Finite Group Databasebeta

← #7679701

Subgroups — #7679701

Order 512.

6990 conjugacy classes of subgroups.

The subgroup lattice has 1265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3512C212yesmaximal, complemented
2#59826C214yesmaximal, complemented
3#59312C212yesmaximal, complemented
4#59304C212yesmaximal, complemented
5#59304C214yesmaximal, complemented
6#59258C212yesmaximal, complemented
7#59213C212yesmaximal, complemented
8#45264C214yesmaximal, complemented
9#45135C214yesmaximal, complemented
10#43526C218yesmaximal, complemented
11#39353C212yesmaximal, complemented
12#39352C212yesmaximal, complemented
13#37799C214yesmaximal, complemented
14#37798C214yesmaximal, complemented
15#36117C212yesmaximal, complemented
16#36116C212yesmaximal, complemented
17#35639C212yesmaximal, complemented
18#35517C212yesmaximal, complemented
19#35273C211yesmaximal, characteristic, complemented
20#35255C212yesmaximal, complemented
21#34937C211yesmaximal, characteristic, complemented
22C2×#2552C211yesmaximal, characteristic, complemented
23#34206C211yesmaximal, characteristic, complemented
24#34183C211yesmaximal, characteristic, complemented
25C4⋊C4×#41C211yesmaximal, characteristic, complemented
26C4×#537C211yesmaximal, characteristic, complemented
27#3512—232no—
28C2×#553C2218yes—
29C2×#553C2218yes—
30C2×#553C2214yes—
31C2×#553C2214yes—
32C2×#552C2214yes—
33C2×#552C2214yes—
34C2×#541C2214yes—
35C2×#540C2214yes—
36C2×#537C2212yes—
37C2×#537C2211yescharacteristic
38C2×#532C2212yes—
39C2×#532C2211yescharacteristic
40C2×#529C2214yes—
41C2×#529C2214yes—
42C22×#125C2212yes—
43C2×#520C2212yes—
44C2×#520C2212yes—
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47C2×C4×#41C2212yes—
48#2857C2212yes—
49#2856C2212yes—
50#2855C2214yes—
51#2854C2214yes—
52#2725C2218yes—
53#2722C2218yes—
54#2721C2218yes—
55#2719C2218yes—
56#2718C2218yes—
57#2718C2218yes—
58#2718C2218yes—
59#2708C2218yes—
60#2706C2218yes—
61#2701C2218yes—
62#2695C2218yes—
63#2671C2218yes—
64#2625C2214yes—
65#2624C2214yes—
66#2620C2214yes—
67#2579C2218yes—
68#2552C2212yes—
69#2552C2212yes—
70#2552C2214yes—
71#2552C2212yes—
72#2552C2214yes—
73#2552C2212yes—
74#2552C2214yes—
75#2548C2211yescharacteristic
76#2547C2211yescharacteristic
77#2546C2211yescharacteristic
78#2545C2212yes—
79#2544C2212yes—
80#2543C2214yes—
81#2541C2211yescharacteristic
82#2538C2212yes—
83#2538C2212yes—
84#2537C2214yes—
85#2537C2212yes—
86#2537C2212yes—
87#2512C2214yes—
88#2506C2214yes—
89#2501C2214yes—
90#2501C2214yes—
91#2496C2214yes—
92#2496C2214yes—
93#2496C2214yes—
94#2487C2218yes—
95#2487C2214yes—
96#2486C2214yes—
97#2486C2214yes—
98#2485C2214yes—
99#2485C2214yes—
100#2479C2218yes—
101#2478C2218yes—
102#2475C2218yes—
103#2470C2218yes—
104#2468C2218yes—
105#2466C2218yes—
106#2454C2214yes—
107#2454C2214yes—
108#2453C2214yes—
109#2453C2214yes—
110#2448C2214yes—
111#2447C2214yes—
112#2446C2214yes—
113#2445C2214yes—
114#2444C2218yes—
115#2444C2218yes—
116#2443C2218yes—
117#2443C2218yes—
118#2443C2218yes—
119#2442C2214yes—
120#2442C2214yes—
121#2441C2214yes—
122#2441C2214yes—
123#2441C2218yes—
124#2425C2218yes—
125#2423C2214yes—
126#2422C2218yes—
127#2422C2214yes—
128#2422C2214yes—
129#2421C2214yes—
130#2420C2214yes—
131#2419C2218yes—
132#2416C2214yes—
133#2416C2212yes—
134#2416C2212yes—
135#2416C2214yes—
136#2416C2214yes—
137#2413C2218yes—
138#2392C2214yes—
139C2×#398C2214yes—
140#2367C2214yes—
141#2366C2212yes—
142#2365C2212yes—
143#2361C2214yes—
