Finite Group Databasebeta

← #10583881

Subgroups — #10583881

Order 512.

6433 conjugacy classes of subgroups.

The subgroup lattice has 1457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62930C211yesmaximal, characteristic, complemented
2#62914C211yesmaximal, characteristic, complemented
3#62561C214yesmaximal, complemented
4#62532C212yesmaximal, complemented
5#62342C214yesmaximal, complemented
6#62280C214yesmaximal, complemented
7#62245C211yesmaximal, characteristic, complemented
8#62190C214yesmaximal, complemented
9#62110C212yesmaximal, complemented
10#62040C214yesmaximal, complemented
11#61962C212yesmaximal, complemented
12#61807C214yesmaximal, complemented
13#61759C214yesmaximal, complemented
14#61720C211yesmaximal, characteristic, complemented
15#61679C214yesmaximal, complemented
16#61617C214yesmaximal, complemented
17#61585C211yesmaximal, characteristic, complemented
18#61496C214yesmaximal, complemented
19D8×#41C212yesmaximal, complemented
20#61211C214yesmaximal, complemented
21#61171C214yesmaximal, complemented
22C2×#3303C211yesmaximal, characteristic, complemented
23#60306C211yesmaximal, characteristic, complemented
24#3558—24no—
25#3549C2214yescomplemented
26#3548C2214yescomplemented
27#3547C2214yescomplemented
28#3546C2214yescomplemented
29#3542—24no—
30#3542—24no—
31#3540—24no—
32#3537C2214yescomplemented
33#3536—24no—
34#3536C2214yescomplemented
35#3534—24no—
36#3520C2214yescomplemented
37#3519C2214yescomplemented
38#3511C2212yescomplemented
39#3511C2212yescomplemented
40#3506C2214yescomplemented
41#3496C2214yescomplemented
42#3496C2211yescharacteristic, complemented
43#3496C2211yescharacteristic, complemented
44#3494C2214yescomplemented
45#3493—21no—
46#3492—21no—
47#3488—22no—
48#3488—22no—
49#3488C2214yescomplemented
50C2×#555C2211yescharacteristic, complemented
51D4×#41C2212yescomplemented
52D4×#41C2212yescomplemented
53C2×#547C2211yescharacteristic, complemented
54#3460C2211yescharacteristic
55#3449—21no—
56C2×#537—21no—
57#3397C2214yescomplemented
58#3391C2212yescomplemented
59#3384C2214yescomplemented
60Q8×D8C2212yescomplemented
61#3367C2214yescomplemented
62#3366C2214yescomplemented
63#3360C2214yescomplemented
64#3360C2214yescomplemented
65#3358C2212yescomplemented
66#3358C2212yescomplemented
67#3357C2218yescomplemented
68#3354C2214yescomplemented
69#3354C2214yescomplemented
70#3354C2214yescomplemented
71#3346C2218yescomplemented
72#3346C2218yescomplemented
73#3345C2218yescomplemented
74#3334C2214yescomplemented
75#3334C2214yescomplemented
76#3334C2212yescomplemented
77#3330C2214yescomplemented
78#3330C2214yescomplemented
79#3330C2214yescomplemented
80#3325C2214yescomplemented
81#3325C2214yescomplemented
82#3325C2214yescomplemented
83#3322C2218yescomplemented
84#3322C2218yescomplemented
85#3319C2218yescomplemented
86#3319C2218yescomplemented
87#3318C2218yescomplemented
88#3309C2218yescomplemented
89#3309C2218yescomplemented
90#3308C2218yescomplemented
91#3305C2218yescomplemented
92#3303C2214yescomplemented
93#3303C2214yescomplemented
