Finite Group Databasebeta

← #7720059

Subgroups — #7720059

Order 512.

6692 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3547C211yesmaximal, characteristic, complemented
2C2×#3544C211yesmaximal, characteristic, complemented
3#51328C218yesmaximal, complemented
4#51327C218yesmaximal, complemented
5#45303C214yesmaximal, complemented
6#45237C214yesmaximal, complemented
7#44971C214yesmaximal, complemented
8#44869C214yesmaximal, complemented
9#39618C211yesmaximal, characteristic, complemented
10#39617C211yesmaximal, characteristic, complemented
11#39491C211yesmaximal, characteristic, complemented
12#39491C212yesmaximal, complemented
13#39489C211yesmaximal, characteristic, complemented
14#39485C212yesmaximal, complemented
15#37871C212yesmaximal, complemented
16#37864C212yesmaximal, complemented
17#37423C212yesmaximal, complemented
18#37304C212yesmaximal, complemented
19#36559C211yesmaximal, characteristic, complemented
20Q8×#124C211yesmaximal, characteristic, complemented
21#36187C211yesmaximal, characteristic, complemented
22#36164C211yesmaximal, characteristic, complemented
23#35330C212yesmaximal, complemented
24#35289C211yesmaximal, characteristic, complemented
25#35281C211yesmaximal, characteristic, complemented
26#35276C212yesmaximal, complemented
27#35201C211yesmaximal, characteristic, complemented
28#34624C211yesmaximal, characteristic, complemented
29#34151C211yesmaximal, characteristic, complemented
30#3547—216no—
31#3544—216no—
32C2×#563C2214yes—
33C2×#562C2214yes—
34C2×Q82C2211yescharacteristic
35C2×#555C2211yescharacteristic
36C2×#555C2211yescharacteristic
37C2×#555C2212yes—
38C2×#554C2211yescharacteristic
39C2×#554C2211yescharacteristic
40C2×#554C2211yescharacteristic
41C2×#553C2212yes—
42C2×#552C2212yes—
43C2×#552C2212yes—
44C2×#552C2212yes—
45C2×D4×Q8C2211yescharacteristic
46C2×#548C2212yes—
47C2×#547C2212yes—
48C2×#547C2212yes—
49C2×#547C2211yescharacteristic
50C2×#544C2212yes—
51C2×#544C2212yes—
52C2×#544C2212yes—
53C2×#542C2212yes—
54C2×#542C2212yes—
55C2×#542C2214yes—
56C2×#540C2212yes—
57C2×#537C2212yes—
58C2×#536C2214yes—
59C2×#536C2212yes—
60C2×#533C2211yescharacteristic
61C2×#532C2211yescharacteristic
62C22×C4⋊Q8C2211yescharacteristic
63C2×#529C2211yescharacteristic
64C2×#529C2211yescharacteristic
65#2868C2211yescharacteristic
66#2868C2211yescharacteristic
67#2862C2212yes—
68#2862C2212yes—
69#2862C2211yescharacteristic
70#2862C2211yescharacteristic
71#2861C2212yes—
72#2859C2212yes—
73#2859C2212yes—
74#2858C2212yes—
75#2856C2212yes—
76#2850C2212yes—
77#2725C2218yes—
78#2723C2218yes—
79#2716C2218yes—
80#2715C2218yes—
81#2710C2218yes—
82#2710C2218yes—
83#2710C2218yes—
84#2708C2218yes—
85#2706C2218yes—
86#2701C2218yes—
87#2700C2218yes—
88#2694C2218yes—
89#2692C2218yes—
90#2690C2218yes—
91#2687C2218yes—
92#2681C2218yes—
93#2677C2218yes—
94#2674C2218yes—
95#2674C2218yes—
96#2672C2218yes—
97#2663C2214yes—
98#2662C2214yes—
99#2661C2214yes—
100#2660C2211yescharacteristic
101#2660C2212yes—
102#2660C2212yes—
103#2660C2212yes—
104#2660C2212yes—
105#2657C2211yescharacteristic
106#2641C2211yescharacteristic
107#2640C2211yescharacteristic
108#2640C2214yes—
109#2620C2211yescharacteristic
110#2620C2212yes—
111#2620C2211yescharacteristic
112#2619C2211yescharacteristic
113#2619C2211yescharacteristic
114#2619C2212yes—
115#2604C2214yes—
116#2568C2212yes—
117#2568C2211yescharacteristic
118#2567C2211yescharacteristic
119#2567C2214yes—
120#2566C2212yes—
121#2566C2212yes—
122#2566C2212yes—
123#2565C2212yes—
124#2563C2212yes—
125#2563C2211yescharacteristic