144#2354C2214yes—
145#2354C2212yes—
146#2352C2214yes—
147#2351C2212yes—
148Q8×C4⋊C4C2212yes—
149Q8×C4⋊C4C2211yescharacteristic
150Q8×C4⋊C4C2211yescharacteristic
151Q8×C4⋊C4C2212yes—
152#2349C2214yes—
153#2349C2212yes—
154D4×C4⋊C4C2214yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2214yes—
157D4×C4⋊C4C2211yescharacteristic
158D4×C4⋊C4C2211yescharacteristic
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2214yes—
164#2344C2214yes—
165#2325C2214yes—
166#2325C2214yes—
167#2324C2212yes—
168#2324C2212yes—
169#2323C2212yes—
170#2323C2212yes—
171#2317C2212yes—
172#2317C2214yes—
173#2316C2211yescharacteristic
174#2311C2211yescharacteristic
175#2311C2211yescharacteristic
176#2311C2212yes—
177#2311C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182C4×#121C2214yes—
183C4×#121C2212yes—
184C4×#121C2212yes—
185C4×#121C2214yes—
186#2297C2212yes—
187#2296C2212yes—
188#2296C2214yes—
189C2×#389C2212yes—
190C2×#389C2212yes—
191#2285C2211yescharacteristic
192#2285C2212yes—
193#2285C2212yes—
194C2×#384C2211yescharacteristic
195C2×#384C2212yes—
196C2×#384C2212yes—
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2211yescharacteristic
199C2×C4×C4⋊C4C2211yescharacteristic
200C22×#41C2312yes—
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203#553—232no—
204#553—264no—
205#553—264no—
206#553—232no—
207#552—232no—
208#552—232no—
209#541—232no—
210#540—232no—
211#537—216no—
212#537D4116yescomplemented
213#532—216no—
214#532—28no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2312yes—
217C2×#127C2311yescharacteristic
218C2×#127C2312yes—
219#529—232no—
220#529—232no—
221C2×#126C2318yes—
222C2×#126C2318yes—
223C2×#126C2318yes—
224C2×#126C2318yes—
225C2×#125—216no—
226C2×#125C2314yes—
227C2×#125C2314yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#125C2318yes—
231C2×#125C2318yes—
232C2×#124C2312yes—
233C2×#124C2312yes—
234C2×#124C2312yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×#123C2318yes—
238C2×#123C2318yes—
239C2×#123C2318yes—
240C2×#123C2318yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2312yes—
245C2×#121C2312yes—
246C2×#121C2314yes—
247C2×#121C2318yes—
248C2×#121C2318yes—
249C2×#121C2312yes—
250C2×#121C2318yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2314yes—
255C2×#121C2312yes—
256C2×#121C2312yes—
257C2×#121C2314yes—
258C2×#121C2312yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261#520—216no—
262#520—216no—
263C4×#41—216no—
264C4×#41—28no—
265C4×#41—28no—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2314yes—
274C2×C4×D4C2318yes—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2314yes—
284C2×C4×D4C2318yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2318yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2318yes—
293C2×C4×D4C2314yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2314yes—
297C2×C4×D4C2314yes—
298C2×#117C2311yescharacteristic
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2312yes—
304C2×#117C2318yes—
305C2×#117C2314yes—
306C2×#117C2318yes—
307C2×#117C2314yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2314yes—
311C22×C4⋊C4C2314yes—
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2312yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C4⋊C4C2314yes—
323C22×C4⋊C4C2311yescharacteristic
324C22×C42C2314yes—
325C22×C42C2312yes—
326C22×C42C2312yes—
327C22×C42C2312yes—
328C22×C42C2312yes—
329C22×C42C2311yescharacteristic
330#400C2318yes—
331#400C2318yes—
332#400C2318yes—
333#400C2318yes—
