Finite Group Databasebeta

← #7655074

Subgroups — #7655074

Order 512.

6766 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42441C214yesmaximal, complemented
4#42299C218yesmaximal, complemented
5#39864C214yesmaximal, complemented
6#39851C218yesmaximal, complemented
7#39619C211yesmaximal, characteristic, complemented
8#39616C211yesmaximal, characteristic, complemented
9#39171C211yesmaximal, characteristic, complemented
10#39168C211yesmaximal, characteristic, complemented
11#38095C212yesmaximal, complemented
12#38091C212yesmaximal, complemented
13#37870C212yesmaximal, complemented
14#37869C212yesmaximal, complemented
15#37616C211yesmaximal, characteristic, complemented
16#37545C212yesmaximal, complemented
17#36443C214yesmaximal, complemented
18#36419C211yesmaximal, characteristic, complemented
19#36412C211yesmaximal, characteristic, complemented
20#36188C211yesmaximal, characteristic, complemented
21#36185C211yesmaximal, characteristic, complemented
22#35817C214yesmaximal, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35211C212yesmaximal, complemented
25#35179C211yesmaximal, characteristic, complemented
26#35103C212yesmaximal, complemented
27#34972C211yesmaximal, characteristic, complemented
28#34947C212yesmaximal, complemented
29#34127C211yesmaximal, characteristic, complemented
30#3518—216no—
31#3480—216no—
32C2×#559C2211yescharacteristic
33C2×#559C2212yes—
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#556C2211yescharacteristic
37C2×#556C2212yes—
38C2×#556C2214yes—
39C2×#556C2212yes—
40C2×#556C2211yescharacteristic
41C2×#556C2212yes—
42C2×#555C2211yescharacteristic
43C2×#555C2212yes—
44C2×#553C2214yes—
45C2×#553C2212yes—
46C2×#550C2211yescharacteristic
47C2×D4×Q8C2211yescharacteristic
48C2×#548C2212yes—
49C2×#548C2212yes—
50C2×#542C2214yes—
51C2×#542C2212yes—
52C2×#533C2211yescharacteristic
53C2×#533C2212yes—
54C2×#532C2212yes—
55C2×#532C2211yescharacteristic
56C2×#529C2212yes—
57C2×#529C2212yes—
58C2×#529C2211yescharacteristic
59C2×#529C2214yes—
60C2×#519C2212yes—
61C2×C4×#41C2212yes—
62C2×C4×#41C2212yes—
63C2×C4×#41C2211yescharacteristic
64C22×C4×Q8C2211yescharacteristic
65#2868C2211yescharacteristic
66#2862C2211yescharacteristic
67#2858C2211yescharacteristic
68#2858C2211yescharacteristic
69#2857C2212yes—
70#2856C2212yes—
71#2855C2214yes—
72#2852C2218yes—
73#2850C2212yes—
74#2850C2212yes—
75#2814C2218yes—
76#2813C2214yes—
77#2720C2218yes—
78#2715C2218yes—
79#2713C2218yes—
80#2712C2218yes—
81#2696C2218yes—
82#2695C2218yes—
83#2688C2218yes—
84#2686C2218yes—
85#2686C2218yes—
86#2674C2218yes—
87#2672C2218yes—
88#2671C2218yes—
89#2660C2212yes—
90#2660C2212yes—
91#2640C2212yes—
92#2640C2212yes—
93#2638C2218yes—
94#2637C2218yes—
95#2636C2214yes—
96#2630C2218yes—
97#2627C2214yes—
98#2620C2214yes—
99#2620C2214yes—
100#2620C2212yes—
101#2619C2212yes—
102#2618C2218yes—
103#2609C2218yes—
104#2604C2214yes—
105#2601C2218yes—
106#2601C2218yes—
107#2600C2218yes—
108#2599C2218yes—
109#2582C2214yes—
110#2581C2214yes—
111#2568C2211yescharacteristic
112#2568C2211yescharacteristic
113#2568C2211yescharacteristic
114#2568C2212yes—
115#2567C2211yescharacteristic
116#2567C2211yescharacteristic
117#2567C2212yes—
118#2566C2212yes—
119#2566C2212yes—
120#2566C2212yes—
121#2566C2212yes—
122#2565C2212yes—
123#2565C2212yes—
124#2565C2212yes—
125#2565C2211yescharacteristic
126#2565C2211yescharacteristic
127#2564C2218yes—
128#2563C2212yes—
129#2559C2218yes—
130#2555C2218yes—
131#2548C2211yescharacteristic
132#2547C2214yes—
133#2545C2212yes—
