Finite Group Databasebeta

← #10579353

Subgroups — #10579353

Order 512.

6339 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62805C211yesmaximal, characteristic, complemented
2#412C211yesmaximal, characteristic, complemented
3#62106C212yesmaximal, complemented
4#62105C212yesmaximal, complemented
5#62104C216yesmaximal, complemented
6#62103C216yesmaximal, complemented
7#62102C213yesmaximal, complemented
8#62101C213yesmaximal, complemented
9#62100C211yesmaximal, characteristic, complemented
10#62099C211yesmaximal, characteristic, complemented
11#62098C213yesmaximal, complemented
12#62097C213yesmaximal, complemented
13#62096C211yesmaximal, characteristic, complemented
14#62095C211yesmaximal, characteristic, complemented
15Q8×#135C212yesmaximal, complemented
16#61303C212yesmaximal, complemented
17#61234C216yesmaximal, complemented
18#61124C216yesmaximal, complemented
19#60900C213yesmaximal, complemented
20#60846C213yesmaximal, complemented
21#60536C213yesmaximal, complemented
22C2×#3076C213yesmaximal, complemented
23C2×#2988C211yesmaximal, characteristic, complemented
24#3523—21no—
25#3520—23no—
26#3518C2212yescomplemented
27#3515C2216yescomplemented
28#3511C2213yescomplemented
29#3509C2213yescomplemented
30#3503C2211yescharacteristic
31#3499C2211yescharacteristic
32#3495—23no—
33#3489—21no—
34#3483C2211yescharacteristic
35#3482—21no—
36#3482—23no—
37#3482—21no—
38#3482C2211yescharacteristic
39#3482C2213yes—
40#3481—23no—
41#3481C2213yes—
42#3480—21no—
43#3480C2211yescharacteristic
44#3480C2213yes—
45Q8×#41C2211yescharacteristic
46Q8×#41C2211yescharacteristic
47Q8×#41C2212yescomplemented
48#3475—23no—
49#3475—23no—
50#3475C2213yes—
51#3475C2213yes—
52#3475C2216yescomplemented
53D4×#41—21no—
54D4×#41C2213yes—
55D4×#41C2211yescharacteristic
56#3461—23no—
57#3444—23no—
58#3444C2213yes—
59#3444C2213yescomplemented
60C2×#533C2213yescomplemented
61C4×2−1+4—21no—
62C2×C4×#41—21no—
63C2×C4×#41C2213yes—
64C2×C4×#41C2211yescharacteristic
65#3383C2216yescomplemented
66Q8×Q16C2212yescomplemented
67#3381C2216yescomplemented
68#3381C2216yescomplemented
69#3380C2216yescomplemented
70Q8×SD16C2212yescomplemented
71Q8×SD16C2212yescomplemented
72Q8×D8C2212yescomplemented
73#3365C2216yescomplemented
74#3364C2216yescomplemented
75#3363C2212yescomplemented
76#3362C2212yescomplemented
77#3361C2216yescomplemented
78#3360C2216yescomplemented
79#3359C2212yescomplemented
80#3358C2212yescomplemented
81#3342C2216yescomplemented
82#3341C2216yescomplemented
83#3340C2216yescomplemented
84#3340C2216yescomplemented
85#3339C22112yescomplemented
86#3338C2216yescomplemented
87#3337C22112yescomplemented
88#3337C22112yescomplemented
89#3336C22112yescomplemented
90#3335C2216yescomplemented
91#3335C2216yescomplemented
92#3334C2216yescomplemented
93#3305C2216yescomplemented
94#3304C2216yescomplemented
95#3303C2216yescomplemented
96#3302C2216yescomplemented
97#3301C22112yescomplemented
98#3300C22112yescomplemented
99#3299C2216yescomplemented
100#3298C2216yescomplemented
101#3297C22112yescomplemented
102#3296C22112yescomplemented
103#3295C2216yescomplemented
104#3294C2216yescomplemented
105#3250C22112yescomplemented
106#3249C2213yescomplemented
107#3248C2216yescomplemented
108#3248C2216yescomplemented
109#3247C2216yescomplemented
110#3247C2216yescomplemented
111#3246C2213yescomplemented
112#3246C2213yescomplemented
113#3245C2213yescomplemented
114#3233C2216yescomplemented
115#3233C2216yescomplemented
116#3232C22112yescomplemented
117#3231C2216yescomplemented
118#3230C2213yescomplemented
119#3229C2213yescomplemented
120#3228C2216yescomplemented
121#3227C2213yescomplemented
122#3226C2213yescomplemented
123#3160C2216yescomplemented
124#3131C2216yescomplemented