334#399C2318yes—
335#399C2318yes—
336#399C2318yes—
337#399C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2314yes—
346#398C2318yes—
347#397C2318yes—
348#397C2318yes—
349#397C2318yes—
350#397C2314yes—
351#397C2318yes—
352#397C2318yes—
353#397C2318yes—
354#396C2318yes—
355#396C2318yes—
356#396C2318yes—
357#396C2318yes—
358#396C2314yes—
359#396C2314yes—
360#394C2318yes—
361#394C2318yes—
362#394C2318yes—
363#394C2318yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2318yes—
368#394C2318yes—
369#392C2314yes—
370#391C2312yes—
371#391C2312yes—
372#391C2314yes—
373#391C2314yes—
374#391C2312yes—
375#391C2312yes—
376#390C2312yes—
377#390C2312yes—
378#390C2314yes—
379#390C2314yes—
380#390C2314yes—
381#390C2312yes—
382#390C2314yes—
383#390C2314yes—
384#390C2312yes—
385#390C2314yes—
386#390C2312yes—
387#390C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2318yes—
395#389C2318yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2312yes—
403#389C2312yes—
404#389C2314yes—
405#389C2314yes—
406#389C2318yes—
407#389C2314yes—
408#389C2314yes—
409#389C2312yes—
410#389C2312yes—
411#389C2314yes—
412#389C2318yes—
413#389C2314yes—
414#389C2312yes—
415#389C2312yes—
416#389C2314yes—
417#389C2314yes—
418#389C2318yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2314yes—
430#388C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2314yes—
443#386C2314yes—
444#386C2314yes—
445#386C2314yes—
446#386C2314yes—
447#386C2318yes—
448#386C2318yes—
449#386C2314yes—
450#386C2314yes—
451#386C2318yes—
452#386C2314yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2314yes—
457#385C2318yes—
458#385C2318yes—
459#385C2314yes—
460#385C2314yes—
461#385C2318yes—
462#385C2318yes—
463#385C2314yes—
464#385C2314yes—
465#385C2314yes—
466#385C2314yes—
467#385C2314yes—
468#385C2318yes—
469#384C2314yes—
470#384C2312yes—
471#384C2312yes—
472#384C2311yescharacteristic
473#384C2311yescharacteristic
474#384C2312yes—
475#384C2312yes—
476#384C2314yes—
477#384C2314yes—
478#384C2312yes—
479#384C2314yes—
480#384C2318yes—
481#384C2314yes—
482#384C2312yes—
483#382C2312yes—
484#382C2314yes—
485#382C2314yes—
486#381C2318yes—
487#381C2318yes—
488#380C2312yes—
489#380C2312yes—
490#380C2312yes—
491#380C2312yes—
492#380C2314yes—
493#380C2314yes—
494#380C2314yes—
495#380C2314yes—
496#380C2314yes—
497#380C2312yes—
498#380C2312yes—
499#380C2314yes—
500#380C2314yes—
501#380C2312yes—
502#380C2312yes—
503#380C2312yes—
504#380C2314yes—
505#380C2314yes—
506#380C2312yes—
507#380C2314yes—
508#380C2318yes—
509#380C2318yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2312yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2311yescharacteristic
520C4×C4⋊C4C2311yescharacteristic
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2314yes—
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2314yes—
527C4×C4⋊C4C2314yes—
528C4×C4⋊C4C2311yescharacteristic
529C4×C4⋊C4C2311yescharacteristic
530C4×C4⋊C4C2312yes—
531C4×C22⋊C4C2314yes—
532C4×C22⋊C4C2318yes—
533C4×C22⋊C4C2314yes—
534C4×C22⋊C4C2314yes—
535C4×C22⋊C4C2314yes—
536C2×#95C2312yes—
537C2×#95C2312yes—
538C2×#95C2314yes—
539C2×#95C2314yes—
540C2×#41—28no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—28no—
544C2×#41—24no—
545C2×#41—24no—
546C2×#41—28no—
547C2×#41C2×D418yes—
548C2×#41C2×D418yes—
549C22×Q8C2412yes—
550C22×Q8C2411yescharacteristic
551C22×Q8C2411yescharacteristic
552C22×D4C2412yes—
553C22×D4C2414yes—
554C22×D4C2412yes—
555C22×D4C2412yes—
556C22×D4C2412yes—