94#3303C2214yescomplemented
95#3303C2214yescomplemented
96#3303C2214yescomplemented
97#3303C2214yescomplemented
98#3301C2218yescomplemented
99#3301C2218yescomplemented
100#3297C2218yescomplemented
101#3297C2218yescomplemented
102#3295C2218yescomplemented
103#3294C2212yescomplemented
104#3294C2214yescomplemented
105#3294C2214yescomplemented
106#3294C2214yescomplemented
107#3294C2212yescomplemented
108#3294C2214yescomplemented
109D4×D8C2214yescomplemented
110D4×D8C2214yescomplemented
111D4×D8C2212yescomplemented
112#3274C2218yescomplemented
113#3272C2214yescomplemented
114#3272C2214yescomplemented
115#3272C2214yescomplemented
116#3265C2218yescomplemented
117#3264C2218yescomplemented
118#3264C2218yescomplemented
119#3257C2218yescomplemented
120#3254C2214yescomplemented
121#3253C2214yescomplemented
122#3245C2212yescomplemented
123#3243C2218yescomplemented
124#3235C2214yescomplemented
125#3231C2214yescomplemented
126#3227C2212yescomplemented
127#3220C2218yescomplemented
128#3214C2214yescomplemented
129#3207C2214yescomplemented
130#3206C2212yescomplemented
131#3198C2218yescomplemented
132#3198C2218yescomplemented
133#3198C2218yescomplemented
134#3193C2214yescomplemented
135#3192C2214yescomplemented
136#3186C2214yescomplemented
137#3179C2218yescomplemented
138#3169C2212yescomplemented
139#3169C2214yescomplemented
140#3167C2214yescomplemented
141#3136C2214yescomplemented
142#3131C2214yescomplemented
143C2×#487C2211yescharacteristic, complemented
144#3119C2218yescomplemented
145#3118C2218yescomplemented
146#3110C2214yescomplemented
147#3109C2214yescomplemented
148#3100C2212yescomplemented
149#3100C2214yescomplemented
150#3100C2212yescomplemented
151#3100C2214yescomplemented
152#3098C2218yescomplemented
153#3098C2214yescomplemented
154#3094C2214yescomplemented
155C2×#485C2212yescomplemented
156#3083C2214yescomplemented
157#3077C2214yescomplemented
158C2×#476C2211yescharacteristic, complemented
159#3062C2218yescomplemented
160#3062C2214yescomplemented
161C2×#466C2214yescomplemented
162C2×#465C2212yescomplemented
163#3041C2214yescomplemented
164#3036C2214yescomplemented
165C2×#461C2211yescharacteristic, complemented
166#3008C2218yescomplemented
167#3008C2214yescomplemented
168#3006C2214yescomplemented
169C2×#449C2212yescomplemented
170#2993C2214yescomplemented
171#2989C2212yescomplemented
172#2981C2214yescomplemented
173#2976C2214yescomplemented
174#2975C2211yescharacteristic, complemented
175#2966C2214yescomplemented
176C8×#41C2212yescomplemented
177#2946C2214yescomplemented
178C2×C4×D8C2214yescomplemented
179C2×C4×D8C2211yescharacteristic, complemented
180#2931C2214yescomplemented
181#2929C2214yescomplemented
182C2×C8×D4C2211yescharacteristic, complemented
183#2897C2214yescomplemented
184C2×#416C2212yescomplemented
185C2×H(5,𝔽2)—21no—
186C2×H(5,𝔽2)—21no—
187C2×H(5,𝔽2)C2314yes—
188C22×#41—22no—
189C22×#41—22no—
190C22×#41C2312yes—
191C2×AGL(1,ℤ/8)C2314yes—
192C2×AGL(1,ℤ/8)C2314yes—
193C2×AGL(1,ℤ/8)C2318yes—
194C22×SD16C2312yes—
195C22×D8C2311yescharacteristic
196C22×D8C2314yes—