125#3108C2216yescomplemented
126#3107C2213yescomplemented
127#3107C2213yescomplemented
128#3106C2213yescomplemented
129#3106C2213yescomplemented
130#3105C2216yescomplemented
131#3104C2213yescomplemented
132#3103C2213yescomplemented
133#3102C2216yescomplemented
134#3102C2216yescomplemented
135#3101C2213yescomplemented
136#3100C2213yescomplemented
137#3091C2216yescomplemented
138#3091C22112yescomplemented
139#3076C2213yes—
140#3076C2216yes—
141#3076C2216yescomplemented
142#3076C2216yescomplemented
143#3076C2216yescomplemented
144#3076C2216yescomplemented
145#3076C2216yescomplemented
146#3076C2216yescomplemented
147#3076C2216yescomplemented
148#3076C2213yescomplemented
149C2×#479C2216yescomplemented
150C2×#477C2213yescomplemented
151C2×#475C2213yescomplemented
152C2×#478C2216yescomplemented
153C2×#476C2213yescomplemented
154C2×#474C2213yescomplemented
155#3050C22112yescomplemented
156#3035C2211yescharacteristic
157#3035C2216yescomplemented
158#3035C2213yescomplemented
159#3002C2216yes—
160#2988C2211yescharacteristic
161#2988C2211yescharacteristic
162#2988C2213yescomplemented
163#2988C2213yescomplemented
164#2988C2216yescomplemented
165#2988C2212yescomplemented
166C2×C8×Q8C2212yescomplemented
167C4×#135C2216yes—
168C4×#135C2216yescomplemented
169C2×C8×D4C2216yescomplemented
170C2×#431C2213yescomplemented
171C2×#427C2216yescomplemented
172C22×C4⋊C8C2213yescomplemented
173C2×#416C2216yes—
174C2×2−1+4—21no—
175C22×#41—21no—
176C22×#41D411yescharacteristic
177C22×#41C2313yes—
178C2×#135C2312yes—
179C2×#135C2316yes—
180C23×C8C2316yes—
181#559—23no—
182#559C2313yes—
183Q82C2312yes—
184Q82C2311yescharacteristic
185#557—21no—
186#557—21no—
187#557—23no—
188#557C2311yescharacteristic
189#557C2316yes—
190#557C2313yes—
191#556—23no—
192#556—23no—
193#556—23no—
194#556—23no—
195#556—26no—
196#556C2313yes—
197#556C2313yes—
198#556C2316yes—
199#555—23no—
200#555C2313yes—
201#555C2316yes—
202#554—23no—
203#554—23no—
204#554—26no—
205#554C2316yes—
206#554C2313yes—
207#554C2313yes—
208#554C2316yes—
209#553—26no—
210#553—23no—
211#553—23no—
212#553—23no—
213#553C2316yes—
214#553C23112yes—
215#552—23no—
216#552—26no—
217#552—26no—
218#552—23no—
219#552—212no—
220#552—26no—
221#552—23no—
222#552—26no—
223#552C2316yes—
224#552C23112yes—
225#551—26no—
226#551—26no—
227#551—26no—
228#551—212no—
229#550—21no—
230#550C2313yes—
231#550C2311yescharacteristic
232D4×Q8—21no—
233D4×Q8—22no—
234D4×Q8—21no—
235D4×Q8—23no—
236D4×Q8C2313yes—
237D4×Q8C2312yes—
238D4×Q8C2311yescharacteristic
239#548—21no—
240#548—22no—
241#548—21no—
242#548—21no—
243#548—26no—
244#548C2316yes—
245#547—23no—
246#547—26no—
247#547—23no—
248#547—23no—
249#547—23no—
250#547C2313yes—
251#547C2313yes—
252#547C2316yes—
253#546—23no—
254#546—23no—
255#546—26no—
256#546—23no—
257#546—26no—
258#546C2316yes—
259D42—23no—
260D42C2313yes—
261#544—23no—
262#542—26no—
263#542—26no—
264#541—26no—
265#541—26no—
266#539—212no—
267#537—23no—
268#536—23no—
269#536—23no—
270#533—23no—
271#533—23no—
272#533—26no—
273#533—23no—
274#533—23no—
275#533—23no—
276#533—23no—
277#533—23no—
278#533C2313yes—
279#533C2313yes—
280#533C2313yes—
281#533C2313yes—
282#533C2313yes—
283#533C2316yes—
284#533C2313yes—
285#533C2316yes—
286#533C2316yes—
287#532—23no—
288#532—23no—
289#532—23no—
290#532C2313yes—
291#532C2311yescharacteristic
292#532C2313yes—
293#532C2313yes—
294#532C2313yes—
295#532C2313yes—
296C2×C4⋊Q8C2313yes—
297C2×C4⋊Q8C2313yes—
298#529—23no—
299#529—23no—
300#529—26no—
301#529—23no—
302#529—26no—
303#529—23no—
304#529—212no—
305#529—26no—
306#529—26no—
307#529—26no—
308#529—23no—
309#529—23no—
310#529—23no—
311#529—23no—
312#529—23no—
313#529—23no—
314#529—23no—
315#529—23no—
316#529C2316yes—
317#529C2316yes—