126#2563C2211yescharacteristic
127#2563C2211yescharacteristic
128#2563C2211yescharacteristic
129#2563C2211yescharacteristic
130#2563C2212yes—
131#2555C2218yes—
132#2554C2218yes—
133#2550C2218yes—
134#2550C2218yes—
135#2549C2218yes—
136#2549C2218yes—
137#2547C2214yes—
138#2546C2214yes—
139#2542C2211yescharacteristic
140#2542C2212yes—
141#2538C2214yes—
142#2537C2214yes—
143#2504C2212yes—
144#2504C2212yes—
145#2504C2212yes—
146#2504C2212yes—
147#2503C2212yes—
148#2502C2214yes—
149#2501C2212yes—
150#2500C2212yes—
151#2500C2212yes—
152#2500C2212yes—
153#2500C2212yes—
154#2499C2212yes—
155#2499C2212yes—
156#2492C2214yes—
157#2492C2218yes—
158#2491C2218yes—
159#2489C2214yes—
160#2488C2218yes—
161#2475C2218yes—
162#2474C2218yes—
163#2470C2218yes—
164#2466C2218yes—
165#2464C2218yes—
166#2461C2218yes—
167#2452C2218yes—
168#2441C2214yes—
169#2440C2214yes—
170#2436C2214yes—
171#2434C2214yes—
172#2430C2218yes—
173#2425C2218yes—
174#2423C2214yes—
175#2422C2214yes—
176#2417C2214yes—
177#2415C2218yes—
178#2415C2214yes—
179#2415C2214yes—
180#2409C2214yes—
181#2407C2218yes—
182#2407C2214yes—
183#2392C2214yes—
184#2388C2214yes—
185#2374C2214yes—
186#2373C2214yes—
187#2370C2212yes—
188#2367C2212yes—
189#2363C2212yes—
190#2362C2212yes—
191#2354C2214yes—
192D4×C4⋊C4C2214yes—
193Q8×C22⋊C4C2214yes—
194#2339C2214yes—
195#2328C2212yes—
196#2326C2212yes—
197#2323C2214yes—
198#2317C2212yes—
199#2317C2212yes—
200#2317C2212yes—
201#2317C2212yes—
202#2311C2214yes—
203C4×#127C2211yescharacteristic
204C4×#127C2211yescharacteristic
205C4×#127C2212yes—
206C4×#124C2212yes—
207C4×#124C2211yescharacteristic
208C4×#124C2211yescharacteristic
209#2298C2212yes—
210#2295C2211yescharacteristic
211#2293C2212yes—
212#2293C2211yescharacteristic
213#2290C2212yes—
214#2285C2212yes—
215C2×#382C2212yes—
216C42×Q8C2211yescharacteristic
217C42×D4C2211yescharacteristic
218C4×#117C2212yes—
219C4×#117C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2314yes—
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226#563—232no—
227#562—232no—
228Q82—28no—
229#555—28no—
230#555—216no—
231#555—28no—
232#554—28no—
233#554—28no—
234#554—28no—
235#553—216no—
236#552—216no—
237#552—216no—
238#552—216no—
239D4×Q8—28no—
240#548—216no—
241#547—216no—
242#547—216no—
243#547—28no—
244#544—216no—
245#544—216no—
246#544—216no—
247#542—232no—
248#542—216no—
249#542—216no—
250#540—216no—
251#537—216no—
252#536—232no—
253#536—216no—
254#533—28no—
255#532—28no—
256C2×C4⋊Q8—28no—
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×#127C2311yescharacteristic
274C2×#127C2311yescharacteristic
275C2×#127C2311yescharacteristic
276#529—28no—
277#529D4116yescomplemented
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2311yescharacteristic
286C2×#125C2312yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2312yes—
290C2×#125C2314yes—
291C2×#125C2311yescharacteristic
292C2×#124C2311yescharacteristic
293C2×#124C2311yescharacteristic
294C2×#124C2311yescharacteristic
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#124C2314yes—
301C2×#124C2318yes—
302C2×#124C2311yescharacteristic
303C2×#123C2312yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2318yes—
313C2×#123C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2311yescharacteristic
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2318yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×#121C2311yescharacteristic
339C2×#121C2311yescharacteristic
340C2×#121C2311yescharacteristic
341C2×#121C2312yes—
342C2×#121C2314yes—
343C2×#121C2312yes—
344C2×#121C2314yes—
345C2×#121C2312yes—
