×D414yes—
1047C22⋊C4—24no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—28no—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—24no—
1062C22⋊C4—28no—
1063C22⋊C4—24no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—48no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—48no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—48no—
1074C22⋊C4—48no—
1075C22⋊C4—44no—
1076C22⋊C4—48no—
1077C22⋊C4—48no—
1078C22⋊C4—44no—
1079C22⋊C4—48no—
1080C22⋊C4—48no—
1081C22⋊C4—48no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—44no—
1085C22⋊C4C22×D418yes—
1086C22⋊C4C22×D418yes—
1087C22⋊C4C22×D418yes—
1088C42—28no—
1089C42—24no—
1090C42—24no—
1091C42—24no—
1092C42—28no—
1093C42—28no—
1094C42—24no—
1095C42—28no—
1096C42—42no—
1097C42—44no—
1098C42—48no—
1099C42—42no—
1100C42—44no—
1101C42C22×D414yes—
1102C42C22×D414yes—
1103C42C22×D414yes—
1104C42C22×D418yes—
1105C42C22×D418yes—
1106C42C22×D414yes—
1107C42C22×D418yes—
1108C23—22no—
1109C23—24no—
1110C23—24no—
1111C23—22no—
1112C23—21no—
1113C23—22no—
1114C23—21no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—24no—
1119C23—22no—
1120C23—24no—
1121C23—28no—
1122C23—22no—
1123C23—24no—
1124C23—28no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—24no—
1129C23—22no—
1130C23—24no—
1131C23—22no—
1132C23—22no—
1133C23C23×D414yes—
1134C23C23×D412yes—
1135C23C2611yescharacteristic
1136Q8—28no—
1137Q8—48no—
1138Q8—44no—
1139Q8—48no—
1140Q8—44no—
1141Q8—48no—
1142Q8—88no—
1143D4—28no—
1144D4—48no—
1145D4—44no—
1146D4—416no—
1147D4—48no—
1148D4—48no—
1149D4—44no—
1150D4—48no—
1151D4—84no—
1152D4—88no—
1153D4—88no—
1154D4—84no—
1155D4—88no—
1156D4—88no—
1157D4—88no—
1158D4—88no—
1159D4—88no—
1160D4—168no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—28no—
1172C2×C4—216no—
1173C2×C4—28no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—28no—
1191C2×C4—28no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—28no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—28no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—44no—
1208C2×C4—48no—
1209C2×C4—48no—
1210C2×C4—416no—
1211C2×C4—48no—
1212C2×C4—48no—
1213C2×C4—48no—
1214C2×C4—48no—
1215C2×C4—84no—
1216C2×C4—88no—
1217C2×C4—88no—
1218C2×C4—88no—
1219C2×C4—84no—
1220C2×C4—816no—
1221C2×C4C23×D412yes—
1222C2×C4C23×D412yes—
1223C2×C4C23×D414yes—
1224C2×C4C23×D412yes—
1225C2×C4C23×D412yes—
1226C2×C4C23×D414yes—
1227C2×C4C23×D414yes—
1228C2×C4C23×D412yes—
1229C2×C4C23×D412yes—
1230C2×C4#58514yes—
1231C2×C4#58514yes—
1232C22—22no—
1233C22—24no—
1234C22—22no—
1235C22—24no—
1236C22—22no—
1237C22—24no—
1238C22—42no—
1239C22—44no—
1240C22—44no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—42no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—48no—
1255C22—42no—
1256C22—48no—
1257C22—42no—
1258C22—44no—
1259C22C24×D411yescharacteristic
1260C22C2×#58512yes—
1261C22C2×#58512yes—
1262C22H(7,𝔽2)11yescharacteristic
1263C222−1+611yescharacteristic
1264C4—22no—
1265C4—24no—
1266C4—22no—
1267C4—22no—
1268C4—24no—
1269C4—22no—
1270C4—24no—
1271C4—42no—
1272C4—44no—
1273C4—42no—
1274C4—44no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—44no—
1280C4—44no—
1281C4—44no—
1282C4—48no—
1283C4#344914yes—
1284C4#350014yes—
1285C2—42no—
1286C2—44no—
1287C2—82no—
1288C2—82no—
1289C2—84no—
1290C2C2×#344911yescharacteristic
1291C2C2×#350011yescharacteristic
1292C2#6285311yescharacteristic
1293C2#6296712yes—
1294C2#6296912yes—
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×#3517C2semidirect
2. C2×#3461C2semidirect
3. #42985C2semidirect
4. #42944C2semidirect
5. #42913C2semidirect
6. #42910C2semidirect
7. #42393C2semidirect
8. #42391C2semidirect
9. #39725C2semidirect
10. #39724C2semidirect
11. #38909C2semidirect
12. #38908C2semidirect
13. #38033C2semidirect
14. #38032C2semidirect
15. #37559C2semidirect
16. #37551C2semidirect
17. #36746C2semidirect
18. #35625C2semidirect
19. #35292C2semidirect
20. #35247C2semidirect
21. #35234C2semidirect
22. #35180C2semidirect
23. #35169C2semidirect
24. #34955C2semidirect
25. #34911C2semidirect
26. #34127C2semidirect
315. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#34612
#429852
#429442
#429132
#429102
#423932
#423912
#397252
#397242
#389092
#389082
#380332
#380322
#375592
#375512
#367462
#356252
#352922
#352472
#352342
#351802
#351692
#349552
#349112
#341272