318#529C2316yes—
319#529C2316yes—
320C2×#125C2316yes—
321#525—23no—
322#525—23no—
323#525—23no—
324#525—23no—
325#525—23no—
326#525—26no—
327#525—26no—
328#525—23no—
329#525C2316yes—
330#525C2316yes—
331C2×C22⋊Q8—23no—
332C2×C22⋊Q8—23no—
333#520—21no—
334#520—26no—
335#520—23no—
336#519—22no—
337#519—23no—
338C4×#41—21no—
339C4×#41—21no—
340C4×#41—21no—
341C4×#41—23no—
342C4×#41—23no—
343C4×#41—26no—
344C4×#41—23no—
345C4×#41—23no—
346C4×#41—23no—
347C4×#41—23no—
348C4×#41—23no—
349C4×#41—23no—
350C4×#41—23no—
351C4×#41—23no—
352C4×#41—23no—
353C4×#41D411yescharacteristic
354C4×#41D413yes—
355C4×#41D413yes—
356C4×#41D411yescharacteristic
357C4×#41C2311yescharacteristic
358C4×#41C2313yes—
359C4×#41C2313yes—
360C4×#41C2313yes—
361C4×#41C2313yes—
362C4×#41C2313yes—
363C4×#41C2313yes—
364C4×#41C2313yes—
365C4×#41C2316yes—
366C4×#41C2311yescharacteristic
367C4×#41C2313yes—
368C4×#41C2313yes—
369C4×#41C2311yescharacteristic
370C2×C4×Q8—21no—
371C2×C4×Q8—21no—
372C2×C4×Q8—22no—
373C2×C4×Q8—23no—
374C2×C4×Q8—23no—
375C2×C4×Q8D411yescharacteristic
376C2×C4×Q8C2313yes—
377C2×C4×Q8C2313yes—
378C2×C4×Q8C2311yescharacteristic
379C2×C4×D4—23no—
380C2×C4×D4—23no—
381C2×C4×D4—23no—
382C2×C4×D4—23no—
383C2×C4×D4D413yes—
384C2×C4×D4C2313yes—
385C2×C4×D4C2313yes—
386C2×C4×D4C2313yes—
387C2×#117—23no—
388C2×#117—23no—
389C2×#117D413yes—
390C2×#117C2316yes—
391C2×#117C2313yes—
392C22×C42—23no—
393C22×C42C2313yes—
394#500C2316yes—
395#500C2316yes—
396#499C23112yes—
397#499C23112yes—
398#498C2316yes—
399#498C2316yes—
400#488C23112yes—
401#488C23112yes—
402#487C2316yes—
403#487C2316yes—
404#486C2316yes—
405#486C2316yes—
406#485C2316yes—
407#485C23112yes—
408#485C2316yes—
409#485C23112yes—
410#484C2316yes—
411#484C23112yes—
412#483C2316yes—
413#483C23112yes—
414#482C2316yes—
415#482C23112yes—
416#482C2316yes—
417#482C23112yes—
418#481C2316yes—
419#481C23112yes—
420#480C2316yes—
421#480C23112yes—
422#479C2316yes—
423#479C23112yes—
424#479C23112yes—
425#479C23112yes—
426#479C23112yes—
427#479C2316yes—
428#478C2316yes—
429#478C23112yes—
430#478C23112yes—
431#478C23112yes—
432#478C23112yes—
433#478C2316yes—
434#477C2313yes—
435#477C2316yes—
436#477C2316yes—
437#477C2316yes—
438#477C2316yes—
439#477C2313yes—
440#476C2313yes—
441#476C2316yes—
442#476C2316yes—
443#476C2316yes—
444#476C2316yes—
445#476C2313yes—
446#475C2313yes—
447#475C2316yes—
448#475C2316yes—
449#475C2316yes—
450#475C2316yes—
451#475C2313yes—
452#474C2313yes—
453#474C2316yes—
454#474C2316yes—
455#474C2316yes—
456#474C2316yes—
457#474C2313yes—
458#467C23112yes—
459#467C23112yes—
460#466C23112yes—
461#466C23112yes—
462#465C23112yes—
463#465C23112yes—
464#465C23112yes—
465#465C23112yes—
466#464C2312yes—
467#464C2316yes—
468#464C23112yes—
469#463C2312yes—
470#463C2316yes—
471#463C23112yes—
472#462C2311yescharacteristic
473#462C2313yes—
474#462C2316yes—
475#461C2311yescharacteristic
476#461C2313yes—
477#461C2316yes—
478#460C2311yescharacteristic
479#460C2313yes—
480#460C2316yes—
481#459C2311yescharacteristic
482#459C2313yes—
483#459C2316yes—
484#452C2316yes—
485#452C2316yes—
486#451C2316yes—
487#450C2316yes—
488#449C2316yes—
489#449C2316yes—
490#448C2316yes—
491#447C2316yes—
492C8×Q8C2312yes—
493C8×Q8C2312yes—
494C8×Q8C2316yes—
495C8×Q8C2316yes—
496C4×Q16C2316yes—
497C4×Q16C2316yes—
498C4×Q16C2316yes—
499C4×Q16C2316yes—
500C4×SD16C2316yes—
501C4×SD16C2316yes—
502C4×SD16C2316yes—
503C4×SD16C2316yes—
504C4×SD16C2316yes—
505C4×SD16C2316yes—
506C4×SD16C2316yes—
507C4×SD16C2316yes—
508C4×D8C2316yes—
509C4×D8C2316yes—
510C4×D8C2316yes—
511C4×D8C2316yes—
512C8×D4C2316yes—
513C8×D4C2316yes—
514C8×D4C23112yes—
515C8×D4C23112yes—
516C8×D4C2316yes—
517C8×D4C2316yes—
518#431C2313yes—
519#431C2313yes—
520#431C2316yes—