197C22×D8C2314yes—
198C2×#131C2314yes—
199C23×C8C2312yes—
200#562—28no—
201#562—28no—
202#562—28no—
203H(3,𝔽4)—28no—
204#560—28no—
205#560—28no—
206#559—28no—
207#556—24no—
208#556—22no—
209#556C2314yes—
210#555—24no—
211#555—24no—
212#555—22no—
213#555C2314yes—
214#555C2314yes—
215#555C2314yes—
216#555C2318yes—
217#554—24no—
218#554—22no—
219#554C2314yes—
220#554C2318yes—
221#553—24no—
222#553—24no—
223#553—24no—
224#553C2318yes—
225#553C2318yes—
226#553C2318yes—
227#552—24no—
228#552—24no—
229#551—28no—
230#551—28no—
231#550—24no—
232#550—24no—
233#550C2318yes—
234#550C2312yes—
235#550C2312yes—
236D4×Q8C2312yes—
237D4×Q8C2312yes—
238#548—24no—
239#548—24no—
240#548—22no—
241#548—22no—
242#548—24no—
243#548C2318yes—
244#547—24no—
245#547—24no—
246#547—22no—
247#547C2314yes—
248#547C2314yes—
249#547C2314yes—
250#547C2312yes—
251#547C2314yes—
252#547C2314yes—
253#547C2312yes—
254#547C2314yes—
255#547C2314yes—
256#546—24no—
257#546—24no—
258#546—28no—
259#546—28no—
260#546—28no—
261#546—28no—
262#546—28no—
263#546—24no—
264#546—22no—
265#546—22no—
266#546—24no—
267#546—24no—
268#546—24no—
269#546C2318yes—
270#546C2318yes—
271D42—24no—
272D42—24no—
273D42—28no—
274D42—28no—
275D42C2314yes—
276D42C2312yes—
277D42C2314yes—
278D42C2312yes—
279D42C2314yes—
280D42C2314yes—
281D42C2318yes—
282#544D411yescharacteristic
283#544C2314yes—
284#543—24no—
285#542—28no—
286#542—24no—
287#542—24no—
288#542—24no—
289#542D414yes—
290#542C2318yes—
291#540—24no—
292#540—28no—
293#540D414yes—
294#540C2318yes—
295#539—28no—
296#539—24no—
297#538—28no—
298#538—28no—
299#538—24no—
300#538—24no—
301#538—28no—
302#538—24no—
303#538D414yes—
304#537—22no—
305#537—22no—
306#537—24no—
307#537—24no—
308#537—24no—
309#537—24no—
310#537—24no—
311#537—24no—
312#537—21no—
313#537—21no—
314#537D411yescharacteristic
315#537C2314yes—
316#537C2318yes—
317#536—24no—
318#535—24no—
319#535—24no—
320#535—24no—
321#535—24no—
322#535—28no—
323#535D412yes—
324#535C2314yes—
325#535C2314yes—
326#535C2318yes—
327#534—24no—
328#534—28no—
329#534—24no—
330#534—22no—
331#534—22no—
332#533C2314yes—
333#533C2314yes—
334#532—24no—
335#532C2314yes—
336#532C2312yes—
337#532C2314yes—
338#532C2312yes—
339#532C2314yes—
340#532C2314yes—
341#532C2314yes—
342C2×C4⋊Q8C2311yescharacteristic
343C2×C4⋊Q8C2311yescharacteristic
344#529—24no—
345#529C2314yes—
346C2×#124—22no—
347#525—24no—
348#525—24no—
349#525—24no—
350#525—24no—
351#525—24no—
352#525—22no—
353#525—22no—
354#525—24no—
355#525—24no—
356#525C2314yes—
357C2×#123—22no—
358C2×C22⋊Q8—24no—
359C2×C22⋊Q8C2312yes—
360C2×#121—21no—
361C2×#121—21no—
362C2×#121—24no—
363C2×#121—24no—
364C2×#121—24no—
365C2×#121—24no—
366C2×#121C2314yes—
367C2×#121C2314yes—
368C2×#121C2312yes—
369#520—22no—
370#520—22no—
371#520C2314yes—
372#520C2314yes—
373#518C2314yes—
374C4×#41C2312yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2314yes—
379C2×C4×D4C2311yescharacteristic
380C2×#117—21no—
381C2×#117C2312yes—
382C22×C4⋊C4—21no—
383#501C2318yes—
384#500C2312yes—
385#500C2314yes—
386#498C2314yes—