134#2545C2211yescharacteristic
135#2545C2211yescharacteristic
136#2545C2214yes—
137#2544C2212yes—
138#2544C2212yes—
139#2544C2214yes—
140#2542C2212yes—
141#2542C2211yescharacteristic
142#2541C2211yescharacteristic
143#2521C2218yes—
144#2503C2211yescharacteristic
145#2501C2211yescharacteristic
146#2500C2212yes—
147#2500C2212yes—
148#2500C2212yes—
149#2500C2212yes—
150#2500C2212yes—
151#2499C2212yes—
152#2499C2212yes—
153#2499C2212yes—
154#2496C2218yes—
155#2479C2218yes—
156#2477C2218yes—
157#2469C2218yes—
158#2468C2218yes—
159#2466C2218yes—
160#2465C2218yes—
161#2461C2218yes—
162#2459C2218yes—
163#2452C2214yes—
164#2451C2214yes—
165#2448C2214yes—
166#2446C2214yes—
167#2436C2214yes—
168#2436C2211yescharacteristic
169#2434C2211yescharacteristic
170#2434C2214yes—
171#2432C2212yes—
172#2432C2214yes—
173#2431C2212yes—
174#2429C2214yes—
175#2428C2214yes—
176#2427C2214yes—
177#2427C2214yes—
178#2417C2218yes—
179#2413C2214yes—
180#2407C2214yes—
181#2396C2218yes—
182#2396C2214yes—
183#2367C2214yes—
184#2365C2214yes—
185#2363C2214yes—
186#2362C2214yes—
187#2355C2212yes—
188#2352C2214yes—
189D4×C4⋊C4C2212yes—
190#2347C2212yes—
191#2343C2214yes—
192#2339C2212yes—
193#2328C2212yes—
194#2327C2212yes—
195#2326C2212yes—
196#2326C2212yes—
197#2326C2214yes—
198#2325C2218yes—
199#2317C2212yes—
200#2310C2212yes—
201C4×C4⋊Q8C2211yescharacteristic
202C4×C4⋊Q8C2211yescharacteristic
203C4×#124C2211yescharacteristic
204C4×#124C2211yescharacteristic
205C4×C22⋊Q8C2218yes—
206C4×#123C2214yes—
207#2297C2212yes—
208#2297C2212yes—
209#2295C2211yescharacteristic
210#2295C2211yescharacteristic
211#2290C2212yes—
212#2290C2212yes—
213#2285C2211yescharacteristic
214#2285C2212yes—
215#2285C2212yes—
216#2283C2212yes—
217C42×D4C2211yescharacteristic
218C42×D4C2211yescharacteristic
219C4×#117C2211yescharacteristic
220C2×C4×C4⋊C4C2212yes—
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2311yescharacteristic
224C23×Q8C2311yescharacteristic
225C23×Q8C2312yes—
226#559—28no—
227#559—216no—
228Q82—28no—
229#557—28no—
230#556—216no—
231#556—28no—
232#556—216no—
233#556—28no—
234#556—216no—
235#556—232no—
236#555—216no—
237#555—28no—
238#553—216no—
239#553—232no—
240#550—28no—
241D4×Q8—28no—
242#548—216no—
243#548—216no—
244#542—232no—
245#542—216no—
246#533—28no—
247#533—216no—
248#532—216no—
249#532—28no—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2314yes—
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2314yes—
261C2×#127C2311yescharacteristic
262C2×#127C2312yes—
263C2×#127C2312yes—
264#529—232no—
265#529—216no—
266#529—28no—
267#529—216no—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2311yescharacteristic
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#124C2311yescharacteristic
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2311yescharacteristic
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2312yes—
290C2×#124C2314yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2311yescharacteristic
295C2×#124C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2312yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2311yescharacteristic
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2318yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×#121C2311yescharacteristic
317C2×#121C2312yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2312yes—
324C2×#121C2318yes—
325C2×#121C2314yes—
326#519—216no—
327C4×#41—216no—
328C4×#41—216no—
329C4×#41D4116yescomplemented