521#431C2316yes—
522#431C2313yes—
523#431C2313yes—
524#427C23112yes—
525#427C2316yes—
526#427C23112yes—
527#427C23112yes—
528#427C2316yes—
529C2×#107C2316yes—
530C2×#107C2316yes—
531C2×#106C2316yes—
532C2×#106C2316yes—
533C2×C4⋊C8C2316yes—
534C2×C4⋊C8C2313yes—
535C2×C4⋊C8C2313yes—
536C2×C4⋊C8C2313yes—
537C2×C4⋊C8C2316yes—
538C2×C4⋊C8C2311yescharacteristic
539C2×C4⋊C8C2316yes—
540C2×C4⋊C8C2316yes—
541#416C2316yes—
542#416C23112yes—
543#416C2316yes—
544#416C23112yes—
545#416C23112yes—
546#416C2316yes—
547#416C2312yes—
548C2×#103C2316yes—
549C2×#103C2316yes—
550C2×#102C2316yes—
551C2×#102C2316yes—
552C2×C22⋊C8C2316yes—
553C2×C4×C8C2316yes—
5542−1+4—48no—
555C2×#41—28no—
556C2×#41—21no—
557C2×#41—23no—
558C2×#41—26no—
559C2×#41—23no—
560C2×#41—23no—
561C2×#41—23no—
562C2×#41—23no—
563C2×#41—23no—
564C2×#41—23no—
565C2×#41—212no—
566C2×#41—46no—
567C2×#41—48no—
568C2×#41C2×D413yes—
569C2×#41C2×D413yes—
570C2×#41C2×D411yescharacteristic
571C2×#41C2×D411yescharacteristic
572C2×#41C2412yes—
573C2×#41C2413yes—
574C2×#41C2413yes—
575C2×#41C2413yes—
576C2×#41C2411yescharacteristic
577C22×Q8—21no—
578C22×Q8—22no—
579C22×Q8—23no—
580C22×Q8—23no—
581C22×Q8C2×D411yescharacteristic
582C22×Q8C2413yes—
583C22×D4—23no—
584C22×D4—23no—
585C22×D4C2×D413yes—
586C22×D4C2413yes—
587C23×C4—23no—
588C23×C4—23no—
589C23×C4—23no—
590C23×C4C2×D413yes—
591C23×C4C2×D413yes—
592C23×C4C2413yes—
593#135—28no—
594#135—412no—
595C2×Q16C2412yes—
596C2×Q16C2416yes—
597C2×SD16C2412yes—
598C2×SD16C2412yes—
599C2×SD16C2416yes—
600C2×SD16C2416yes—
601C2×D8C2412yes—
602C2×D8C2416yes—
603C22×C8—412no—
604C22×C8C2416yes—
605C22×C8C2412yes—
606C22×C8C2416yes—
607C22×C8C2416yes—
608C22×C8C24112yes—
609C4⋊Q8—23no—
610C4⋊Q8—26no—
611C4⋊Q8—23no—
612C4⋊Q8—23no—
613C4⋊Q8—26no—
614C4⋊Q8—23no—
615C4⋊Q8—23no—
616C4⋊Q8—23no—
617C4⋊Q8—23no—
618C4⋊Q8C2411yescharacteristic
619C4⋊Q8C2413yes—
620C4⋊Q8C2413yes—
621C4⋊Q8C2413yes—
622C4⋊Q8C2416yes—
623C4⋊Q8C2416yes—
624C4⋊Q8C2413yes—
625C4⋊Q8C2413yes—
626#127—23no—
627#127C2411yescharacteristic
628#127C2413yes—
629#126—26no—
630#126—26no—
631#126—212no—
632#126—26no—
633#126—26no—
634#126—212no—
635#126—212no—
636#126—26no—
637#126—26no—
638#126—26no—
639#126—26no—
640#125—26no—
641#125—23no—
642#125—26no—
643#125—23no—
644#125—212no—
645#125—26no—
646#125—212no—
647#125—26no—
648#125—26no—
649#125—23no—
650#125—23no—
651#125—23no—
652#125—23no—
653#125C2416yes—
654#125C24112yes—
655#125C2416yes—
656#124—23no—
657#124—23no—
658#124—26no—
659#124—26no—
660#124—26no—
661#124—212no—
662#124—23no—
663#124—23no—
664#124—23no—
665#124—23no—
666#124C2412yes—
667#124C2416yes—
668#123—26no—
669#123—212no—
670#123—26no—
671#123—26no—
672#123—26no—
673#123—26no—
674#123—26no—
675#123—26no—
676#123—26no—
677#123—26no—
678#123—26no—
679#123—26no—
680#123—26no—
681#123—212no—
682#123—212no—
683C22⋊Q8—23no—
684C22⋊Q8—23no—
685C22⋊Q8—26no—
686C22⋊Q8—23no—
687C22⋊Q8—23no—
688C22⋊Q8—26no—
689C22⋊Q8—26no—
690C22⋊Q8—26no—
691C22⋊Q8—26no—
692C22⋊Q8—26no—
693C22⋊Q8—26no—
694C22⋊Q8—23no—
695C22⋊Q8—23no—
696C22⋊Q8—23no—
697C22⋊Q8—23no—
698C22⋊Q8—23no—
699C22⋊Q8—23no—
700C22⋊Q8—23no—
701C22⋊Q8—26no—
702C22⋊Q8—23no—
703C22⋊Q8—26no—
704C22⋊Q8—26no—
705C22⋊Q8—26no—
706C22⋊Q8—212no—
707C22⋊Q8—26no—
708C22⋊Q8—26no—
709C22⋊Q8—212no—
710C22⋊Q8C2416yes—
711C22⋊Q8C2416yes—
712C22⋊Q8C2416yes—
713C22⋊Q8C2416yes—
714#121—26no—
715#121—23no—
716#121—26no—
717#121—23no—
718#121—212no—
719#121—26no—
720#121—21no—
721#121—21no—
722#121—23no—
723#121—23no—
724#121—23no—
725#121—23no—
726#121—23no—
727#121—23no—
728#121—23no—
729#121—23no—
730#121—26no—
731#121—26no—
732#121C2416yes—
733#121C2416yes—
734#121C2416yes—
735#121C2416yes—
736#120—26no—
737#120—26no—
738#120—26no—