387#496C2318yes—
388#493C2312yes—
389#493C2314yes—
390#492C2314yes—
391#490C2318yes—
392#489C2318yes—
393#488C2318yes—
394#488C2318yes—
395#487C2314yes—
396#487C2314yes—
397#487C2314yes—
398#486C2312yes—
399#486C2314yes—
400#486C2312yes—
401#486C2314yes—
402#486C2314yes—
403#485C2318yes—
404#485C2318yes—
405#485C2318yes—
406#485C2318yes—
407#484C2318yes—
408#484C2318yes—
409#482C2318yes—
410#482C2318yes—
411#482C2318yes—
412#482C2318yes—
413#481C2318yes—
414#481C2318yes—
415#481C2318yes—
416#480C2314yes—
417#480C2314yes—
418#480C2318yes—
419#480C2314yes—
420#480C2314yes—
421#480C2314yes—
422#480C2318yes—
423#480C2314yes—
424#479C2318yes—
425#479C2318yes—
426#478C2318yes—
427#478C2318yes—
428#477C2318yes—
429#476C2314yes—
430#476C2314yes—
431#476C2318yes—
432#476C2314yes—
433#476C2314yes—
434#474C2312yes—
435#474C2312yes—
436#474C2314yes—
437#474C2314yes—
438#474C2312yes—
439#474C2314yes—
440#474C2314yes—
441#474C2314yes—
442#474C2314yes—
443#474C2312yes—
444#469C2318yes—
445#469C2318yes—
446#469C2318yes—
447#469C2318yes—
448#468C2318yes—
449#468C2318yes—
450#468C2318yes—
451#468C2318yes—
452#466C2314yes—
453#466C2314yes—
454#466C2314yes—
455#466C2318yes—
456#466C2318yes—
457#466C2314yes—
458#466C2314yes—
459#466C2314yes—
460#466C2318yes—
461#465C2318yes—
462#465C2318yes—
463#465C2318yes—
464#465C2318yes—
465#463C2318yes—
466#463C2318yes—
467#463C2318yes—
468#463C2318yes—
469#461C2314yes—
470#461C2314yes—
471#461C2314yes—
472#461C2314yes—
473#460C2318yes—
474#459C2312yes—
475#459C2314yes—
476#459C2312yes—
477#459C2314yes—
478#459C2312yes—
479#459C2314yes—
480#459C2312yes—
481#459C2314yes—
482#459C2314yes—
483#459C2314yes—
484#459C2318yes—
485#450C2318yes—
486#450C2318yes—
487#449C2318yes—
488#449C2318yes—
489#449C2318yes—
490#449C2318yes—
491#449C2318yes—
492#449C2318yes—
493#449C2318yes—
494#449C2318yes—
495#448C2318yes—
496#447C2314yes—
497#447C2314yes—
498#447C2314yes—
499#447C2314yes—
500#447C2314yes—
501#447C2314yes—
502#447C2318yes—
503#447C2318yes—
504#447C2318yes—
505#447C2318yes—
506#446C2314yes—
507C8×Q8C2312yes—
508C8×Q8C2312yes—
509#442C2318yes—
510#442C2318yes—
511#440C2318yes—
512#440C2318yes—
513C4×SD16C2318yes—
514C4×SD16C2318yes—
515C4×D8C2314yes—
516C4×D8C2314yes—
517C4×D8C2314yes—
518C4×D8C2314yes—
519C4×D8C2312yes—
520C4×D8C2314yes—
521C4×D8C2314yes—
522C4×D8C2312yes—
523C4×D8C2312yes—
524C4×D8C2314yes—
525C4×D8C2312yes—
526C4×D8C2314yes—
527C4×D8C2314yes—
528C4×D8C2314yes—
529#436C2314yes—
530#436C2314yes—
531#436C2314yes—
532#436C2318yes—
533#435C2318yes—
534#435C2318yes—
535#435C2318yes—
536C8×D4C2314yes—
537C8×D4C2314yes—
538C8×D4C2312yes—
539C8×D4C2314yes—
540C8×D4C2314yes—
541C8×D4C2318yes—
542C8×D4C2312yes—
543#433C2318yes—
544#432C2314yes—
545#431C2312yes—
546#431C2314yes—
547#428C2318yes—
548#428C2314yes—
549#428C2314yes—
550C2×#107C2311yescharacteristic
551C2×#107C2314yes—
552C2×#107C2314yes—
553C2×#106C2312yes—
554#424C2314yes—
555#423C2314yes—
556C2×C4⋊C8C2311yescharacteristic
557#418C2318yes—
558#418C2314yes—
559#418C2314yes—
560#417C2314yes—