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#121C2318yes—
349C2×#121C2311yescharacteristic
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2318yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2311yescharacteristic
373C2×#117C2311yescharacteristic
374C2×#117C2312yes—
375C2×#117C2311yescharacteristic
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2312yes—
379C2×#117C2312yes—
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2314yes—
383C2×#117C2314yes—
384C2×#117C2312yes—
385C2×#117C2312yes—
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2312yes—
392C22×C42C2312yes—
393C22×C42C2311yescharacteristic
394#400C2314yes—
395#400C2318yes—
396#400C2318yes—
397#399C2314yes—
398#399C2318yes—
399#399C2318yes—
400#398C2318yes—
401#398C2314yes—
402#398C2318yes—
403#398C2318yes—
404#398C2318yes—
405#398C2318yes—
406#397C2314yes—
407#397C2318yes—
408#397C2318yes—
409#397C2318yes—
410#397C2318yes—
411#397C2318yes—
412#397C2318yes—
413#396C2318yes—
414#396C2318yes—
415#396C2318yes—
416#396C2314yes—
417#396C2314yes—
418#396C2318yes—
419#395C2314yes—
420#395C2318yes—
421#395C2318yes—
422#395C2314yes—
423#395C2318yes—
424#395C2318yes—
425#394C2314yes—
426#394C2314yes—
427#394C2318yes—
428#394C2314yes—
429#394C2314yes—
430#394C2318yes—
431#394C2314yes—
432#394C2314yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2318yes—
443#393C2318yes—
444#393C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2318yes—
448#392C2314yes—
449#392C2314yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2318yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2314yes—
458#391C2318yes—
459#391C2318yes—
460#391C2318yes—
461#391C2314yes—
462#391C2314yes—
463#391C2318yes—
464#391C2312yes—
465#390C2311yescharacteristic
466#390C2312yes—
467#390C2312yes—
468#390C2311yescharacteristic
469#390C2311yescharacteristic
470#390C2311yescharacteristic
471#390C2314yes—
472#390C2314yes—
473#390C2318yes—
474#390C2312yes—
475#390C2311yescharacteristic
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2318yes—
480#390C2318yes—
481#390C2312yes—
482#390C2314yes—
483#390C2311yescharacteristic
484#389C2318yes—
485#389C2318yes—
486#389C2314yes—
487#389C2318yes—
488#389C2318yes—
489#389C2318yes—
490#389C2318yes—
491#389C2318yes—
492#389C2318yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#388C2318yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2318yes—
512#388C2318yes—
513#387C2318yes—
514#387C2318yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2318yes—
520#386C2318yes—
521#386C2318yes—
522#386C2318yes—
523#386C2318yes—
524#386C2318yes—
525#386C2318yes—
526#386C2314yes—
527#386C2318yes—
528#385C2318yes—
529#385C2318yes—
530#385C2318yes—
531#385C2318yes—
532#385C2318yes—
533#385C2318yes—
534#385C2318yes—
535#385C2318yes—
536#385C2314yes—
537#384C2311yescharacteristic
538#384C2312yes—
539#384C2311yescharacteristic
540#384C2312yes—
541#384C2312yes—
542#384C2312yes—
543#384C2312yes—
544#384C2314yes—
545#384C2314yes—
546#384C2312yes—
547#382C2312yes—
548#382C2312yes—
549#382C2312yes—
550#382C2312yes—
551#382C2312yes—
552#382C2312yes—
553#382C2312yes—
554#382C2312yes—
555#382C2311yescharacteristic
556#382C2312yes—
557#382C2312yes—
558#382C2311yescharacteristic
559#382C2318yes—
560#381C2318yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2318yes—
567#380C2318yes—
568#380C2318yes—
569C4×C4⋊C4C2311yescharacteristic
570C4×C4⋊C4C2311yescharacteristic
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2318yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2314yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2314yes—