739#120—26no—
740C4×Q8—21no—
741C4×Q8—21no—
742C4×Q8—22no—
743C4×Q8—23no—
744C4×Q8—23no—
745C4×Q8—26no—
746C4×Q8—26no—
747C4×Q8—23no—
748C4×Q8—26no—
749C4×Q8—23no—
750C4×Q8—23no—
751C4×Q8—23no—
752C4×Q8—26no—
753C4×Q8—26no—
754C4×Q8—26no—
755C4×Q8—26no—
756C4×Q8—26no—
757C4×Q8—23no—
758C4×Q8—23no—
759C4×Q8—23no—
760C4×Q8—23no—
761C4×Q8—23no—
762C4×Q8—23no—
763C4×Q8—23no—
764C4×Q8—23no—
765C4×Q8C2×D411yescharacteristic
766C4×Q8C2×D411yescharacteristic
767C4×Q8C2×D413yes—
768C4×Q8C2×D411yescharacteristic
769C4×Q8C2×D413yes—
770C4×Q8C2×D413yes—
771C4×Q8C2411yescharacteristic
772C4×Q8C2411yescharacteristic
773C4×Q8C2413yes—
774C4×Q8C2413yes—
775C4×Q8C2413yes—
776C4×Q8C2413yes—
777C4×Q8C2413yes—
778C4×Q8C2413yes—
779C4×Q8C2416yes—
780C4×Q8C2416yes—
781C4×Q8C2411yescharacteristic
782C4×Q8C2413yes—
783C4×D4—23no—
784C4×D4—23no—
785C4×D4—26no—
786C4×D4—21no—
787C4×D4—21no—
788C4×D4—26no—
789C4×D4—26no—
790C4×D4—23no—
791C4×D4—23no—
792C4×D4—23no—
793C4×D4—23no—
794C4×D4—23no—
795C4×D4—23no—
796C4×D4—23no—
797C4×D4—23no—
798C4×D4—23no—
799C4×D4—23no—
800C4×D4—23no—
801C4×D4—23no—
802C4×D4—23no—
803C4×D4—23no—
804C4×D4—26no—
805C4×D4—26no—
806C4×D4—26no—
807C4×D4—26no—
808C4×D4—26no—
809C4×D4—26no—
810C4×D4—26no—
811C4×D4—26no—
812C4×D4—23no—
813C4×D4—23no—
814C4×D4—26no—
815C4×D4—26no—
816C4×D4—212no—
817C4×D4—23no—
818C4×D4—23no—
819C4×D4—23no—
820C4×D4—23no—
821C4×D4—23no—
822C4×D4—23no—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—23no—
826C4×D4—23no—
827C4×D4—23no—
828C4×D4—23no—
829C4×D4C2×D413yes—
830C4×D4C2×D413yes—
831C4×D4C2×D416yes—
832C4×D4C2×D413yes—
833C4×D4C2×D413yes—
834C4×D4C2×D413yes—
835C4×D4C2×D416yes—
836C4×D4C2×D416yes—
837C4×D4C2×D413yes—
838C4×D4C2411yescharacteristic
839C4×D4C2411yescharacteristic
840C4×D4C2413yes—
841C4×D4C2413yes—
842C4×D4C2413yes—
843C4×D4C2413yes—
844C4×D4C2413yes—
845C4×D4C2413yes—
846C4×D4C2416yes—
847C4×D4C2416yes—
848C4×D4C2413yes—
849C4×D4C2416yes—
850C4×D4C2413yes—
851#117—23no—
852#117—23no—
853#117—23no—
854#117—26no—
855#117—26no—
856#117—23no—
857#117—23no—
858#117—23no—
859#117—23no—
860#117—23no—
861#117—26no—
862#117—26no—
863#117—212no—
864#117—21no—
865#117—26no—
866#117—23no—
867#117—23no—
868#117—23no—
869#117—23no—
870#117—23no—
871#117—23no—
872#117—23no—
873#117—26no—
874#117—26no—
875#117—26no—
876#117—26no—
877#117C2×D413yes—
878#117C2×D413yes—
879#117C2×D416yes—
880#117C2×D416yes—
881#117C2×D413yes—
882#117C2×D413yes—
883#117C2411yescharacteristic
884#117C2416yes—
885#117C2413yes—
886#117C2413yes—
887#117C2413yes—
888#117C24112yes—
889C2×C4⋊C4—23no—
890C2×C4⋊C4—23no—
891C2×C4⋊C4—26no—
892C2×C4⋊C4—23no—
893C2×C4⋊C4—26no—
894C2×C4⋊C4—23no—
895C2×C4⋊C4—23no—
896C2×C4⋊C4—23no—
897C2×C4⋊C4—26no—
898C2×C4⋊C4C2×D413yes—
899C2×C4⋊C4C2×D413yes—
900C2×C4⋊C4C2413yes—
901C2×C4⋊C4C2413yes—
902C2×C4⋊C4C2416yes—
903C2×C4⋊C4C2416yes—
904C2×C22⋊C4—23no—
905C2×C22⋊C4—26no—
906C2×C22⋊C4—23no—
907C2×C22⋊C4—23no—
908C2×C22⋊C4—26no—
909C2×C22⋊C4C2×D416yes—
910C2×C42—23no—
911C2×C42—26no—
912C2×C42—23no—
913C2×C42—23no—
914C2×C42—23no—
915C2×C42—23no—
916C2×C42—23no—
917C2×C42—26no—
918C2×C42—23no—
919C2×C42—23no—
920C2×C42—23no—
921C2×C42—23no—
922C2×C42—21no—
923C2×C42C2×D413yes—
924C2×C42C2×D413yes—
925C2×C42C2×D413yes—
926C2×C42C2×D413yes—
927C2×C42C2×D413yes—
928C2×C42C2×D413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2411yescharacteristic
935#107C2416yes—
936#107C2416yes—
937#107C24112yes—
938#107C24112yes—
939#107C2416yes—
940#107C2416yes—
941#106C2416yes—
942#106C2416yes—
943#106C24112yes—
944#106C24112yes—
945#106C2416yes—
946#106C2416yes—
947C4⋊C8C2413yes—
948C4⋊C8C2413yes—
949C4⋊C8C2416yes—
950C4⋊C8C2416yes—
951C4⋊C8C2416yes—
952C4⋊C8C24112yes—
953C4⋊C8C2411yescharacteristic
