Finite Group Databasebeta

← #7712462

Subgroups — #7712462

Order 512.

7176 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×#3551C212yesmaximal, complemented
2#59837C218yesmaximal, complemented
3#46281C214yesmaximal, complemented
4#46280C214yesmaximal, complemented
5#39485C212yesmaximal, complemented
6#39484C211yesmaximal, characteristic, complemented
7#39483C211yesmaximal, characteristic, complemented
8#39454C214yesmaximal, complemented
9#39452C214yesmaximal, complemented
10#39392C218yesmaximal, complemented
11#39357C212yesmaximal, complemented
12#39356C211yesmaximal, characteristic, complemented
13#39355C211yesmaximal, characteristic, complemented
14#37542C212yesmaximal, complemented
15#37388C212yesmaximal, complemented
16#37300C212yesmaximal, complemented
17#36631C211yesmaximal, characteristic, complemented
18#36631C211yesmaximal, characteristic, complemented
19#36396C212yesmaximal, complemented
20#36386C212yesmaximal, complemented
21#36376C212yesmaximal, complemented
22#36362C212yesmaximal, complemented
23#35308C212yesmaximal, complemented
24#35256C212yesmaximal, complemented
25C4×#532C211yesmaximal, characteristic, complemented
26#3551—232no—
27C2×#563C2214yescomplemented
28C2×#560C2214yes—
29C2×#555C2214yes—
30C2×#553C2212yes—
31C2×#553C2212yescomplemented
32C2×#552C2212yes—
33C2×#552C2212yescomplemented
34C2×#551C2214yescomplemented
35C2×#548C2212yes—
36C2×#548C2212yescomplemented
37C2×#546C2212yes—
38C2×#546C2212yescomplemented
39C2×#540C2214yes—
40C2×#540C2214yescomplemented
41C2×#538C2214yes—
42C2×#538C2214yescomplemented
43C2×#537C2212yes—
44C2×#537C2212yes—
45C2×#536C2212yescomplemented
46C2×#536C2212yescomplemented
47C2×#535C2212yes—
48C2×#535C2212yescomplemented
49C2×#532C2211yescharacteristic
50C2×#529C2212yescomplemented
51C2×#529C2212yescomplemented
52C2×C4×#41C2212yescomplemented
53#2861C2212yescomplemented
54#2861C2212yescomplemented
55#2860C2214yescomplemented
56#2860C2214yescomplemented
57#2859C2211yescharacteristic, complemented
58#2859C2211yescharacteristic, complemented
59#2858C2211yescharacteristic
60#2858C2211yescharacteristic
61#2857C2211yescharacteristic, complemented
62#2857C2211yescharacteristic, complemented
63#2857C2212yescomplemented
64#2856C2212yes—
65#2856C2211yescharacteristic
66#2856C2211yescharacteristic
67#2854C2214yescomplemented
68#2854C2214yescomplemented
69#2850C2212yes—
70#2850C2212yescomplemented
71#2850C2212yescomplemented
72#2850C2212yescomplemented
73#2823C2218yescomplemented
74#2730C2218yescomplemented
75#2729C2218yescomplemented
76#2727C2214yescomplemented
77#2726C2214yescomplemented
78#2725C2218yescomplemented
79#2724C2214yes—
80#2708C2218yescomplemented
81#2701C2218yescomplemented
82#2701C2218yescomplemented
83#2686C2218yescomplemented
84#2683C2214yescomplemented
85#2682C2214yes—
86#2682C2214yescomplemented
87#2682C2214yescomplemented
88#2681C2218yescomplemented
89#2679C2214yes—
90#2678C2218yescomplemented
91#2678C2218yescomplemented
92#2673C2218yescomplemented
93#2668C2218yescomplemented
94#2630C2218yescomplemented
95#2630C2218yescomplemented
96#2621C2212yescomplemented
97#2621C2212yescomplemented
98#2620C2212yes—
99#2620C2212yescomplemented
100#2620C2212yescomplemented
101#2620C2212yescomplemented
102#2619C2212yes—
103#2619C2212yes—
104#2609C2218yescomplemented
105#2566C2212yescomplemented
106#2566C2212yescomplemented
