Finite Group Databasebeta

← #10582809

Subgroups — #10582809

Order 512.

5795 conjugacy classes of subgroups.

The subgroup lattice has 1113 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62840C211yesmaximal, characteristic, complemented
2#62825C211yesmaximal, characteristic, complemented
3#62549C218yesmaximal, complemented
4#62484C218yesmaximal, complemented
5#62242C214yesmaximal, complemented
6#62241C214yesmaximal, complemented
7#62238C214yesmaximal, complemented
8#62237C214yesmaximal, complemented
9#61877C212yesmaximal, complemented
10#61876C212yesmaximal, complemented
11#61800C214yesmaximal, complemented
12#61774C218yesmaximal, complemented
13#61009C214yesmaximal, complemented
14#60967C212yesmaximal, complemented
15#60882C214yesmaximal, complemented
16#60861C212yesmaximal, complemented
17#60281C211yesmaximal, characteristic, complemented
18#3567—24no—
19#3563—22no—
20#3563C2214yes—
21#3559—22no—
22#3559C2214yes—
23#3556C2211yescharacteristic
24#3553—24no—
25#3548C2211yescharacteristic
26#3548C2212yes—
27#3539—24no—
28#3539C2214yes—
29#3517—22no—
30#3517C2214yes—
31#3517C2214yes—
32#3515—22no—
33#3515—24no—
34#3515C2214yes—
35#3515C2218yes—
36#3515C2214yes—
37#3512—24no—
38#3512C2212yes—
39#3512C2212yes—
40#3512C2214yes—
41#3504C2212yes—
42#3504C2212yes—
43#3492—24no—
44#3492C2214yes—
45#3444C2211yescharacteristic
46#3444C2212yes—
47#3444C2211yescharacteristic
48C22×#125C2211yescharacteristic
49#3390C2218yescomplemented
50#3389C2218yescomplemented
51#3388C2218yescomplemented
52#3388C2218yescomplemented
53#3374C2218yescomplemented
54#3372C2218yescomplemented
55#3368C2218yescomplemented
56#3366C2218yescomplemented
57#3355C2218yes—
58#3352C2218yes—
59#3351C2218yes—
60#3351C2218yes—
61#3346C2218yes—
62#3346C2218yescomplemented
63#3345C2218yes—
64#3345C2218yescomplemented
65#3344C2218yes—
66#3344C2218yescomplemented
67#3343C2218yes—
68#3343C2218yescomplemented
69#3333C2218yes—
70#3332C2218yes—
71#3331C2218yes—
72#3330C2218yes—
73#3317C2218yes—
74#3317C2218yescomplemented
75#3315C2218yes—
76#3315C2218yescomplemented
77#3309C2218yes—
78#3309C2218yescomplemented
79#3307C2218yes—
80#3307C2218yescomplemented
81#3261C2214yescomplemented
82#3260C2214yescomplemented
83#3260C2214yescomplemented
84#3259C2214yescomplemented
85#3255C2212yes—
86#3254C2212yes—
87#3254C2212yes—
88#3253C2212yes—
89#3242C2218yes—
90#3242C2218yescomplemented
91#3241C2218yes—
92#3241C2218yescomplemented
93#3236C2214yes—
94#3236C2214yes—
95#3234C2214yes—
96#3234C2214yes—
97#3233C2214yes—
98#3233C2214yes—
99#3233C2218yescomplemented
100#3232C2218yes—
101#3232C2218yes—
102#3232C2218yescomplemented
103#3232C2218yescomplemented
104#3212C2214yes—
105#3212C2214yes—
106#3212C2218yescomplemented
107#3204C2218yes—
108#3203C2218yes—
109#3197C2218yes—
110#3183C2218yes—
111#3183C2218yescomplemented
112#3168C2218yescomplemented
113#3166C2214yes—
114#3166C2214yescomplemented