954C4⋊C8C2411yescharacteristic
955C4⋊C8C2412yes—
956#103C2416yes—
957#103C2416yes—
958#103C24112yes—
959#103C24112yes—
960#103C2412yes—
961#103C2412yes—
962#103C2416yes—
963#103C2416yes—
964#103C2416yes—
965#103C2416yes—
966#102C2416yes—
967#102C2416yes—
968#102C24112yes—
969#102C24112yes—
970#102C2412yes—
971#102C2412yes—
972#102C2416yes—
973#102C2416yes—
974#102C2416yes—
975#102C2416yes—
976C22⋊C8C2416yes—
977C22⋊C8C2416yes—
978C22⋊C8C2416yes—
979C22⋊C8C2416yes—
980C4×C8C2416yes—
981C4×C8C2416yes—
982C4×C8C2416yes—
983C4×C8C2416yes—
984C24—23no—
985C24C22×D413yes—
986#41—24no—
987#41—212no—
988#41—212no—
989#41—22no—
990#41—26no—
991#41—26no—
992#41—24no—
993#41—26no—
994#41—24no—
995#41—26no—
996#41—412no—
997#41—43no—
998#41—43no—
999#41—412no—
1000#41—44no—
1001#41—412no—
1002#41—424no—
1003#41—412no—
1004#41—412no—
1005#41—86no—
1006#41—86no—
1007#41#13518yescomplemented
1008#412−1+414yescomplemented
1009C2×Q8—24no—
1010C2×Q8—23no—
1011C2×Q8—23no—
1012C2×Q8—23no—
1013C2×Q8—23no—
1014C2×Q8—26no—
1015C2×Q8—23no—
1016C2×Q8—26no—
1017C2×Q8—26no—
1018C2×Q8—43no—
1019C2×Q8—44no—
1020C2×Q8—48no—
1021C2×Q8—412no—
1022C2×Q8—86no—
1023C2×Q8C22×D413yes—
1024C2×Q8C22×D411yescharacteristic
1025C2×Q8C2513yes—
1026C2×Q8C2512yes—
1027C2×Q8C2511yescharacteristic
1028C2×D4—21no—
1029C2×D4—212no—
1030C2×D4—26no—
1031C2×D4—22no—
1032C2×D4—23no—
1033C2×D4—23no—
1034C2×D4—26no—
1035C2×D4—26no—
1036C2×D4—23no—
1037C2×D4—26no—
1038C2×D4—26no—
1039C2×D4—23no—
1040C2×D4—21no—
1041C2×D4—21no—
1042C2×D4—23no—
1043C2×D4—23no—
1044C2×D4—43no—
1045C2×D4—412no—
1046C2×D4—412no—
1047C2×D4C22×D416yes—
1048C2×D4C22×D413yes—
1049C2×D4C22×D413yes—
1050C2×D4C2513yes—
1051C2×D4C2512yes—
1052C2×D4C2511yescharacteristic
1053C22×C4—212no—
1054C22×C4—21no—
1055C22×C4—26no—
1056C22×C4—26no—
1057C22×C4—23no—
1058C22×C4—23no—
1059C22×C4—26no—
1060C22×C4—23no—
1061C22×C4—26no—
1062C22×C4—21no—
1063C22×C4—21no—
1064C22×C4—23no—
1065C22×C4—23no—
1066C22×C4—23no—
1067C22×C4—23no—
1068C22×C4—23no—
1069C22×C4—23no—
1070C22×C4—26no—
1071C22×C4—22no—
1072C22×C4—23no—
1073C22×C4—23no—
1074C22×C4—23no—
1075C22×C4—26no—
1076C22×C4—412no—
1077C22×C4—412no—
1078C22×C4—83no—
1079C22×C4—86no—
1080C22×C4C22×D411yescharacteristic
1081C22×C4C22×D413yes—
1082C22×C4C22×D413yes—
1083C22×C4C22×D413yes—
1084C22×C4C22×D413yes—
1085C22×C4C22×D413yes—
1086C22×C4C22×D413yes—
1087C22×C4C22×D413yes—
1088C22×C4C22×D413yes—
1089C22×C4C22×D411yescharacteristic
1090C22×C4C22×D413yes—
1091C22×C4C22×D413yes—
1092C22×C4C22×D413yes—
1093C22×C4C22×D413yes—
1094C22×C4C22×D413yes—
1095C22×C4C2513yes—
1096C22×C4C2513yes—
1097C22×C4C2511yescharacteristic
1098Q16—24no—
1099Q16—46no—
1100SD16—24no—
1101SD16—24no—
1102SD16—46no—
1103SD16—46no—
1104D8—24no—
1105D8—46no—
1106C2×C8—24no—
1107C2×C8—212no—
1108C2×C8—46no—
1109C2×C8—412no—
1110C2×C8—46no—
1111C2×C8C2512yes—
1112C2×C8C2512yes—
1113C2×C8C2516yes—
1114C2×C8C2516yes—
1115C4⋊C4—21no—
1116C4⋊C4—21no—
1117C4⋊C4—23no—
1118C4⋊C4—23no—
1119C4⋊C4—26no—
1120C4⋊C4—26no—
1121C4⋊C4—212no—
1122C4⋊C4—26no—
1123C4⋊C4—23no—
1124C4⋊C4—23no—
1125C4⋊C4—26no—
1126C4⋊C4—26no—
1127C4⋊C4—23no—
1128C4⋊C4—23no—
1129C4⋊C4—23no—
1130C4⋊C4—23no—
1131C4⋊C4—23no—
1132C4⋊C4—23no—
1133C4⋊C4—212no—
1134C4⋊C4—26no—
1135C4⋊C4—23no—
1136C4⋊C4—23no—
1137C4⋊C4—26no—
1138C4⋊C4—26no—
1139C4⋊C4—21no—
1140C4⋊C4—21no—
1141C4⋊C4—26no—
1142C4⋊C4—23no—
1143C4⋊C4—23no—
1144C4⋊C4—26no—
1145C4⋊C4—26no—
1146C4⋊C4—26no—
1147C4⋊C4—26no—
1148C4⋊C4—26no—
1149C4⋊C4C22×D413yes—
1150C4⋊C4C22×D413yes—
1151C4⋊C4C22×D413yes—
1152C4⋊C4C22×D416yes—
1153C4⋊C4C22×D413yes—
1154C4⋊C4C22×D416yes—
1155C4⋊C4C2516yes—
1156C4⋊C4C2516yes—
1157C4⋊C4C2511yescharacteristic
1158C4⋊C4C2511yescharacteristic
1159C4⋊C4C2513yes—