107#2565C2212yescomplemented
108#2565C2212yescomplemented
109#2560C2218yescomplemented
110#2559C2218yes—
111#2558C2218yescomplemented
112#2557C2218yescomplemented
113#2556C2218yescomplemented
114#2554C2218yescomplemented
115#2545C2212yescomplemented
116#2545C2212yescomplemented
117#2544C2212yes—
118#2544C2212yes—
119#2543C2218yescomplemented
120#2534C2218yes—
121#2521C2218yescomplemented
122#2504C2212yescomplemented
123#2503C2212yescomplemented
124#2502C2212yescomplemented
125#2501C2212yescomplemented
126#2500C2212yes—
127#2500C2212yescomplemented
128#2499C2212yescomplemented
129#2499C2212yescomplemented
130#2478C2218yescomplemented
131#2472C2218yescomplemented
132#2470C2218yescomplemented
133#2466C2218yescomplemented
134#2464C2218yescomplemented
135#2464C2218yescomplemented
136#2461C2218yescomplemented
137#2455C2218yescomplemented
138#2436C2212yescomplemented
139#2435C2212yescomplemented
140#2434C2212yescomplemented
141#2433C2212yes—
142#2432C2212yes—
143#2432C2212yes—
144#2431C2212yes—
145#2431C2212yes—
146#2429C2218yescomplemented
147#2428C2218yescomplemented
148#2427C2218yescomplemented
149#2426C2218yescomplemented
150#2425C2218yescomplemented
151#2425C2218yescomplemented
152#2425C2218yescomplemented
153#2424C2218yes—
154#2424C2218yescomplemented
155#2424C2218yescomplemented
156#2424C2218yescomplemented
157#2364C2218yescomplemented
158#2359C2218yescomplemented
159#2358C2218yescomplemented
160#2342C2218yescomplemented
161#2317C2212yescomplemented
162#2317C2212yescomplemented
163C4×C4⋊Q8C2211yescharacteristic, complemented
164C4×C4⋊Q8C2211yescharacteristic, complemented
165C4×C4⋊Q8C2212yescomplemented
166C4×#127C2211yescharacteristic
167C4×#127C2211yescharacteristic
168C4×#127C2212yes—
169C4×#124C2212yescomplemented
170C4×#124C2212yescomplemented
171C4×#124C2214yescomplemented
172C4×#121C2212yes—
173C4×#121C2214yescomplemented
174C4×#121C2214yescomplemented
175C4×#121C2212yescomplemented
176C4×#121C2214yescomplemented
177#2297C2212yes—
178#2297C2212yescomplemented
179#2297C2212yescomplemented
180C2×#391C2212yescomplemented
181#2293C2211yescharacteristic
182#2293C2214yescomplemented
183#2293C2214yescomplemented
184#2293C2211yescharacteristic, complemented
185#2293C2212yescomplemented
186C2×#390C2212yescomplemented
187#2285C2211yescharacteristic, complemented
188C42×D4C2211yescharacteristic
189C42×D4C2212yescomplemented
190C42×D4C2211yescharacteristic, complemented
191C2×C43C2211yescharacteristic, complemented
192C22×#41C2312yes—
193C22×#41C2312yes—
194C22×#41C2312yes—
195C23×Q8C2312yes—
196C23×D4C2312yes—
197#563—232no—
198#560—232no—
199#555—232no—
200#553—216no—
201#553—216no—
202#552—216no—
203#552—216no—
204#551—232no—
205#548—216no—
206#548—216no—
207#546—216no—
208#546—216no—
209#540—232no—
210#540—232no—
211#538—232no—
212#538—232no—
213#537—216no—
214#537—216no—
215#536—216no—
216#536—48no—
217#535—216no—
218#535—48no—
219#532D4116yescomplemented
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2312yes—
224C2×C4⋊Q8C2311yescharacteristic
225C2×#127C2311yescharacteristic
226C2×#127C2314yes—
227C2×#127C2311yescharacteristic
228C2×#127C2312yes—
229C2×#127C2311yescharacteristic
230#529—216no—
231#529—216no—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#126C2314yes—
236C2×#126C2314yes—
237C2×#126C2314yes—
238C2×#125C2312yes—
239C2×#125C2312yes—
240C2×#125C2314yes—