557C22×D4C2411yescharacteristic
558C22×D4C2411yescharacteristic
559C22×D4C2418yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2412yes—
563C22×D4C2414yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2414yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2411yescharacteristic
570C23×C4C2414yes—
571C23×C4C2412yes—
572C23×C4C2418yes—
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2412yes—
576C23×C4C2418yes—
577C23×C4C2414yes—
578C23×C4C2414yes—
579C23×C4C2412yes—
580C23×C4C2412yes—
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C4⋊Q8—28no—
584C4⋊Q8—24no—
585#127—28no—
586#127—24no—
587#126—232no—
588#126—232no—
589#126—232no—
590#126—232no—
591#125—216no—
592#125—216no—
593#125—216no—
594#125—216no—
595#125—232no—
596#125—232no—
597#124—28no—
598#124—28no—
599#124—28no—
600#123—232no—
601#123—232no—
602#123—232no—
603#123—232no—
604#123—88no—
605#123—88no—
606C22⋊Q8—216no—
607C22⋊Q8—216no—
608C22⋊Q8C2×D4116yes—
609C22⋊Q8C2×D4116yes—
610#121—216no—
611#121—216no—
612#121—216no—
613#121—232no—
614#121—232no—
615#121—232no—
616#121—216no—
617#121—28no—
618#121—28no—
619#121—48no—
620#121—44no—
621#121—44no—
622#121—84no—
623#121C2×D4116yes—
624#121C2×D4132yes—
625#121C2×D4116yes—
626C4×Q8—28no—
627C4×Q8—28no—
628C4×Q8—216no—
629C4×Q8—216no—
630C4×Q8—24no—
631C4×Q8—24no—
632C4×Q8—24no—
633C4×Q8—24no—
634C4×D4—216no—
635C4×D4—216no—
636C4×D4—28no—
637C4×D4—28no—
638C4×D4—216no—
639C4×D4—232no—
640C4×D4—232no—
641C4×D4—232no—
642C4×D4—216no—
643C4×D4—216no—
644C4×D4—28no—
645C4×D4—28no—
646C4×D4—28no—
647C4×D4—28no—
648C4×D4—216no—
649C4×D4—232no—
650C4×D4—24no—
651C4×D4—24no—
652C4×D4—24no—
653C4×D4—24no—
654C4×D4—28no—
655C4×D4—28no—
656C4×D4—48no—
657C4×D4—48no—
658#117—28no—
659#117—216no—
660#117—216no—
661#117—24no—
662#117—24no—
663#117—216no—
664#117—232no—
665#117—232no—
666#117—28no—
667#117—28no—
668C2×C4⋊C4—28no—
669C2×C4⋊C4—216no—
670C2×C4⋊C4—216no—
671C2×C4⋊C4—216no—
672C2×C4⋊C4—24no—
673C2×C4⋊C4—216no—
674C2×C4⋊C4—44no—
675C2×C4⋊C4—48no—
676C2×C4⋊C4—44no—
677C2×C4⋊C4—42no—
678C2×C4⋊C4—42no—
679C2×C4⋊C4—44no—
680C2×C4⋊C4—82no—
681C2×C4⋊C4—84no—
682C2×C4⋊C4—84no—
683C2×C4⋊C4C2×D418yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2418yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2418yes—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2418yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2418yes—
722C2×C4⋊C4C2418yes—
723C2×C4⋊C4C2418yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2418yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2412yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2412yes—
748C2×C22⋊C4C2412yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2418yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2418yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2418yes—
760C2×C22⋊C4C2418yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2418yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2418yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C42—28no—
772C2×C42—216no—
773C2×C42—28no—
774C2×C42—28no—
775C2×C42—44no—
776C2×C42#4118yes—
777C2×C42C2414yes—
778C2×C42C2418yes—
779C2×C42C2418yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2412yes—
785C2×C42C2412yes—
786C2×C42C2412yes—
787C2×C42C2414yes—
788C2×C42C2412yes—
789C2×C42C2412yes—
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2412yes—
793C2×C42C2414yes—
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798#95C2412yes—