115C2×#499C2214yescomplemented
116#3142C2214yes—
117#3142C2214yescomplemented
118#3131C2214yescomplemented
119#3120C2218yes—
120#3120C2218yescomplemented
121#3119C2218yes—
122#3119C2218yescomplemented
123#3116C2214yes—
124#3116C2214yes—
125#3115C2214yes—
126#3115C2214yes—
127#3099C2218yes—
128#3098C2218yes—
129#3092C2214yes—
130#3092C2214yes—
131#3084C2218yescomplemented
132#3083C2218yescomplemented
133#3080C2214yes—
134#3080C2214yes—
135#2995C2214yes—
136#2995C2214yes—
137#2987C2212yes—
138#2980C2212yes—
139#2978C2214yes—
140#2965C2218yes—
141#2922C2214yes—
142#2920C2212yes—
143#564—24no—
144#564—22no—
145#563—24no—
146#563—24no—
147#562—22no—
148#562—24no—
149#562—24no—
150#560—28no—
151#557—22no—
152#557—24no—
153#557C2314yes—
154#557C2318yes—
155#557C2314yes—
156#554—22no—
157#554—28no—
158#554—24no—
159#554—28no—
160#554—24no—
161#554C2318yes—
162#554C2314yes—
163#554C2318yes—
164#554C2314yes—
165#553—28no—
166#553—28no—
167#553—28no—
168#553—24no—
169#553—24no—
170#553—28no—
171#553—28no—
172#553—28no—
173#553—24no—
174#553—28no—
175#553—28no—
176#553—24no—
177#553C2318yes—
178#553C2318yes—
179#553C2318yes—
180#552—28no—
181#552—28no—
182#552—24no—
183#552—24no—
184#552—24no—
185#552—28no—
186#552—28no—
187#552—28no—
188#552—24no—
189#552—28no—
190#552—28no—
191#552C2318yes—
192#552C2318yes—
193#552C2318yes—
194#550—24no—
195#550—22no—
196#550—24no—
197#550C2318yes—
198#550C2314yes—
199#550C2314yes—
200#547—28no—
201#547—24no—
202#547—22no—
203#547—28no—
204#547—24no—
205#547—24no—
206#547C2318yes—
207#547C2314yes—
208#547C2318yes—
209#547C2314yes—
210#544—24no—
211#544—24no—
212#544C2318yes—
213#544C2314yes—
214#541—22no—
215#541—28no—
216#541—24no—
217#541—24no—
218#541—28no—
219#541C2314yes—
220#541C2314yes—
221#541C2314yes—
222#540—22no—
223#540—28no—
224#540—24no—
225#540—28no—
226#540—24no—
227#540—28no—
228#540C2314yes—
229#540C2314yes—
230#540C2314yes—
231#539—28no—
232#539—28no—
233#539—28no—
234#539—24no—
235#539—28no—
236#539—24no—
237#539—28no—
238#539—28no—
239#539—28no—
240#537—24no—
241#537—24no—
242#537—24no—
243#537C2318yes—
244#537C2314yes—
245#533—22no—
246#533D412yes—
247#533C2312yes—
248#533C2312yes—
249#533C2312yes—
250#533C2314yes—
251#533C2312yes—
252#533C2311yescharacteristic
253#533C2311yescharacteristic
254#532—24no—
255#532D412yes—
256#532C2314yes—
257#532C2312yes—
258#532C2311yescharacteristic
259#532C2312yes—
260#532C2312yes—
261#532C2312yes—
262#532C2311yescharacteristic
263#529—24no—
264#529—24no—
265#529—24no—
266#529—22no—
267#529—22no—
268#529—22no—
269#529—22no—
270#529—22no—
271#529—22no—
272#529D414yes—
273#529D414yes—
274#529C2318yes—
275#529C2318yes—
276#529C2314yes—
277#529C2314yes—
278#529C2314yes—
279#529C2314yes—
280C2×#125—22no—
281C2×#125—24no—
282C2×#125—22no—
283C2×#125—22no—
284C2×#125—22no—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291#525—22no—
292#525—22no—
293#525—22no—
294#525—28no—