241C2×#125C2314yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245C2×#124C2314yes—
246C2×#124C2314yes—
247C2×#124C2314yes—
248C2×#124C2314yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#124C2312yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2318yes—
264C2×#123C2318yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2318yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2312yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2318yes—
297C2×#121C2318yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2311yescharacteristic
301C2×#120C2314yes—
302C2×#120C2314yes—
303C2×#120C2314yes—
304C2×#120C2314yes—
305C2×#120C2318yes—
306C2×#120C2318yes—
307C4×#41—48no—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2314yes—
335C2×#117C2314yes—
336C2×#117C2314yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C22×C4⋊C4C2312yes—
340C22×C4⋊C4C2312yes—
341C22×C22⋊C4C2314yes—
342C22×C22⋊C4C2314yes—
343C22×C22⋊C4C2318yes—
344C22×C42C2311yescharacteristic
345C22×C42C2312yes—
346C22×C42C2311yescharacteristic
347C22×C42C2312yes—
348C22×C42C2312yes—
349C22×C42C2312yes—
350C22×C42C2311yescharacteristic
351#400C2318yes—
352#399C2318yes—
353#398C2318yes—
354#398C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#397C2318yes—
359#397C2318yes—
360#397C2318yes—
361#397C2318yes—
362#397C2318yes—
363#396C2318yes—
364#396C2318yes—
365#396C2318yes—
366#396C2318yes—
367#396C2318yes—
368#396C2318yes—
369#396C2318yes—
370#396C2318yes—
371#395C2318yes—
372#394C2318yes—
373#394C2318yes—
374#394C2318yes—
375#394C2318yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#394C2318yes—
385#393C2318yes—
386#392C2318yes—
387#392C2318yes—
388#392C2318yes—
389#392C2318yes—
390#392C2318yes—
391#391C2318yes—
392#391C2312yes—
393#391C2312yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#390C2318yes—
402#390C2312yes—
403#390C2312yes—
404#390C2314yes—
405#390C2314yes—
406#390C2314yes—
407#390C2314yes—
408#390C2312yes—
409#390C2312yes—
410#390C2312yes—
411#390C2312yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2314yes—
419#390C2312yes—
420#390C2314yes—
421#390C2314yes—
422#390C2318yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2312yes—
427#389C2312yes—
428#389C2318yes—
429#389C2318yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2318yes—
435#389C2314yes—
436#389C2314yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#386C2318yes—
460#386C2318yes—
461#386C2318yes—
462#386C2318yes—
463#386C2318yes—
464#386C2318yes—
465#386C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2314yes—
470#386C2314yes—
471#386C2318yes—
472#386C2318yes—
473#385C2318yes—
474#385C2318yes—
475#385C2318yes—
476#385C2318yes—
477#385C2318yes—
478#385C2318yes—
479#385C2318yes—
480#385C2318yes—
481#384C2312yes—
482#384C2311yescharacteristic
483#384C2311yescharacteristic
484#384C2311yescharacteristic
485#384C2311yescharacteristic
486#384C2312yes—
487#384C2312yes—
488#382C2312yes—
489#382C2312yes—
490#382C2312yes—
491#382C2312yes—
492#382C2312yes—
493#381C2318yes—
494#380C2318yes—
495#380C2314yes—
496#380C2314yes—
497#380C2312yes—
498#380C2312yes—
499#379C2318yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2318yes—
520C2×#95C2318yes—
521C43C2311yescharacteristic
522C43C2312yes—
523C43C2311yescharacteristic
524C43C2311yescharacteristic
525C43C2311yescharacteristic
526C43C2312yes—