799#95C2414yes—
800#95C2412yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2412yes—
806#95C2414yes—
807#95C2418yes—
808#95C2418yes—
809#95C2414yes—
810#95C2414yes—
811#95C2418yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2418yes—
821#95C2418yes—
822#95C2418yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2418yes—
827#95C2418yes—
828C24C2514yes—
829C24C2512yes—
830C24C2512yes—
831C24C2511yescharacteristic
832#41—232no—
833#41—232no—
834#41—432no—
835C2×Q8—24no—
836C2×Q8—22no—
837C2×Q8—22no—
838C2×Q8—24no—
839C2×Q8—22no—
840C2×Q8—22no—
841C2×Q8—24no—
842C2×Q8C22×D414yes—
843C2×Q8C22×D414yes—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—28no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—216no—
852C2×D4—28no—
853C2×D4—28no—
854C2×D4—24no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—48no—
870C2×D4—42no—
871C2×D4—48no—
872C2×D4—44no—
873C2×D4—42no—
874C2×D4—44no—
875C2×D4C22×D418yes—
876C2×D4C22×D418yes—
877C2×D4C22×D414yes—
878C2×D4C22×D414yes—
879C2×D4C22×D4116yes—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—28no—
890C22×C4—28no—
891C22×C4—28no—
892C22×C4—216no—
893C22×C4—28no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—24no—
897C22×C4—28no—
898C22×C4—28no—
899C22×C4—24no—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—216no—
904C22×C4—24no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—41no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—41no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—44no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—44no—
917C22×C4—48no—
918C22×C4—44no—
919C22×C4—42no—
920C22×C4—44no—
921C22×C4—48no—
922C22×C4—48no—
923C22×C4—42no—
924C22×C4—44no—
925C22×C4—48no—
926C22×C4—42no—
927C22×C4—44no—
928C22×C4—42no—
929C22×C4C22×D418yes—
930C22×C4C22×D418yes—
931C22×C4C22×D418yes—
932C22×C4C22×D414yes—
933C22×C4C2×#4114yes—
934C22×C4C2×#4114yes—
935C22×C4C2×#4114yes—
936C22×C42−1+414yes—
937C22×C4C2514yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2512yes—
942C22×C4C2514yes—
943C22×C4C2514yes—
944C22×C4C2512yes—
945C22×C4C2512yes—
946C22×C4C2512yes—
947C22×C4C2514yes—
948C22×C4C2512yes—
949C22×C4C2518yes—
950C22×C4C2512yes—
951C22×C4C2512yes—
952C22×C4C2514yes—
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2511yescharacteristic
959C4⋊C4—24no—
960C4⋊C4—24no—
961C4⋊C4—28no—
962C4⋊C4—216no—
963C4⋊C4—216no—
964C4⋊C4—28no—
965C4⋊C4—216no—
966C4⋊C4—216no—
967C4⋊C4—216no—
968C4⋊C4—216no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—216no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—24no—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—48no—
999C4⋊C4—42no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—48no—
1003C4⋊C4—48no—
1004C4⋊C4—48no—
1005C4⋊C4—42no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4C22×D418yes—
1011C4⋊C4C22×D418yes—
1012C4⋊C4C22×D4116yes—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—216no—
1018C22⋊C4—28no—
1019C22⋊C4—216no—
1020C22⋊C4—24no—
1021C22⋊C4—24no—
1022C22⋊C4—28no—
1023C22⋊C4—216no—
1024C22⋊C4—216no—
1025C22⋊C4—28no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—48no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—48no—
1038C22⋊C4—44no—
1039C22⋊C4—48no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—48no—
1044C22⋊C4C22×D4116yes—
1045C22⋊C4C22×D4116yes—
1046C42—24no—
1047C42—28no—
1048C42—28no—
1049C42—28no—
1050C42—24no—
1051C42—24no—
1052C42—24no—
1053C42—216no—