295#525D414yes—
296#525C2314yes—
297#525C2312yes—
298#525C2312yes—
299#520—24no—
300#520—28no—
301#520—24no—
302#520C2318yes—
303#520C2314yes—
304#520C2314yes—
305C4×#41—22no—
306C4×#41—22no—
307C4×#41—22no—
308C4×#41C2314yes—
309C4×#41C2312yes—
310C4×#41C2314yes—
311C4×#41C2312yes—
312C22×C4⋊C4—22no—
313C22×C4⋊C4C2312yes—
314C22×C42C2311yescharacteristic
315#501C2318yes—
316#501C2318yes—
317#501C2318yes—
318#501C2318yes—
319#499C2318yes—
320#499C2318yes—
321#499C2318yes—
322#499C2318yes—
323#499C2318yes—
324#495C2318yes—
325#491C2318yes—
326#491C2318yes—
327#490C2318yes—
328#490C2318yes—
329#488C2318yes—
330#488C2318yes—
331#488C2318yes—
332#488C2318yes—
333#487C2318yes—
334#486C2318yes—
335#485C2318yes—
336#485C2318yes—
337#485C2318yes—
338#485C2318yes—
339#484C2318yes—
340#484C2318yes—
341#484C2318yes—
342#484C2318yes—
343#483C2318yes—
344#483C2318yes—
345#483C2318yes—
346#483C2318yes—
347#482C2318yes—
348#482C2318yes—
349#482C2318yes—
350#482C2318yes—
351#481C2318yes—
352#481C2318yes—
353#481C2318yes—
354#481C2318yes—
355#480C2318yes—
356#480C2318yes—
357#480C2318yes—
358#480C2318yes—
359#479C2318yes—
360#479C2318yes—
361#479C2318yes—
362#479C2318yes—
363#479C2318yes—
364#479C2318yes—
365#479C2318yes—
366#479C2318yes—
367#478C2318yes—
368#478C2318yes—
369#478C2318yes—
370#478C2318yes—
371#478C2318yes—
372#478C2318yes—
373#478C2318yes—
374#478C2318yes—
375#477C2318yes—
376#477C2314yes—
377#477C2314yes—
378#476C2318yes—
379#476C2314yes—
380#476C2314yes—
381#475C2318yes—
382#475C2314yes—
383#475C2314yes—
384#474C2318yes—
385#474C2314yes—
386#474C2314yes—
387#470C2318yes—
388#470C2318yes—
389#469C2318yes—
390#469C2318yes—
391#468C2318yes—
392#468C2318yes—
393#468C2318yes—
394#468C2318yes—
395#467C2318yes—
396#466C2318yes—
397#465C2318yes—
398#465C2318yes—
399#462C2318yes—
400#462C2314yes—
401#462C2314yes—
402#461C2318yes—
403#461C2314yes—
404#461C2314yes—
405#460C2318yes—
406#460C2314yes—
407#460C2314yes—
408#459C2318yes—
409#459C2314yes—
410#459C2314yes—
411#452C2318yes—
412#452C2318yes—
413#452C2318yes—
414#452C2318yes—
415#449C2318yes—
416#449C2318yes—
417#449C2318yes—
418#449C2318yes—
419#446C2318yes—
420#446C2318yes—
421#442C2318yes—
422#442C2318yes—
423#441C2318yes—
424#441C2318yes—
425#440C2318yes—
426#440C2318yes—
427#440C2318yes—
428#440C2318yes—
429C4×Q16C2318yes—
430C4×SD16C2318yes—
431C4×SD16C2318yes—
432C4×D8C2318yes—
433#436C2318yes—
434#436C2318yes—
435#435C2318yes—
436#435C2318yes—
437#435C2318yes—
438#435C2318yes—
439#433C2318yes—
440#433C2318yes—
441#432C2314yes—
442#432C2314yes—
443#431C2314yes—
444#431C2314yes—
445#431C2318yes—
446#428C2314yes—
447#428C2314yes—
448#428C2314yes—
449#428C2314yes—
450#428C2318yes—
451#428C2318yes—
452C2×#107C2318yes—
453C2×#106C2318yes—
454#424C2314yes—
455#424C2314yes—
456#423C2312yes—
457#423C2312yes—
458#417C2314yes—
459#417C2318yes—
460#417C2314yes—
461#417C2318yes—
462#417C2314yes—