330C2×C4×Q8—28no—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2314yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2314yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2314yes—
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×#117C2312yes—
372C2×#117C2314yes—
373C2×#117C2314yes—
374C2×#117C2314yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2314yes—
379C2×#117C2312yes—
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2311yescharacteristic
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2314yes—
388C22×C42C2314yes—
389C22×C42C2312yes—
390C22×C42C2312yes—
391C22×C42C2312yes—
392C22×C42C2311yescharacteristic
393C22×C42C2312yes—
394#400C2318yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#399C2318yes—
400#399C2314yes—
401#399C2314yes—
402#398C2318yes—
403#398C2318yes—
404#398C2318yes—
405#398C2314yes—
406#398C2314yes—
407#398C2318yes—
408#398C2318yes—
409#397C2318yes—
410#397C2318yes—
411#397C2318yes—
412#397C2318yes—
413#397C2318yes—
414#396C2318yes—
415#396C2318yes—
416#396C2318yes—
417#396C2318yes—
418#396C2314yes—
419#396C2318yes—
420#396C2314yes—
421#396C2318yes—
422#395C2318yes—
423#395C2314yes—
424#395C2314yes—
425#395C2318yes—
426#395C2314yes—
427#395C2318yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2318yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#394C2314yes—
437#394C2318yes—
438#394C2318yes—
439#393C2318yes—
440#393C2318yes—
441#393C2314yes—
442#393C2318yes—
443#392C2318yes—
444#392C2318yes—
445#392C2314yes—
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2311yescharacteristic
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2318yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2318yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2311yescharacteristic
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2314yes—
475#390C2311yescharacteristic
476#390C2318yes—
477#390C2314yes—
478#390C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2318yes—
484#389C2318yes—
485#389C2318yes—
486#389C2312yes—
487#389C2312yes—
488#388C2314yes—
489#388C2318yes—
490#388C2318yes—
491#388C2318yes—
492#388C2318yes—
493#388C2318yes—
494#388C2318yes—
495#388C2318yes—
496#388C2314yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#387C2314yes—
505#387C2318yes—
506#387C2318yes—
507#387C2318yes—
508#387C2314yes—
509#387C2318yes—
510#387C2318yes—
511#387C2318yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2318yes—
517#387C2318yes—
518#386C2318yes—
519#386C2318yes—
520#386C2318yes—
521#386C2318yes—
522#386C2318yes—
523#386C2318yes—
524#386C2318yes—
525#386C2318yes—
526#386C2314yes—
527#386C2314yes—
528#386C2318yes—
529#386C2314yes—
530#385C2318yes—
531#385C2318yes—
532#385C2318yes—
533#385C2318yes—
534#385C2318yes—
535#385C2318yes—
536#385C2318yes—
537#385C2318yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#384C2311yescharacteristic
542#384C2311yescharacteristic
543#384C2312yes—
544#384C2312yes—
545#384C2312yes—
546#384C2312yes—
547#384C2312yes—
548#384C2314yes—
549#384C2312yes—
550#383C2314yes—
551#382C2311yescharacteristic
552#382C2312yes—
553#382C2312yes—
554#382C2312yes—
555#382C2311yescharacteristic
556#382C2312yes—
557#382C2312yes—
558#382C2312yes—
559#382C2314yes—
560#381C2318yes—
561#381C2314yes—
562#381C2314yes—
563#380C2318yes—
564#380C2318yes—
565#380C2318yes—
566#380C2318yes—
567#380C2312yes—
568#380C2314yes—
569#380C2312yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2311yescharacteristic
575C4×C4⋊C4C2311yescharacteristic
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2311yescharacteristic
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2318yes—