1054C42—216no—
1055C42—24no—
1056C42—24no—
1057C42—24no—
1058C42—24no—
1059C42—24no—
1060C42—24no—
1061C42—28no—
1062C42—44no—
1063C42C2×#4114yes—
1064C42C2×#4114yes—
1065C42C2×#4114yes—
1066C42C2×#4114yes—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23C23×D414yes—
1091C23C23×D414yes—
1092C23C23×D412yes—
1093C23C22×#4112yes—
1094C23C2×2−1+412yes—
1095C23C2611yescharacteristic
1096Q8—28no—
1097Q8—28no—
1098Q8—48no—
1099D4—216no—
1100D4—216no—
1101D4—28no—
1102D4—28no—
1103D4—416no—
1104D4—416no—
1105D4—48no—
1106D4—48no—
1107D4—84no—
1108D4—88no—
1109D4—816no—
1110D4—88no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—24no—
1122C2×C4—21no—
1123C2×C4—216no—
1124C2×C4—216no—
1125C2×C4—28no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—28no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—28no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—28no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—48no—
1166C2×C4—44no—
1167C2×C4—48no—
1168C2×C4—48no—
1169C2×C4—416no—
1170C2×C4—48no—
1171C2×C4—48no—
1172C2×C4—816no—
1173C2×C4—84no—
1174C2×C4—88no—
1175C2×C4—84no—
1176C2×C4—88no—
1177C2×C4—816no—
1178C2×C4—84no—
1179C2×C4—88no—
1180C2×C4#547116yes—
1181C2×C4C23×D414yes—
1182C2×C4C23×D414yes—
1183C2×C4C23×D418yes—
1184C2×C4C23×D412yes—
1185C2×C4C23×D412yes—
1186C2×C4C22×#4112yes—
1187C2×C4C22×#4112yes—
1188C2×C4C22×#4112yes—
1189C2×C4C22×#4112yes—
1190C2×C4C22×#4112yes—
1191C2×C4C22×#4112yes—
1192C2×C4C2×2−1+412yes—
1193C2×C4C2×2−1+412yes—
1194C2×C4#58512yes—
1195C2×C4#58512yes—
1196C22—22no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22C2×#54714yes—
1224C22C24×D411yescharacteristic
1225C22C23×#4111yescharacteristic
1226C22C22×2−1+411yescharacteristic
1227C22C2×#58511yescharacteristic
1228C22C2×#58511yescharacteristic
1229C22H(7,𝔽2)11yescharacteristic
1230C222−1+611yescharacteristic
1231C4—28no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—24no—
1236C4—24no—
1237C4—44no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—44no—
1242C4—48no—
1243C4—42no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—44no—
1249C4—44no—
1250C4C2×#54714yes—
1251C4C2×#54714yes—
1252C4#351214yescomplemented
1253C2—24no—
1254C2—44no—
1255C2—44no—
1256C2—84no—
1257C2C22×#54711yescharacteristic
1258C2C2×#351211yescharacteristic
1259C2#6285611yescharacteristic
1260C2#6292611yescharacteristic
1261C2#6295611yescharacteristic
1262C2#6298811yescharacteristic
1263C2#6300311yescharacteristic
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×#3512C2semidirect
2. #59826C2semidirect
3. #59312C2semidirect
4. #59304C2semidirect
5. #59304C2semidirect
6. #59258C2semidirect
7. #59213C2semidirect
8. #45264C2semidirect
9. #45135C2semidirect
10. #43526C2semidirect
11. #39353C2semidirect
12. #39352C2semidirect
13. #37799C2semidirect
14. #37798C2semidirect
15. #36117C2semidirect
16. #36116C2semidirect
17. #35639C2semidirect
18. #35517C2semidirect
19. #35273C2semidirect
20. #35255C2semidirect
21. #34937C2semidirect
22. C2×#2552C2semidirect
23. #34206C2semidirect
24. #34183C2semidirect
25. C4⋊C4×#41C2semidirect
26. C4×#537C2semidirect
212. #537D4semidirect
1252. C4#3512semidirect

Maximal subgroups

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

subgroupindex
C2×#35122
#598262
#593122
#593042
#592582
#592132
#452642
#451352
#435262
#393532
#393522
#377992
#377982
#361172
#361162
#356392
#355172
#352732
#352552
#349372
C2×#25522
#342062
#341832
C4⋊C4×#412
C4×#5372