463#417C2314yes—
464#416C2318yes—
465#416C2318yes—
466#408C2314yes—
467#408C2314yes—
468#407C2314yes—
469C4×M16C2314yes—
470C4×M16C2314yes—
471C2×C4×C8C2314yes—
472C2×#41—24no—
473C2×#41—28no—
474C2×#41—24no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41C2×D414yes—
479C2×#41C2412yes—
480C2×#41C2414yes—
481C2×#41C2418yes—
482C2×#41C2412yes—
483C23×C4—22no—
484C23×C4C2×D412yes—
485C23×C4C2411yescharacteristic
486C2×Q16C2418yes—
487C2×SD16C2418yes—
488C2×SD16C2418yes—
489C2×D8C2418yes—
490C2×M16C2414yes—
491C2×M16C2414yes—
492C2×M16C2414yes—
493C2×M16C2414yes—
494C22×C8C2414yes—
495C22×C8C2414yes—
496C4⋊Q8—24no—
497C4⋊Q8—28no—
498C4⋊Q8—24no—
499C4⋊Q8—28no—
500C4⋊Q8C2×D412yes—
501C4⋊Q8C2×D411yescharacteristic
502C4⋊Q8C2411yescharacteristic
503C4⋊Q8C2412yes—
504C4⋊Q8C2414yes—
505C4⋊Q8C2412yes—
506C4⋊Q8C2412yes—
507C4⋊Q8C2412yes—
508C4⋊Q8C2418yes—
509#127—24no—
510#127—28no—
511#127C2×D411yescharacteristic
512#127C2411yescharacteristic
513#127C2412yes—
514#127C2414yes—
515#126—28no—
516#126—28no—
517#126—28no—
518#126—28no—
519#126—28no—
520#126—28no—
521#126—28no—
522#126—28no—
523#126—28no—
524#126—24no—
525#126—24no—
526#126—24no—
527#126—28no—
528#126—28no—
529#126C2×D418yes—
530#125—28no—
531#125—28no—
532#125—28no—
533#125—24no—
534#125—24no—
535#125—24no—
536#125—28no—
537#125—28no—
538#125—28no—
539#125—28no—
540#125—28no—
541#125—28no—
542#125—28no—
543#125—28no—
544#125—28no—
545#125—22no—
546#125—24no—
547#125—24no—
548#125—22no—
549#125—24no—
550#125—24no—
551#125—24no—
552#125—22no—
553#125—28no—
554#125—28no—
555#125—22no—
556#125—22no—
557#125C2×D414yes—
558#125C2×D412yes—
559#125C2414yes—
560#125C2414yes—
561#125C2418yes—
562#125C2414yes—
563#125C2412yes—
564#125C2414yes—
565#125C2414yes—
566#125C2418yes—
567#124—22no—
568#124—22no—
569#124—22no—
570#124C2×D412yes—
571#124C2×D414yes—
572#124C2412yes—
573#124C2414yes—
574#123—28no—
575#123—28no—
576#123—28no—
577#123—24no—
578#123—24no—
579#123—24no—
580#123—22no—
581#123—24no—
582#123—28no—
583#123—28no—
584#123—28no—
585#123—28no—
586#123—28no—
587#123—28no—
588#123—28no—
589#123—28no—
590#123—28no—
591#123—28no—
592#123—28no—
593#123—28no—
594#123—28no—
595#123—28no—
596#123C2×D418yes—
597#123C2×D414yes—
598C22⋊Q8—24no—
599C22⋊Q8—24no—
600C22⋊Q8—28no—
601C22⋊Q8—28no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—28no—
609C22⋊Q8—24no—
610C22⋊Q8—28no—
611C22⋊Q8—28no—
612C22⋊Q8—28no—
613C22⋊Q8—28no—
614C22⋊Q8—28no—
615C22⋊Q8—28no—
616C22⋊Q8—28no—
617C22⋊Q8—28no—
618C22⋊Q8—28no—
619C22⋊Q8—28no—
620C22⋊Q8C2×D414yes—
621C22⋊Q8C2×D414yes—
622C22⋊Q8C2×D414yes—
623C22⋊Q8C2414yes—
624C22⋊Q8C2414yes—
625C22⋊Q8C2414yes—
626C22⋊Q8C2418yes—
627C22⋊Q8C2418yes—
628#121—28no—
629#121—28no—
630#121—24no—
631#121—24no—
632#121—28no—
633#121—28no—
634#121—28no—
635#121—28no—
636#121—28no—
637#121—28no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—22no—
643#121—22no—