1160C4⋊C4C2513yes—
1161C22⋊C4—21no—
1162C22⋊C4—26no—
1163C22⋊C4—26no—
1164C22⋊C4—23no—
1165C22⋊C4—23no—
1166C22⋊C4—23no—
1167C22⋊C4—212no—
1168C22⋊C4—26no—
1169C22⋊C4—26no—
1170C22⋊C4—26no—
1171C22⋊C4—21no—
1172C22⋊C4—21no—
1173C22⋊C4—26no—
1174C22⋊C4—26no—
1175C22⋊C4—23no—
1176C22⋊C4—23no—
1177C22⋊C4—23no—
1178C22⋊C4—23no—
1179C22⋊C4—23no—
1180C22⋊C4—23no—
1181C22⋊C4—22no—
1182C22⋊C4—22no—
1183C22⋊C4—26no—
1184C22⋊C4—26no—
1185C22⋊C4—26no—
1186C22⋊C4—26no—
1187C22⋊C4—26no—
1188C22⋊C4—26no—
1189C22⋊C4C22×D416yes—
1190C22⋊C4C22×D416yes—
1191C22⋊C4C22×D416yes—
1192C22⋊C4C22×D416yes—
1193C42—21no—
1194C42—21no—
1195C42—23no—
1196C42—23no—
1197C42—23no—
1198C42—23no—
1199C42—23no—
1200C42—23no—
1201C42—23no—
1202C42—23no—
1203C42—26no—
1204C42—212no—
1205C42—26no—
1206C42—21no—
1207C42—23no—
1208C42—26no—
1209C42C22×D413yes—
1210C42C22×D413yes—
1211C42C22×D413yes—
1212C42C22×D413yes—
1213C42C22×D413yes—
1214C42C22×D413yes—
1215C42C22×D413yes—
1216C42C22×D413yes—
1217C42C22×D411yescharacteristic
1218C42C22×D413yes—
1219C42C22×D411yescharacteristic
1220C42C22×D413yes—
1221C42C2513yes—
1222C42C2513yes—
1223C42C2511yescharacteristic
1224C42C2511yescharacteristic
1225C23—21no—
1226C23—26no—
1227C23—26no—
1228C23—22no—
1229C23—23no—
1230C23—43no—
1231C23—46no—
1232C23—46no—
1233C23—83no—
1234C23C23×D413yes—
1235C23C23×D411yescharacteristic
1236C23C23×D413yes—
1237Q8—21no—
1238Q8—26no—
1239Q8—22no—
1240Q8—23no—
1241Q8—22no—
1242Q8—23no—
1243Q8—46no—
1244Q8—46no—
1245Q8—46no—
1246Q8—412no—
1247Q8—46no—
1248Q8—86no—
1249Q8—83no—
1250Q8C2×#13514yes—
1251Q8C2×2−1+412yes—
1252D4—24no—
1253D4—212no—
1254D4—22no—
1255D4—23no—
1256D4—21no—
1257D4—22no—
1258D4—23no—
1259D4—26no—
1260D4—46no—
1261D4—46no—
1262D4—42no—
1263D4—46no—
1264D4—46no—
1265D4—44no—
1266D4—412no—
1267D4—412no—
1268D4—46no—
1269D4—42no—
1270D4—83no—
1271D4—86no—
1272D4—86no—
1273D4C2×#135112yes—
1274D4C2×2−1+412yes—
1275C2×C4—21no—
1276C2×C4—26no—
1277C2×C4—26no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—26no—
1283C2×C4—26no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—26no—
1287C2×C4—26no—
1288C2×C4—26no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—26no—
1296C2×C4—26no—
1297C2×C4—41no—
1298C2×C4—43no—
1299C2×C4—43no—
1300C2×C4—43no—
1301C2×C4—43no—
1302C2×C4—43no—
1303C2×C4—46no—
1304C2×C4—46no—
1305C2×C4—46no—
1306C2×C4—42no—
1307C2×C4—46no—
1308C2×C4—46no—
1309C2×C4—412no—
1310C2×C4—46no—
1311C2×C4—44no—
1312C2×C4—42no—
1313C2×C4—46no—
1314C2×C4—46no—
1315C2×C4—46no—
1316C2×C4—412no—
1317C2×C4—83no—
1318C2×C4—83no—
1319C2×C4—86no—
1320C2×C4—83no—
1321C2×C4—86no—
1322C2×C4C2×#135112yes—
1323C2×C4C23×D413yes—
1324C2×C4C23×D411yescharacteristic
1325C2×C4C23×D413yes—
1326C2×C4C23×D411yescharacteristic
1327C2×C4C23×D411yescharacteristic
1328C2×C4C23×D413yes—
1329C2×C4C23×D413yes—
1330C2×C4C23×D413yes—
1331C2×C4C23×D411yescharacteristic
1332C2×C4C23×D413yes—
1333C2×C4C23×D411yescharacteristic
1334C2×C4C2×2−1+412yes—
1335C2×C4#58512yes—
1336C2×C4C2611yescharacteristic
1337C8—22no—
1338C8—22no—
1339C8—26no—
1340C8—26no—
1341C22—23no—
1342C22—21no—
1343C22—21no—
1344C22—23no—
1345C22—23no—
1346C22—22no—
1347C22—23no—
1348C22—23no—
1349C22—412no—
1350C22—41no—
1351C22—41no—
1352C22—43no—
1353C22—42no—
1354C22—42no—
1355C22—43no—
1356C22—43no—
1357C22—42no—
1358C22—812no—
1359C22#348912yes—
1360C22C22×#13516yes—
1361C22C24×D411yescharacteristic
1362C4—23no—
1363C4—23no—
1364C4—22no—
1365C4—21no—
1366C4—23no—
1367C4—21no—
1368C4—21no—
1369C4—23no—
1370C4—23no—
1371C4—43no—
1372C4—42no—
1373C4—41no—
1374C4—43no—
1375C4—46no—
1376C4—41no—
1377C4—43no—
1378C4—46no—
1379C4#348912yes—
1380C4C22×#13512yes—
1381C4C22×#13516yes—
1382C4C22×2−1+411yescharacteristic