527C25C2414yes—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—44no—
531C2×#41—44no—
532C2×#41—44no—
533C2×#41—44no—
534C2×#41—44no—
535C2×#41—44no—
536C2×#41C2×D4116yes—
537C22×Q8—28no—
538C22×Q8—44no—
539C22×Q8—44no—
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2414yes—
543C22×Q8C2412yes—
544C22×D4—28no—
545C22×D4—44no—
546C22×D4—44no—
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2414yes—
550C22×D4C2414yes—
551C22×D4C2414yes—
552C22×D4C2414yes—
553C22×D4C2414yes—
554C22×D4C2414yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2414yes—
559C22×D4C2414yes—
560C22×D4C2418yes—
561C22×D4C2411yescharacteristic
562C22×D4C2412yes—
563C22×D4C2411yescharacteristic
564C22×D4C2412yes—
565C22×D4C2412yes—
566C22×D4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2411yescharacteristic
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2414yes—
576C23×C4C2414yes—
577C23×C4C2414yes—
578C23×C4C2414yes—
579C23×C4C2414yes—
580C23×C4C2412yes—
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C4⋊Q8—216no—
584C4⋊Q8—24no—
585C4⋊Q8—42no—
586C4⋊Q8—44no—
587C4⋊Q8C2×D418yes—
588#127—216no—
589#127—24no—
590#127—42no—
591#127—44no—
592#127C2×D418yes—
593#126—216no—
594#126—216no—
595#126—216no—
596#126—216no—
597#126—216no—
598#126—216no—
599#125—216no—
600#125—216no—
601#125—28no—
602#125—28no—
603#124—216no—
604#124—216no—
605#124—216no—
606#124—216no—
607#124—28no—
608#124—28no—
609#124—28no—
610#124—44no—
611#124—44no—
612#124—44no—
613#124C2×D4116yes—
614#123—216no—
615#123—216no—
616#123—216no—
617#123—216no—
618#123—216no—
619#123—216no—
620#123—216no—
621#123—216no—
622#123—216no—
623#123—216no—
624#123—416no—
625#123—416no—
626C22⋊Q8—216no—
627C22⋊Q8—216no—
628C22⋊Q8—28no—
629C22⋊Q8—28no—
630C22⋊Q8—28no—
631C22⋊Q8—28no—
632C22⋊Q8—28no—
633C22⋊Q8—28no—
634C22⋊Q8—216no—
635C22⋊Q8—216no—
636C22⋊Q8—416no—
637#121—216no—
638#121—216no—
639#121—216no—
640#121—216no—
641#121—216no—
642#121—216no—
643#121—216no—
644#121—216no—
645#121—216no—
646#121—216no—
647#121—28no—
648#121—28no—
649#121—28no—
650#121—28no—
651#121—28no—
652#121—28no—
653#121—216no—
654#121—216no—
655#121—416no—
656#121—48no—
657#121—416no—
658#121—48no—
659#121C2×D418yes—
660#121C2×D4116yes—
661#121C2×D418yes—
662#120—216no—
663#120—216no—
664#120—216no—
665#120—216no—
666#120—416no—
667#120—416no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—48no—
671C4×D4—216no—
672C4×D4—216no—
673C4×D4—216no—
674C4×D4—216no—
675C4×D4—216no—
676C4×D4—216no—
677C4×D4—28no—
678C4×D4—28no—
679C4×D4—48no—
680C4×D4—48no—
681C4×D4—48no—
682C4×D4—48no—
683C4×D4—44no—
684C4×D4—44no—
685C4×D4—48no—
686C4×D4—48no—
687C4×D4C2×D418yes—
688C4×D4C2×D4116yes—
689C4×D4C2×D418yes—
690#117—28no—
691#117—28no—
692#117—216no—
693#117—216no—
694#117—216no—
695#117—216no—
696#117—28no—
697#117—28no—
698#117—44no—
699C2×C4⋊C4—28no—
700C2×C4⋊C4—28no—
701C2×C4⋊C4C2412yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2412yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C22⋊C4—216no—
738C2×C22⋊C4—216no—
739C2×C22⋊C4—416no—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2418yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2418yes—
768C2×C22⋊C4C2418yes—
769C2×C22⋊C4C2418yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2418yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2418yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2418yes—