644#121—28no—
645#121—24no—
646#121—28no—
647#121—28no—
648#121—28no—
649#121—28no—
650#121—28no—
651#121—28no—
652#121—28no—
653#121C2×D414yes—
654#121C2×D414yes—
655#121C2×D414yes—
656#121C2414yes—
657#121C2414yes—
658#121C2414yes—
659#121C2418yes—
660#121C2418yes—
661#120—22no—
662#120—24no—
663#120C2×D414yes—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—28no—
668C4×Q8—22no—
669C4×Q8—22no—
670C4×Q8—22no—
671C4×Q8—22no—
672C4×Q8—22no—
673C4×Q8—22no—
674C4×Q8—28no—
675C4×Q8C2×D414yes—
676C4×Q8C2×D414yes—
677C4×Q8C2414yes—
678C4×Q8C2414yes—
679C4×Q8C2414yes—
680C4×Q8C2418yes—
681C4×Q8C2418yes—
682C4×Q8C2414yes—
683C4×D4—28no—
684C4×D4—24no—
685C4×D4—28no—
686C4×D4—24no—
687C4×D4—24no—
688C4×D4—24no—
689C4×D4—24no—
690C4×D4—24no—
691C4×D4—24no—
692C4×D4—24no—
693C4×D4—24no—
694C4×D4—24no—
695C4×D4—24no—
696C4×D4—28no—
697C4×D4—28no—
698C4×D4—28no—
699C4×D4—24no—
700C4×D4—28no—
701C4×D4—28no—
702C4×D4—28no—
703C4×D4—28no—
704C4×D4—28no—
705C4×D4—28no—
706C4×D4—22no—
707C4×D4—22no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—22no—
711C4×D4—22no—
712C4×D4—28no—
713C4×D4C2×D418yes—
714C4×D4C2×D414yes—
715C4×D4C2×D418yes—
716C4×D4C2×D414yes—
717C4×D4C2414yes—
718C4×D4C2414yes—
719C4×D4C2414yes—
720C4×D4C2418yes—
721C4×D4C2418yes—
722C4×D4C2418yes—
723C4×D4C2414yes—
724#117—22no—
725#117—22no—
726#117—22no—
727#117—28no—
728#117—24no—
729#117—28no—
730#117—28no—
731#117—28no—
732#117—24no—
733#117—24no—
734#117—24no—
735#117—22no—
736#117—24no—
737#117—28no—
738#117—28no—
739#117C2×D414yes—
740#117C2×D418yes—
741#117C2412yes—
742#117C2414yes—
743#117C2418yes—
744#117C2412yes—
745#117C2414yes—
746C2×C4⋊C4—24no—
747C2×C4⋊C4—24no—
748C2×C4⋊C4—24no—
749C2×C4⋊C4—24no—
750C2×C4⋊C4—24no—
751C2×C4⋊C4—24no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—22no—
754C2×C4⋊C4—22no—
755C2×C4⋊C4—28no—
756C2×C4⋊C4—28no—
757C2×C4⋊C4—24no—
758C2×C4⋊C4—24no—
759C2×C4⋊C4—28no—
760C2×C4⋊C4—28no—
761C2×C4⋊C4—28no—
762C2×C4⋊C4—24no—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2418yes—
768C2×C42—24no—
769C2×C42—22no—
770C2×C42C2×D412yes—
771C2×C42C2×D412yes—
772C2×C42C2×D412yes—
773C2×C42C2414yes—
774C2×C42C2412yes—
775C2×C42C2411yescharacteristic
776C2×C42C2412yes—
777C2×C42C2411yescharacteristic
778#107C2418yes—
779#107C2418yes—
780#107C2418yes—
781#107C2418yes—
782#107C2418yes—
783#107C2418yes—
784#106C2418yes—
785#106C2418yes—
786#106C2418yes—
787#106C2418yes—
788#106C2418yes—
789#106C2418yes—
790C4⋊C8C2414yes—
791C4⋊C8C2414yes—
792C4⋊C8C2414yes—
793C4⋊C8C2414yes—
794C4⋊C8C2418yes—
795C4⋊C8C2418yes—
796#103C2418yes—
797#103C2418yes—
798#103C2418yes—
799#103C2418yes—
800#103C2418yes—
801#103C2418yes—
802#103C2418yes—
803#103C2418yes—
804#102C2418yes—
805#102C2418yes—
806#102C2418yes—
807#102C2418yes—
808#102C2418yes—
809#102C2418yes—
810#102C2418yes—
811#102C2418yes—
812C22⋊C8C2418yes—
813C22⋊C8C2418yes—
814C22⋊C8C2418yes—
815C22⋊C8C2418yes—