1383C4C2×#58511yescharacteristic
1384C2—22no—
1385C2—26no—
1386C2—43no—
1387C2—42no—
1388C2—82no—
1389C2—83no—
1390C2C2×#348911yescharacteristic
1391C2C23×#13511yescharacteristic
1392C2#6309011yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62805C2semidirect
2. #412C2semidirect
3. #62106C2semidirect
4. #62105C2semidirect
5. #62104C2semidirect
6. #62103C2semidirect
7. #62102C2semidirect
8. #62101C2semidirect
9. #62100C2semidirect
10. #62099C2semidirect
11. #62098C2semidirect
12. #62097C2semidirect
13. #62096C2semidirect
14. #62095C2semidirect
15. Q8×#135C2semidirect
16. #61303C2semidirect
17. #61234C2semidirect
18. #61124C2semidirect
19. #60900C2semidirect
20. #60846C2semidirect
21. #60536C2semidirect
22. C2×#3076C2semidirect
23. C2×#2988C2semidirect
26. #3518C22semidirect
27. #3515C22semidirect
28. #3511C22semidirect
29. #3509C22semidirect
47. Q8×#41C22semidirect
52. #3475C22semidirect
59. #3444C22semidirect
60. C2×#533C22semidirect
65. #3383C22semidirect
66. Q8×Q16C22semidirect
67. #3381C22semidirect
68. #3381C22semidirect
69. #3380C22semidirect
70. Q8×SD16C22semidirect
71. Q8×SD16C22semidirect
72. Q8×D8C22semidirect
73. #3365C22semidirect
74. #3364C22semidirect
75. #3363C22semidirect
76. #3362C22semidirect
77. #3361C22semidirect
78. #3360C22semidirect
79. #3359C22semidirect
80. #3358C22semidirect
81. #3342C22semidirect
82. #3341C22semidirect
83. #3340C22semidirect
84. #3340C22semidirect
85. #3339C22semidirect
86. #3338C22semidirect
87. #3337C22semidirect
88. #3337C22semidirect
89. #3336C22semidirect
90. #3335C22semidirect
91. #3335C22semidirect
92. #3334C22semidirect
93. #3305C22semidirect
94. #3304C22semidirect
95. #3303C22semidirect
96. #3302C22semidirect
97. #3301C22semidirect
98. #3300C22semidirect
99. #3299C22semidirect
100. #3298C22semidirect
101. #3297C22semidirect
102. #3296C22semidirect
103. #3295C22semidirect
104. #3294C22semidirect
105. #3250C22semidirect
106. #3249C22semidirect
107. #3248C22semidirect
108. #3248C22semidirect
109. #3247C22semidirect
110. #3247C22semidirect
111. #3246C22semidirect
112. #3246C22semidirect
113. #3245C22semidirect
114. #3233C22semidirect
115. #3233C22semidirect
116. #3232C22semidirect
117. #3231C22semidirect
118. #3230C22semidirect
119. #3229C22semidirect
120. #3228C22semidirect
121. #3227C22semidirect
122. #3226C22semidirect
123. #3160C22semidirect
124. #3131C22semidirect
125. #3108C22semidirect
126. #3107C22semidirect
127. #3107C22semidirect
128. #3106C22semidirect
129. #3106C22semidirect
130. #3105C22semidirect
131. #3104C22semidirect
132. #3103C22semidirect
133. #3102C22semidirect
134. #3102C22semidirect
135. #3101C22semidirect
136. #3100C22semidirect
137. #3091C22semidirect
138. #3091C22semidirect
141. #3076C22semidirect
142. #3076C22semidirect
143. #3076C22semidirect
144. #3076C22semidirect
145. #3076C22semidirect
146. #3076C22semidirect
147. #3076C22semidirect
148. #3076C22semidirect
149. C2×#479C22semidirect
150. C2×#477C22semidirect
151. C2×#475C22semidirect
152. C2×#478C22semidirect
153. C2×#476C22semidirect
154. C2×#474C22semidirect
155. #3050C22semidirect
157. #3035C22semidirect
158. #3035C22semidirect
162. #2988C22semidirect
163. #2988C22semidirect
164. #2988C22semidirect
165. #2988C22semidirect
166. C2×C8×Q8C22semidirect
168. C4×#135C22semidirect
169. C2×C8×D4C22semidirect
170. C2×#431C22semidirect
171. C2×#427C22semidirect
172. C22×C4⋊C8C22semidirect
1007. #41#135semidirect
1008. #412−1+4semidirect

Maximal subgroups

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

subgroupindex
#628052
#4122
#621062
#621052
#621042
#621032
#621022
#621012
#621002
#620992
#620982
#620972
#620962
#620952
Q8×#1352
#613032
#612342
#611242
#609002
#608462
#605362
C2×#30762
C2×#29882