585C4×C4⋊C4C2318yes—
586C4×C22⋊C4C2312yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2318yes—
592C4×C22⋊C4C2318yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2311yescharacteristic
596C4×C22⋊C4C2311yescharacteristic
597#376C2312yes—
598#376C2312yes—
599#376C2312yes—
600C2×#95C2314yes—
601C43C2311yescharacteristic
602C43C2311yescharacteristic
603C2×#41—28no—
604C2×#41—28no—
605C2×#41—28no—
606C2×#41—44no—
607C2×#41—44no—
608C2×#41—48no—
609C2×#41C2×D418yes—
610C22×Q8—28no—
611C22×Q8—24no—
612C22×Q8—24no—
613C22×Q8—42no—
614C22×Q8—48no—
615C22×Q8C2411yescharacteristic
616C22×Q8C2412yes—
617C22×Q8C2411yescharacteristic
618C22×Q8C2412yes—
619C22×Q8C2412yes—
620C22×Q8C2411yescharacteristic
621C22×Q8C2411yescharacteristic
622C22×Q8C2414yes—
623C22×Q8C2414yes—
624C22×Q8C2412yes—
625C22×D4C2411yescharacteristic
626C22×D4C2412yes—
627C22×D4C2412yes—
628C22×D4C2414yes—
629C22×D4C2411yescharacteristic
630C22×D4C2414yes—
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2412yes—
635C22×D4C2418yes—
636C22×D4C2412yes—
637C23×C4C2412yes—
638C23×C4C2412yes—
639C23×C4C2414yes—
640C23×C4C2411yescharacteristic
641C23×C4C2412yes—
642C23×C4C2411yescharacteristic
643C23×C4C2412yes—
644C23×C4C2414yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2412yes—
652C4⋊Q8—28no—
653C4⋊Q8—24no—
654C4⋊Q8—28no—
655C4⋊Q8—216no—
656C4⋊Q8—24no—
657C4⋊Q8—28no—
658C4⋊Q8—24no—
659C4⋊Q8—28no—
660C4⋊Q8—24no—
661C4⋊Q8—42no—
662C4⋊Q8—48no—
663#127—28no—
664#127—24no—
665#127—44no—
666#126—216no—
667#126—216no—
668#126—216no—
669#126—216no—
670#126—216no—
671#126—216no—
672#126—216no—
673#126—28no—
674#125—216no—
675#125—28no—
676#125—24no—
677#125—28no—
678#124—28no—
679#124—24no—
680#124—28no—
681#124—28no—
682#124—216no—
683#124—216no—
684#124—216no—
685#124—216no—
686#124—216no—
687#124—24no—
688#124—28no—
689#124—28no—
690#124—48no—
691#124—42no—
692#124—44no—
693#124—48no—
694#123—28no—
695#123—216no—
696#123—216no—
697#123—216no—
698#123—216no—
699#123—48no—
700C22⋊Q8—28no—
701C22⋊Q8—24no—
702C22⋊Q8—28no—
703C22⋊Q8—28no—
704C22⋊Q8—216no—
705C22⋊Q8—28no—
706C22⋊Q8—216no—
707C22⋊Q8—216no—
708C22⋊Q8—28no—
709C22⋊Q8—216no—
710C22⋊Q8—416no—
711C22⋊Q8—48no—
712#121—216no—
713#121—216no—
714#121—28no—
715#121—216no—
716#121—28no—
717#121—24no—
718#121—28no—
719#121—28no—
720#121—28no—
721#121—216no—
722#121—416no—
723#121—48no—
724C4×Q8—28no—
725C4×Q8—28no—
726C4×Q8—28no—
727C4×Q8—28no—
728C4×Q8—216no—
729C4×Q8—24no—
730C4×Q8—28no—
731C4×Q8—24no—
732C4×Q8—24no—
733C4×Q8—24no—
734C4×Q8—28no—
735C4×Q8—28no—
736C4×Q8—216no—
737C4×Q8—28no—
738C4×Q8—28no—
739C4×Q8—24no—
740C4×Q8—216no—
741C4×Q8—28no—
742C4×Q8C2×D418yes—
743C4×Q8C2×D418yes—
744C4×D4—216no—
745C4×D4—216no—
746C4×D4—216no—
747C4×D4—28no—
748C4×D4—216no—
749C4×D4—28no—
750C4×D4—28no—
751C4×D4—216no—
752C4×D4—216no—
753C4×D4—28no—
754C4×D4—28no—
755C4×D4—28no—
756C4×D4—28no—
757C4×D4—24no—
758C4×D4—44no—
759C4×D4—44no—
760C4×D4C2×D4116yes—
761C4×D4C2×D418yes—
762C4×D4C2×D4116yes—
763C4×D4C2×D418yes—
764#117—28no—
765#117—28no—
766#117—28no—
767#117—28no—
768#117—28no—
769#117—216no—
770#117—216no—
771#117—216no—
772#117—216no—
773#117—28no—
774#117—44no—
775#117—44no—
776#117C2×D418yes—
777#117C2×D4116yes—
778C2×C4⋊C4—28no—
779C2×C4⋊C4—24no—
780C2×C4⋊C4—48no—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2418yes—
821C2×C4⋊C4C2418yes—
822C2×C4⋊C4C2418yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2418yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2418yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2418yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2418yes—