584C4×C22⋊C4C2318yes—
585C4×C22⋊C4C2312yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2312yes—
594#376C2312yes—
595#376C2312yes—
596#376C2311yescharacteristic
597#376C2311yescharacteristic
598C2×#95C2318yes—
599C43C2312yes—
600C43C2311yescharacteristic
601C43C2311yescharacteristic
602C43C2312yes—
603C2×#41—216no—
604C2×#41—28no—
605C2×#41—28no—
606C2×#41—48no—
607C2×#41—48no—
608C2×#41—88no—
609C22×Q8—28no—
610C22×Q8—28no—
611C22×Q8—48no—
612C22×Q8—84no—
613C22×Q8C2411yescharacteristic
614C22×Q8C2412yes—
615C22×Q8C2411yescharacteristic
616C22×Q8C2412yes—
617C22×Q8C2412yes—
618C22×Q8C2414yes—
619C22×Q8C2414yes—
620C22×Q8C2414yes—
621C22×Q8C2412yes—
622C22×Q8C2412yes—
623C22×D4C2411yescharacteristic
624C22×D4C2411yescharacteristic
625C22×D4C2411yescharacteristic
626C22×D4C2411yescharacteristic
627C22×D4C2414yes—
628C22×D4C2414yes—
629C22×D4C2412yes—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2412yes—
638C23×C4C2412yes—
639C23×C4C2412yes—
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2411yescharacteristic
643C23×C4C2411yescharacteristic
644C23×C4C2414yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2414yes—
650C23×C4C2414yes—
651C23×C4C2411yescharacteristic
652C4⋊Q8—216no—
653C4⋊Q8—216no—
654C4⋊Q8—216no—
655C4⋊Q8—28no—
656C4⋊Q8—28no—
657C4⋊Q8—28no—
658C4⋊Q8—24no—
659C4⋊Q8—24no—
660C4⋊Q8—28no—
661C4⋊Q8—24no—
662C4⋊Q8—24no—
663C4⋊Q8—24no—
664C4⋊Q8—28no—
665C4⋊Q8—28no—
666C4⋊Q8—84no—
667C4⋊Q8—84no—
668#127—24no—
669#127—24no—
670#127—24no—
671#126—216no—
672#126—216no—
673#126—216no—
674#126—28no—
675#126C2×D4116yes—
676#125—28no—
677#125—216no—
678#125—216no—
679#125—216no—
680#125—24no—
681#125—28no—
682#125—28no—
683#125—28no—
684#125C2×D418yes—
685#124—216no—
686#124—216no—
687#124—216no—
688#124—216no—
689#124—216no—
690#124—24no—
691#124—28no—
692#124—24no—
693#124—24no—
694#124—88no—
695#124C2×D418yes—
696#123—216no—
697#123—28no—
698#123—216no—
699#123—216no—
700#123—216no—
701#123—216no—
702#123—216no—
703#123—216no—
704#123—216no—
705#123—88no—
706#123C2×D4116yes—
707C22⋊Q8—28no—
708C22⋊Q8—28no—
709C22⋊Q8—24no—
710C22⋊Q8—28no—
711C22⋊Q8—28no—
712C22⋊Q8—28no—
713C22⋊Q8—216no—
714C22⋊Q8—28no—
715C22⋊Q8—216no—
716C22⋊Q8—28no—
717C22⋊Q8—216no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—48no—
726C22⋊Q8—88no—
727C22⋊Q8C2×D418yes—
728#121—28no—
729#121—216no—
730#121—216no—
731#121—28no—
732#121—24no—
733#121—24no—
734#121—24no—
735#121—28no—
736#121—28no—
737#121—28no—
738#121—28no—
739#121—216no—
740#121—216no—
741#121—88no—
742#121C2×D418yes—
743C4×Q8—28no—
744C4×Q8—24no—
745C4×Q8—28no—
746C4×Q8—28no—
747C4×Q8—28no—
748C4×Q8—44no—
749C4×Q8C2×D418yes—
750C4×D4—28no—
751C4×D4—28no—
752C4×D4—216no—
753C4×D4—24no—
754C4×D4—24no—
755C4×D4—28no—
756C4×D4—24no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—28no—
760C4×D4—44no—
761C4×D4—48no—
762C4×D4—48no—
763C4×D4—88no—
764C4×D4C2×D4116yes—
765C4×D4C2×D418yes—
766#117—28no—
767#117—28no—
768#117—28no—
769#117—28no—
770#117—216no—
771#117—28no—
772#117—216no—
773#117—28no—
774#117—24no—
775#117—28no—
776#117—24no—
777#117—44no—
778#117C2×D4116yes—
779C2×C4⋊C4—28no—
780C2×C4⋊C4—28no—
781C2×C4⋊C4—28no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—28no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2418yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2418yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2418yes—
828C2×C4⋊C4C2418yes—
829C2×C4⋊C4C2418yes—
830C2×C4⋊C4C2418yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2418yes—