816#97C2418yes—
817#97C2418yes—
818C4×C8C2418yes—
819C4×C8C2418yes—
820C24C22×D411yescharacteristic
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—48no—
826#41—48no—
827#41—44no—
828#41—44no—
829#41—84no—
830#41—84no—
831#41—84no—
832#41—816no—
833#41—84no—
834#41—88no—
835#41—88no—
836C2×Q8—22no—
837C2×Q8—22no—
838C2×Q8—28no—
839C2×Q8—22no—
840C2×Q8C22×D412yes—
841C2×Q8C22×D414yes—
842C2×Q8C2514yes—
843C2×Q8C2512yes—
844C2×D4—22no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—28no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—28no—
855C2×D4—22no—
856C2×D4C22×D414yes—
857C2×D4C22×D412yes—
858C2×D4C22×D418yes—
859C2×D4C22×D414yes—
860C2×D4C2514yes—
861C2×D4C2512yes—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—28no—
866C22×C4—28no—
867C22×C4—22no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—28no—
873C22×C4—28no—
874C22×C4—28no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—82no—
878C22×C4—84no—
879C22×C4C22×D412yes—
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D418yes—
888C22×C4C2511yescharacteristic
889C22×C4C2512yes—
890C22×C4C2514yes—
891Q16—48no—
892SD16—48no—
893SD16—48no—
894D8—48no—
895M16—44no—
896M16—44no—
897M16—44no—
898M16—44no—
899C2×C8—44no—
900C2×C8—44no—
901C2×C8C2518yes—
902C2×C8C2518yes—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—24no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—22no—
913C4⋊C4—24no—
914C4⋊C4—24no—
915C4⋊C4—22no—
916C4⋊C4—24no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—28no—
929C4⋊C4—24no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4C22×D414yes—
938C4⋊C4C22×D418yes—
939C4⋊C4C22×D414yes—
940C4⋊C4C22×D418yes—
941C4⋊C4C22×D414yes—
942C4⋊C4C22×D418yes—
943C4⋊C4C2518yes—
944C4⋊C4C2514yes—
945C4⋊C4C2514yes—
946C4⋊C4C2514yes—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—22no—
953C22⋊C4—24no—
954C22⋊C4—28no—
955C22⋊C4—24no—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—28no—
961C22⋊C4—24no—
962C22⋊C4—28no—
963C22⋊C4—24no—
964C22⋊C4—28no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—28no—
968C22⋊C4C22×D418yes—
969C22⋊C4C22×D418yes—
970C22⋊C4C22×D418yes—
971C22⋊C4C22×D414yes—
972C22⋊C4C22×D418yes—
973C42—24no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—22no—
978C42—28no—
979C42—28no—
980C42—28no—
981C42C22×D412yes—
982C42C22×D411yescharacteristic
983C42C22×D412yes—
984C42C22×D412yes—
985C42C22×D411yescharacteristic
986C42C22×D412yes—
987C42C22×D412yes—
988C42C22×D418yes—
989C42C2511yescharacteristic
990C42C2514yes—
991C42C2512yes—
992C42C2511yescharacteristic
993C23—22no—
994C23—24no—
995C23—41no—
996C23—42no—
997C23C23×D414yes—
998C23C23×D412yes—
999C23C23×D411yescharacteristic
1000Q8—22no—
1001Q8—24no—
1002Q8—22no—
1003Q8—24no—
1004Q8—42no—
1005Q8—44no—
1006Q8—44no—
1007Q8—82no—
1008Q8—82no—
1009Q8—88no—
1010D4—22no—
1011D4—24no—
1012D4—22no—
1013D4—24no—
1014D4—42no—
1015D4—44no—
1016D4—44no—
1017D4—48no—