778C2×C22⋊C4C2418yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C42—24no—
784C2×C42—44no—
785C2×C42—44no—
786C2×C42—44no—
787C2×C42—44no—
788C2×C42—42no—
789C2×C42C2×D418yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2412yes—
794C2×C42C2412yes—
795C2×C42C2414yes—
796C2×C42C2412yes—
797C2×C42C2412yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2412yes—
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2412yes—
807C2×C42C2412yes—
808C2×C42C2412yes—
809C2×C42C2412yes—
810C2×C42C2412yes—
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815C2×C42C2411yescharacteristic
816#95C2418yes—
817#95C2418yes—
818#95C2418yes—
819#95C2418yes—
820#95C2412yes—
821#95C2414yes—
822#95C2412yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835C24—28no—
836C24—44no—
837C24—48no—
838C24—48no—
839C24—44no—
840C24C2514yes—
841C24C2514yes—
842C24C2512yes—
843C24C2512yes—
844C24C2511yescharacteristic
845#41—432no—
846#41—816no—
847#41—816no—
848C2×Q8—24no—
849C2×Q8—24no—
850C2×Q8—28no—
851C2×Q8—24no—
852C2×Q8—24no—
853C2×Q8—24no—
854C2×Q8—24no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—44no—
858C2×Q8—44no—
859C2×Q8—816no—
860C2×Q8C22×D418yes—
861C2×D4—28no—
862C2×D4—28no—
863C2×D4—28no—
864C2×D4—28no—
865C2×D4—28no—
866C2×D4—28no—
867C2×D4—28no—
868C2×D4—28no—
869C2×D4—24no—
870C2×D4—24no—
871C2×D4—28no—
872C2×D4—24no—
873C2×D4—24no—
874C2×D4—28no—
875C2×D4—24no—
876C2×D4—24no—
877C2×D4—28no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—44no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—48no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—48no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—48no—
897C2×D4—44no—
898C2×D4—48no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—48no—
904C2×D4—48no—
905C2×D4—48no—
906C2×D4—816no—
907C2×D4C22×D414yes—
908C2×D4C22×D418yes—
909C2×D4C22×D414yes—
910C2×D4C22×D418yes—
911C2×D4C22×D418yes—
912C2×D4C22×D418yes—
913C22×C4—22no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—22no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—28no—
928C22×C4—28no—
929C22×C4—28no—
930C22×C4—28no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—48no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—48no—
942C22×C4—48no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—48no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4C22×D414yes—
951C22×C4C22×D418yes—
952C22×C4C22×D418yes—
953C22×C4C22×D414yes—
954C22×C4C22×D414yes—
955C22×C4C2512yes—
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2514yes—
964C22×C4C2511yescharacteristic
965C22×C4C2511yescharacteristic
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2511yescharacteristic
975C4⋊C4—24no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—44no—
1004C4⋊C4—48no—
1005C4⋊C4—48no—
1006C4⋊C4—48no—
1007C4⋊C4—44no—
1008C4⋊C4C22×D414yes—
1009C4⋊C4C22×D418yes—
1010C4⋊C4C22×D414yes—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—216no—
1034C22⋊C4—216no—
1035C22⋊C4—216no—
1036C22⋊C4—28no—
1037C22⋊C4—216no—
1038C22⋊C4—28no—
1039C22⋊C4—48no—
1040C22⋊C4—48no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—48no—
1045C22⋊C4—48no—
1046C22⋊C4—48no—
1047C22⋊C4—48no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C22⋊C4C22×D418yes—
1051C22⋊C4C22×D418yes—
1052C22⋊C4C22×D418yes—
1053C22⋊C4C22×D418yes—
1054C42—28no—