863C2×C22⋊C4C2418yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2418yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2418yes—
872C2×C22⋊C4C2418yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2418yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C42—28no—
882C2×C42C2×D418yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2414yes—
888C2×C42C2411yescharacteristic
889C2×C42C2411yescharacteristic
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908#95C2414yes—
909#95C2418yes—
910#95C2418yes—
911#95C2418yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2412yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2418yes—
924#95C2414yes—
925#95C2418yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2418yes—
930#95C2418yes—
931#95C2414yes—
932#95C2418yes—
933#95C2418yes—
934#95C2418yes—
935#95C2418yes—
936#95C2418yes—
937C24C2512yes—
938C24C2512yes—
939C24C2512yes—
940C24C2511yescharacteristic
941C24C2512yes—
942#41—816no—
943#41—816no—
944#41—832no—
945C2×Q8—22no—
946C2×Q8—24no—
947C2×Q8—24no—
948C2×Q8—24no—
949C2×Q8—28no—
950C2×Q8—28no—
951C2×Q8—24no—
952C2×Q8—28no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—22no—
956C2×Q8—24no—
957C2×Q8—28no—
958C2×Q8—48no—
959C2×Q8—48no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—48no—
964C2×Q8—44no—
965C2×Q8—816no—
966C2×Q8—816no—
967C2×Q8C22×D414yes—
968C2×D4—24no—
969C2×D4—28no—
970C2×D4—24no—
971C2×D4—28no—
972C2×D4—24no—
973C2×D4—28no—
974C2×D4—22no—
975C2×D4—22no—
976C2×D4—22no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—22no—
980C2×D4—22no—
981C2×D4—28no—
982C2×D4—22no—
983C2×D4—22no—
984C2×D4—22no—
985C2×D4—22no—
986C2×D4—28no—
987C2×D4—24no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—48no—
995C2×D4—48no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—48no—
1001C2×D4C22×D414yes—
1002C2×D4C22×D418yes—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—24no—
1008C22×C4—28no—
1009C22×C4—28no—
1010C22×C4—28no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—28no—
1015C22×C4—28no—
1016C22×C4—28no—
1017C22×C4—28no—
1018C22×C4—28no—
1019C22×C4—28no—
1020C22×C4—28no—
1021C22×C4—42no—
1022C22×C4—48no—
1023C22×C4—44no—
1024C22×C4—48no—
1025C22×C4—48no—
1026C22×C4—44no—
1027C22×C4—48no—
1028C22×C4—48no—
1029C22×C4—48no—
1030C22×C4C22×D414yes—
1031C22×C4C22×D414yes—
1032C22×C4C22×D418yes—
1033C22×C4C22×D414yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2514yes—
1038C22×C4C2512yes—
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2514yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C4⋊C4—22no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—22no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—24no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—48no—
1097C4⋊C4—44no—
1098C4⋊C4—48no—
1099C4⋊C4—48no—
1100C4⋊C4—44no—
1101C4⋊C4—48no—
1102C4⋊C4—48no—
1103C4⋊C4—48no—
1104C4⋊C4C22×D414yes—
1105C4⋊C4C22×D414yes—
1106C4⋊C4C22×D418yes—
1107C4⋊C4C22×D418yes—
1108C4⋊C4C22×D418yes—
1109C4⋊C4C22×D418yes—
1110C22⋊C4—24no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—28no—
1123C22⋊C4—24no—
1124C22⋊C4—28no—
1125C22⋊C4—24no—
1126C22⋊C4—28no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—24no—
1130C22⋊C4—24no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—48no—
1141C22⋊C4—48no—
1142C22⋊C4—48no—
1143C22⋊C4—48no—
1144C22⋊C4—44no—
1145C22⋊C4—48no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—48no—
1149C22⋊C4C22×D418yes—
1150C22⋊C4C22×D418yes—
1151C22⋊C4C22×D418yes—
1152C22⋊C4C22×D418yes—
1153C22⋊C4C22×D418yes—
1154C42—28no—
1155C42—28no—
1156C42—28no—