1018D4—44no—
1019D4—44no—
1020D4—48no—
1021D4—82no—
1022D4—82no—
1023D4—88no—
1024D4—84no—
1025D4—88no—
1026D4—84no—
1027D4—88no—
1028D4—84no—
1029D4—88no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—28no—
1042C2×C4—42no—
1043C2×C4—41no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—48no—
1051C2×C4—44no—
1052C2×C4—48no—
1053C2×C4—48no—
1054C2×C4—84no—
1055C2×C4—88no—
1056C2×C4—84no—
1057C2×C4—84no—
1058C2×C4—88no—
1059C2×C4—88no—
1060C2×C4—84no—
1061C2×C4—84no—
1062C2×C4—88no—
1063C2×C4—88no—
1064C2×C4C23×D412yes—
1065C2×C4C23×D411yescharacteristic
1066C2×C4C23×D412yes—
1067C2×C4C23×D412yes—
1068C2×C4C23×D412yes—
1069C2×C4C23×D414yes—
1070C2×C4C23×D418yes—
1071C2×C4C23×D412yes—
1072C2×C4C2611yescharacteristic
1073C8—28no—
1074C8—28no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—28no—
1079C22—21no—
1080C22—22no—
1081C22—24no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—42no—
1087C22—44no—
1088C22C24×D411yescharacteristic
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—22no—
1093C4—28no—
1094C4—21no—
1095C4—22no—
1096C4—24no—
1097C4—44no—
1098C4—48no—
1099C4—44no—
1100C4—44no—
1101C4—42no—
1102C4—44no—
1103C42−1+611yescharacteristic
1104C42−1+611yescharacteristic
1105C2—44no—
1106C2—42no—
1107C2—41no—
1108C2—84no—
1109C2—82no—
1110C2#6285911yescharacteristic
1111C2#6309012yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3444 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #62840C2semidirect
2. #62825C2semidirect
3. #62549C2semidirect
4. #62484C2semidirect
5. #62242C2semidirect
6. #62241C2semidirect
7. #62238C2semidirect
8. #62237C2semidirect
9. #61877C2semidirect
10. #61876C2semidirect
11. #61800C2semidirect
12. #61774C2semidirect
13. #61009C2semidirect
14. #60967C2semidirect
15. #60882C2semidirect
16. #60861C2semidirect
17. #60281C2semidirect
49. #3390C22semidirect
50. #3389C22semidirect
51. #3388C22semidirect
52. #3388C22semidirect
53. #3374C22semidirect
54. #3372C22semidirect
55. #3368C22semidirect
56. #3366C22semidirect
62. #3346C22semidirect
64. #3345C22semidirect
66. #3344C22semidirect
68. #3343C22semidirect
74. #3317C22semidirect
76. #3315C22semidirect
78. #3309C22semidirect
80. #3307C22semidirect
81. #3261C22semidirect
82. #3260C22semidirect
83. #3260C22semidirect
84. #3259C22semidirect
90. #3242C22semidirect
92. #3241C22semidirect
99. #3233C22semidirect
102. #3232C22semidirect
103. #3232C22semidirect
106. #3212C22semidirect
111. #3183C22semidirect
112. #3168C22semidirect
114. #3166C22semidirect
115. C2×#499C22semidirect
117. #3142C22semidirect
118. #3131C22semidirect
120. #3120C22semidirect
122. #3119C22semidirect
131. #3084C22semidirect
132. #3083C22semidirect

Maximal subgroups

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

subgroupindex
#628402
#628252
#625492
#624842
#622422
#622412
#622382
#622372
#618772
#618762
#618002
#617742
#610092
#609672
#608822
#608612
#602812