1055C42—28no—
1056C42—28no—
1057C42—28no—
1058C42—22no—
1059C42—24no—
1060C42—24no—
1061C42—24no—
1062C42—24no—
1063C42—24no—
1064C42—24no—
1065C42—24no—
1066C42—22no—
1067C42—22no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—44no—
1074C42—44no—
1075C42C22×D414yes—
1076C42C22×D414yes—
1077C42C22×D414yes—
1078C42C22×D414yes—
1079C42H(5,𝔽2)14yes—
1080C23—22no—
1081C23—22no—
1082C23—21no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23—24no—
1087C23—22no—
1088C23—21no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—24no—
1093C23—24no—
1094C23—24no—
1095C23—24no—
1096C23—28no—
1097C23—28no—
1098C23—28no—
1099C23—24no—
1100C23—28no—
1101C23—24no—
1102C23—88no—
1103C23—88no—
1104C23—88no—
1105C23—816no—
1106C23—168no—
1107C23C23×D414yes—
1108C23C23×D412yes—
1109C23C23×D414yes—
1110C23C2611yescharacteristic
1111Q8—48no—
1112Q8—48no—
1113Q8—48no—
1114Q8—88no—
1115D4—48no—
1116D4—44no—
1117D4—44no—
1118D4—48no—
1119D4—48no—
1120D4—48no—
1121D4—48no—
1122D4—48no—
1123D4—88no—
1124D4—88no—
1125D4—88no—
1126D4—88no—
1127D4—88no—
1128D4—88no—
1129D4—88no—
1130D4—88no—
1131D4—88no—
1132D4—88no—
1133D4—88no—
1134D4—168no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—216no—
1152C2×C4—216no—
1153C2×C4—28no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—28no—
1170C2×C4—28no—
1171C2×C4—28no—
1172C2×C4—24no—
1173C2×C4—28no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—44no—
1178C2×C4—44no—
1179C2×C4—48no—
1180C2×C4—48no—
1181C2×C4—88no—
1182C2×C4—88no—
1183C2×C4—88no—
1184C2×C4—88no—
1185C2×C4—88no—
1186C2×C4—88no—
1187C2×C4—88no—
1188C2×C4—88no—
1189C2×C4—88no—
1190C2×C4C23×D412yes—
1191C2×C4C23×D412yes—
1192C2×C4C23×D414yes—
1193C2×C4C23×D414yes—
1194C2×C4C23×D412yes—
1195C2×C4C23×D412yes—
1196C2×C4C23×D412yes—
1197C2×C4C23×D412yes—
1198C2×C4C2×H(5,𝔽2)14yes—
1199C2×C4C2×H(5,𝔽2)12yes—
1200C2×C4#58514yes—
1201C2×C4#58514yes—
1202C2×C4#58512yes—
1203C22—24no—
1204C22—22no—
1205C22—24no—
1206C22—22no—
1207C22—22no—
1208C22—24no—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—42no—
1213C22—44no—
1214C22—44no—
1215C22—42no—
1216C22—44no—
1217C22—44no—
1218C22—48no—
1219C22—48no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—48no—
1227C22—48no—
1228C22—1616no—
1229C22C24×D411yescharacteristic
1230C22C22×H(5,𝔽2)11yescharacteristic
1231C22C2×#58511yescharacteristic
1232C22C2×#58512yes—
1233C22C2×#58512yes—
1234C4—24no—
1235C4—24no—
1236C4—24no—
1237C4—22no—
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—24no—
1243C4—24no—
1244C4—42no—
1245C4—44no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—44no—
1250C4—44no—
1251C4—44no—
1252C4—44no—
1253C4#349614yes—
1254C2—44no—
1255C2—42no—
1256C2—44no—
1257C2—84no—
1258C2—84no—
1259C2#6274312yes—
1260C2C2×#349611yescharacteristic
1261C2#6281211yescharacteristic
1262C2#6281211yescharacteristic
1263C2#6283012yes—
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×#3551C2semidirect
2. #59837C2semidirect
3. #46281C2semidirect
4. #46280C2semidirect
5. #39485C2semidirect
6. #39484C2semidirect
7. #39483C2semidirect
8. #39454C2semidirect
9. #39452C2semidirect
10. #39392C2semidirect
11. #39357C2semidirect
12. #39356C2semidirect
13. #39355C2semidirect
14. #37542C2semidirect
15. #37388C2semidirect
16. #37300C2semidirect
17. #36631C2semidirect
18. #36631C2semidirect
19. #36396C2semidirect
20. #36386C2semidirect