1157C42—24no—
1158C42—28no—
1159C42—28no—
1160C42—24no—
1161C42—22no—
1162C42—24no—
1163C42—22no—
1164C42—24no—
1165C42—24no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—42no—
1171C42—42no—
1172C42C22×D414yes—
1173C42C22×D414yes—
1174C42C22×D414yes—
1175C42C22×D414yes—
1176C42C22×D418yes—
1177C422−1+414yes—
1178C422−1+414yes—
1179C23—21no—
1180C23—22no—
1181C23—21no—
1182C23—22no—
1183C23—22no—
1184C23—24no—
1185C23—24no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23C23×D414yes—
1203C23C23×D412yes—
1204C23C2611yescharacteristic
1205Q8—28no—
1206Q8—44no—
1207Q8—48no—
1208Q8—84no—
1209Q8—88no—
1210Q8—88no—
1211Q8—84no—
1212Q8—84no—
1213Q8—84no—
1214Q8—88no—
1215D4—28no—
1216D4—48no—
1217D4—416no—
1218D4—48no—
1219D4—44no—
1220D4—44no—
1221D4—44no—
1222D4—84no—
1223D4—88no—
1224D4—84no—
1225D4—88no—
1226D4—84no—
1227D4—84no—
1228D4—88no—
1229D4—88no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—216no—
1244C2×C4—28no—
1245C2×C4—28no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—28no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—28no—
1274C2×C4—24no—
1275C2×C4—28no—
1276C2×C4—28no—
1277C2×C4—44no—
1278C2×C4—416no—
1279C2×C4—48no—
1280C2×C4—48no—
1281C2×C4—48no—
1282C2×C4—88no—
1283C2×C4—88no—
1284C2×C4—88no—
1285C2×C4—88no—
1286C2×C4—88no—
1287C2×C4—88no—
1288C2×C4C23×D412yes—
1289C2×C4C23×D414yes—
1290C2×C4C23×D414yes—
1291C2×C4C23×D412yes—
1292C2×C4C23×D412yes—
1293C2×C4C23×D412yes—
1294C2×C4C23×D414yes—
1295C2×C4C23×D412yes—
1296C2×C4C23×D412yes—
1297C2×C4C2×2−1+414yes—
1298C2×C4C2×2−1+414yes—
1299C2×C4C2×2−1+412yes—
1300C2×C4C2×2−1+412yes—
1301C2×C4#58514yes—
1302C22—22no—
1303C22—24no—
1304C22—22no—
1305C22—24no—
1306C22—22no—
1307C22—24no—
1308C22—42no—
1309C22—44no—
1310C22—44no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—44no—
1322C22—44no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22C24×D411yescharacteristic
1328C22C22×2−1+411yescharacteristic
1329C22C22×2−1+411yescharacteristic
1330C22C2×#58512yes—
1331C22H(7,𝔽2)12yes—
1332C4—24no—
1333C4—22no—
1334C4—22no—
1335C4—24no—
1336C4—22no—
1337C4—22no—
1338C4—24no—
1339C4—24no—
1340C4—24no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—44no—
1346C4—44no—
1347C4—44no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—44no—
1352C4—42no—
1353C4—44no—
1354C4#349914yes—
1355C4#350014yes—
1356C2—42no—
1357C2—44no—
1358C2—82no—
1359C2—82no—
1360C2—82no—
1361C2C2×#349911yescharacteristic
1362C2C2×#350011yescharacteristic
1363C2#6285211yescharacteristic
1364C2#6292612yes—
1365C2#6292912yes—
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×#3547C2semidirect
2. C2×#3544C2semidirect
3. #51328C2semidirect
4. #51327C2semidirect
5. #45303C2semidirect
6. #45237C2semidirect
7. #44971C2semidirect
8. #44869C2semidirect
9. #39618C2semidirect
10. #39617C2semidirect
11. #39491C2semidirect
12. #39491C2semidirect
13. #39489C2semidirect
14. #39485C2semidirect
15. #37871C2semidirect
16. #37864C2semidirect
17. #37423C2semidirect
18. #37304C2semidirect
19. #36559C2semidirect
20. Q8×#124C2semidirect
21. #36187C2semidirect
22. #36164C2semidirect
23. #35330C2semidirect
24. #35289C2semidirect
25. #35281C2semidirect
26. #35276C2semidirect
27. #35201C2semidirect
28. #34624C2semidirect
29. #34151C2semidirect
277. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35472
C2×#35442
#513282
#513272
#453032
#452372
#449712
#448692
#396182
#396172
#394912
#394892
#394852
#378712
#378642
#374232
#373042
#365592
Q8×#1242
#361872
#361642
#353302
#352892
#352812
#352762
#352012
#346242
#341512