859C2×C22⋊C4C2418yes—
860C2×C22⋊C4C2418yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2418yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2418yes—
865C2×C22⋊C4C2418yes—
866C2×C22⋊C4C2418yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C42—28no—
871C2×C42—216no—
872C2×C42—44no—
873C2×C42—44no—
874C2×C42C2×D418yes—
875C2×C42C2×D4116yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2418yes—
926#95C2418yes—
927#95C2414yes—
928#95C2418yes—
929#95C2418yes—
930#95C2418yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2418yes—
935#95C2418yes—
936#95C2418yes—
937#95C2418yes—
938#95C2418yes—
939C24C2512yes—
940C24C2514yes—
941C24C2511yescharacteristic
942C24C2512yes—
943#41—416no—
944#41—432no—
945#41—432no—
946C2×Q8—22no—
947C2×Q8—22no—
948C2×Q8—24no—
949C2×Q8—22no—
950C2×Q8—28no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—28no—
954C2×Q8—24no—
955C2×Q8—22no—
956C2×Q8—24no—
957C2×Q8—22no—
958C2×Q8—24no—
959C2×Q8—22no—
960C2×Q8—28no—
961C2×Q8—22no—
962C2×Q8—28no—
963C2×Q8—22no—
964C2×Q8—42no—
965C2×Q8—48no—
966C2×Q8—48no—
967C2×Q8—44no—
968C2×Q8—416no—
969C2×Q8—432no—
970C2×Q8C22×D414yes—
971C2×Q82−1+414yes—
972C2×D4—28no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—24no—
977C2×D4—22no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—22no—
982C2×D4—28no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—28no—
986C2×D4—22no—
987C2×D4—24no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—48no—
991C2×D4—48no—
992C2×D4—48no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—48no—
996C2×D4—48no—
997C2×D4—48no—
998C2×D4C22×D414yes—
999C2×D4C22×D418yes—
1000C22×C4—22no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—22no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—28no—
1008C22×C4—28no—
1009C22×C4—28no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—28no—
1013C22×C4—28no—
1014C22×C4—28no—
1015C22×C4—28no—
1016C22×C4—44no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—48no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—48no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—48no—
1029C22×C4—44no—
1030C22×C4C22×D414yes—
1031C22×C4C22×D414yes—
1032C22×C4C22×D418yes—
1033C22×C4C22×D414yes—
1034C22×C4C22×D418yes—
1035C22×C4C22×D418yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2511yescharacteristic
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C4⋊C4—24no—
1062C4⋊C4—22no—
1063C4⋊C4—24no—
1064C4⋊C4—22no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—22no—
1070C4⋊C4—24no—
1071C4⋊C4—22no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—48no—
1101C4⋊C4—48no—
1102C4⋊C4—48no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—48no—
1106C4⋊C4—48no—
1107C4⋊C4C22×D414yes—
1108C4⋊C4C22×D418yes—
1109C4⋊C4C22×D414yes—
1110C4⋊C4C22×D418yes—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—24no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—24no—
1132C22⋊C4—28no—
1133C22⋊C4—216no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—48no—
1139C22⋊C4—48no—
1140C22⋊C4—48no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—48no—
1144C22⋊C4—48no—
1145C22⋊C4—48no—
1146C22⋊C4—48no—
1147C22⋊C4C22×D418yes—
1148C22⋊C4C22×D418yes—
1149C22⋊C4C22×D418yes—
1150C42—24no—
1151C42—24no—
1152C42—28no—
1153C42—28no—
1154C42—24no—
1155C42—24no—
1156C42—28no—
1157C42—28no—
1158C42—28no—
1159C42—28no—
1160C42—24no—
1161C42—22no—
1162C42—22no—
1163C42—22no—
1164C42—22no—