21. #36376C2semidirect
22. #36362C2semidirect
23. #35308C2semidirect
24. #35256C2semidirect
25. C4×#532C2semidirect
27. C2×#563C22semidirect
31. C2×#553C22semidirect
33. C2×#552C22semidirect
34. C2×#551C22semidirect
36. C2×#548C22semidirect
38. C2×#546C22semidirect
40. C2×#540C22semidirect
42. C2×#538C22semidirect
45. C2×#536C22semidirect
46. C2×#536C22semidirect
48. C2×#535C22semidirect
50. C2×#529C22semidirect
51. C2×#529C22semidirect
52. C2×C4×#41C22semidirect
53. #2861C22semidirect
54. #2861C22semidirect
55. #2860C22semidirect
56. #2860C22semidirect
57. #2859C22semidirect
58. #2859C22semidirect
61. #2857C22semidirect
62. #2857C22semidirect
63. #2857C22semidirect
67. #2854C22semidirect
68. #2854C22semidirect
70. #2850C22semidirect
71. #2850C22semidirect
72. #2850C22semidirect
73. #2823C22semidirect
74. #2730C22semidirect
75. #2729C22semidirect
76. #2727C22semidirect
77. #2726C22semidirect
78. #2725C22semidirect
80. #2708C22semidirect
81. #2701C22semidirect
82. #2701C22semidirect
83. #2686C22semidirect
84. #2683C22semidirect
86. #2682C22semidirect
87. #2682C22semidirect
88. #2681C22semidirect
90. #2678C22semidirect
91. #2678C22semidirect
92. #2673C22semidirect
93. #2668C22semidirect
94. #2630C22semidirect
95. #2630C22semidirect
96. #2621C22semidirect
97. #2621C22semidirect
99. #2620C22semidirect
100. #2620C22semidirect
101. #2620C22semidirect
104. #2609C22semidirect
105. #2566C22semidirect
106. #2566C22semidirect
107. #2565C22semidirect
108. #2565C22semidirect
109. #2560C22semidirect
111. #2558C22semidirect
112. #2557C22semidirect
113. #2556C22semidirect
114. #2554C22semidirect
115. #2545C22semidirect
116. #2545C22semidirect
119. #2543C22semidirect
121. #2521C22semidirect
122. #2504C22semidirect
123. #2503C22semidirect
124. #2502C22semidirect
125. #2501C22semidirect
127. #2500C22semidirect
128. #2499C22semidirect
129. #2499C22semidirect
130. #2478C22semidirect
131. #2472C22semidirect
132. #2470C22semidirect
133. #2466C22semidirect
134. #2464C22semidirect
135. #2464C22semidirect
136. #2461C22semidirect
137. #2455C22semidirect
138. #2436C22semidirect
139. #2435C22semidirect
140. #2434C22semidirect
146. #2429C22semidirect
147. #2428C22semidirect
148. #2427C22semidirect
149. #2426C22semidirect
150. #2425C22semidirect
151. #2425C22semidirect
152. #2425C22semidirect
154. #2424C22semidirect
155. #2424C22semidirect
156. #2424C22semidirect
157. #2364C22semidirect
158. #2359C22semidirect
159. #2358C22semidirect
160. #2342C22semidirect
161. #2317C22semidirect
162. #2317C22semidirect
163. C4×C4⋊Q8C22semidirect
164. C4×C4⋊Q8C22semidirect
165. C4×C4⋊Q8C22semidirect
169. C4×#124C22semidirect
170. C4×#124C22semidirect
171. C4×#124C22semidirect
173. C4×#121C22semidirect
174. C4×#121C22semidirect
175. C4×#121C22semidirect
176. C4×#121C22semidirect
178. #2297C22semidirect
179. #2297C22semidirect
180. C2×#391C22semidirect
182. #2293C22semidirect
183. #2293C22semidirect
184. #2293C22semidirect
185. #2293C22semidirect
186. C2×#390C22semidirect
187. #2285C22semidirect
189. C42×D4C22semidirect
190. C42×D4C22semidirect
191. C2×C43C22semidirect
219. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35512
#598372
#462812
#462802
#394852
#394842
#394832
#394542
#394522
#393922
#393572
#393562
#393552
#375422
#373882
#373002
#366312
#363962
#363862
#363762
#363622
#353082
#352562
C4×#5322