1165C42—24no—
1166C42—24no—
1167C42—24no—
1168C42—24no—
1169C42—24no—
1170C42—44no—
1171C42—44no—
1172C42—42no—
1173C42C22×D418yes—
1174C42C22×D414yes—
1175C42C22×D418yes—
1176C42C22×D414yes—
1177C42C22×D414yes—
1178C42C22×D418yes—
1179C42C22×D414yes—
1180C23—21no—
1181C23—22no—
1182C23—22no—
1183C23—21no—
1184C23—24no—
1185C23—22no—
1186C23—24no—
1187C23—22no—
1188C23—22no—
1189C23—24no—
1190C23—22no—
1191C23—24no—
1192C23—28no—
1193C23—24no—
1194C23—28no—
1195C23—24no—
1196C23—24no—
1197C23—22no—
1198C23C23×D414yes—
1199C23C23×D412yes—
1200C23C2611yescharacteristic
1201Q8—28no—
1202Q8—28no—
1203Q8—48no—
1204Q8—416no—
1205Q8—48no—
1206Q8—48no—
1207Q8—44no—
1208Q8—44no—
1209Q8—88no—
1210Q8—84no—
1211D4—28no—
1212D4—48no—
1213D4—416no—
1214D4—416no—
1215D4—48no—
1216D4—44no—
1217D4—48no—
1218D4—84no—
1219D4—88no—
1220D4—84no—
1221D4—88no—
1222D4—168no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—28no—
1237C2×C4—28no—
1238C2×C4—216no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—28no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—28no—
1271C2×C4—24no—
1272C2×C4—28no—
1273C2×C4—24no—
1274C2×C4—48no—
1275C2×C4—44no—
1276C2×C4—48no—
1277C2×C4—416no—
1278C2×C4—48no—
1279C2×C4—416no—
1280C2×C4—416no—
1281C2×C4—48no—
1282C2×C4—88no—
1283C2×C4—88no—
1284C2×C4—84no—
1285C2×C4—88no—
1286C2×C4C23×D414yes—
1287C2×C4C23×D412yes—
1288C2×C4C23×D412yes—
1289C2×C4C23×D414yes—
1290C2×C4C23×D414yes—
1291C2×C4C23×D412yes—
1292C2×C4C23×D412yes—
1293C2×C4C23×D412yes—
1294C2×C4C23×D412yes—
1295C2×C4C2×2−1+414yes—
1296C2×C4C2×2−1+412yes—
1297C2×C4#58514yes—
1298C2×C4#58514yes—
1299C2×C4#58512yes—
1300C22—22no—
1301C22—24no—
1302C22—22no—
1303C22—24no—
1304C22—22no—
1305C22—24no—
1306C22—44no—
1307C22—42no—
1308C22—42no—
1309C22—44no—
1310C22—44no—
1311C22—48no—
1312C22—44no—
1313C22—48no—
1314C22—44no—
1315C22—42no—
1316C22—44no—
1317C22—42no—
1318C22—42no—
1319C22—44no—
1320C22C24×D411yescharacteristic
1321C22C22×2−1+411yescharacteristic
1322C22C2×#58511yescharacteristic
1323C22C2×#58512yes—
1324C22C2×#58512yes—
1325C4—24no—
1326C4—24no—
1327C4—22no—
1328C4—24no—
1329C4—22no—
1330C4—24no—
1331C4—22no—
1332C4—22no—
1333C4—24no—
1334C4—44no—
1335C4—42no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C4—42no—
1345C4—44no—
1346C4—42no—
1347C4—44no—
1348C4#344914yes—
1349C4#348914yes—
1350C2—42no—
1351C2—44no—
1352C2—82no—
1353C2—84no—
1354C2C2×#344911yescharacteristic
1355C2C2×#348911yescharacteristic
1356C2#6281211yescharacteristic
1357C2#6302912yes—
1358C2#6303412yes—
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×#3518C2semidirect
2. C2×#3480C2semidirect
3. #42441C2semidirect
4. #42299C2semidirect
5. #39864C2semidirect
6. #39851C2semidirect
7. #39619C2semidirect
8. #39616C2semidirect
9. #39171C2semidirect
10. #39168C2semidirect
11. #38095C2semidirect
12. #38091C2semidirect
13. #37870C2semidirect
14. #37869C2semidirect
15. #37616C2semidirect
16. #37545C2semidirect
17. #36443C2semidirect
18. #36419C2semidirect
19. #36412C2semidirect
20. #36188C2semidirect
21. #36185C2semidirect
22. #35817C2semidirect
23. #35298C2semidirect
24. #35211C2semidirect
25. #35179C2semidirect
26. #35103C2semidirect
27. #34972C2semidirect
28. #34947C2semidirect
29. #34127C2semidirect
329. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×#34802
#424412
#422992
#398642
#398512
#396192
#396162
#391712
#391682
#380952
#380912
#378702
#378692
#376162
#375452
#364432
#364192
#364122
#361882
#361852
#358172
#352982
#352112
#351792
#351032
#349722
#349472
#341272