561#417C2314yes—
562#417C2318yes—
563#416C2314yes—
564#416C2318yes—
565#416C2314yes—
566#416C2318yes—
567#416C2314yes—
568#416C2314yes—
569C2×#103C2312yes—
570C2×#103C2312yes—
571C2×#103C2312yes—
572C2×#102C2314yes—
573C2×#102C2311yescharacteristic
574C2×#102C2312yes—
575C2×#102C2314yes—
576C2×#102C2311yescharacteristic
577C2×#102C2314yes—
578C2×#102C2314yes—
579#408C2314yes—
580#408C2318yes—
581#407C2314yes—
582C2×C22⋊C8C2312yes—
583#405C2314yes—
584C2×C4×C8C2311yescharacteristic
585C2×C4×C8C2314yes—
586H(5,𝔽2)—48no—
587H(5,𝔽2)—84no—
588H(5,𝔽2)—84no—
589H(5,𝔽2)—84no—
590C2×#41—22no—
591C2×#41—24no—
592C2×#41—22no—
593C2×#41—22no—
594C2×#41—24no—
595C2×#41—24no—
596C2×#41—24no—
597C2×#41—24no—
598C2×#41—22no—
599C2×#41—22no—
600C2×#41—22no—
601C2×#41—24no—
602C2×#41—24no—
603C2×#41—24no—
604C2×#41—24no—
605C2×#41—44no—
606C2×#41—82no—
607C2×#41—88no—
608C2×#41—88no—
609C2×#41C2×D412yes—
610C2×#41C2414yes—
611C2×#41C2418yes—
612C2×#41C2414yes—
613C2×#41C2414yes—
614C22×Q8—22no—
615C22×Q8—22no—
616C22×Q8—21no—
617C22×Q8C2412yes—
618C22×D4—22no—
619C22×D4—24no—
620C22×D4—24no—
621C22×D4—22no—
622C22×D4—24no—
623C22×D4—22no—
624C22×D4—24no—
625C22×D4—28no—
626C22×D4—24no—
627C22×D4—24no—
628C22×D4—24no—
629C22×D4—22no—
630C22×D4—28no—
631C22×D4C2×D411yescharacteristic
632C22×D4C2411yescharacteristic
633C22×D4C2414yes—
634C22×D4C2411yescharacteristic
635C22×D4C2414yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C23×C4—21no—
639C23×C4—21no—
640C23×C4—22no—
641C23×C4—24no—
642C23×C4—24no—
643C23×C4C2412yes—
644AGL(1,ℤ/8)—48no—
645AGL(1,ℤ/8)—88no—
646AGL(1,ℤ/8)—84no—
647C2×SD16—82no—
648C2×SD16C2418yes—
649C2×SD16C2418yes—
650C2×SD16C2418yes—
651C2×D8—42no—
652C2×D8—48no—
653C2×D8—84no—
654C2×D8C2412yes—
655C2×D8C2414yes—
656C2×D8C2414yes—
657C2×D8C2418yes—
658C2×D8C2414yes—
659C2×D8C2414yes—
660C2×D8C2412yes—
661C2×D8C2414yes—
662C2×D8C2414yes—
663#131—84no—
664C2×M16C2414yes—
665C2×M16C2418yes—
666C2×M16C2414yes—
667C22×C8—82no—
668C22×C8C2411yescharacteristic
669C22×C8C2414yes—
670C22×C8C2414yes—
671C22×C8C2412yes—
672C22×C8C2414yes—
673C22×C8C2411yescharacteristic
674C22×C8C2414yes—
675C4⋊Q8—24no—
676C4⋊Q8—22no—
677C4⋊Q8—22no—
678C4⋊Q8C2×D414yes—
679C4⋊Q8C2414yes—
680C4⋊Q8C2414yes—
681C4⋊Q8C2412yes—
682C4⋊Q8C2412yes—
683C4⋊Q8C2414yes—
684C4⋊Q8C2414yes—
685#127—24no—
686#127—28no—
687#127—28no—
688#127C2×D414yes—
689#127C2412yes—
690#127C2412yes—
691#127C2414yes—
692#127C2414yes—
693#126—28no—
694#126—28no—
695#126—28no—
696#126—28no—
697#126—28no—
698#126C2×D418yes—
699#125—24no—
700#125—28no—
701#125—24no—
702#125C2×D414yes—
703#125C2418yes—
704#124—24no—
705#124—28no—
706#124—28no—
707#124—28no—
708#124—28no—
709#124—28no—
710#124—28no—
711#124—28no—
712#124—28no—
713#124—24no—
714#124—24no—
715#124—22no—
716#124—22no—
717#124—24no—
718#124C2×D414yes—
719#124C2×D418yes—
720#124C2418yes—
721#123—28no—
722#123—28no—
723#123—28no—
724#123—28no—
725#123—28no—
726#123—28no—
727#123—24no—
728#123—28no—
729#123—24no—
730#123—24no—
731#123—28no—
732#123—24no—
733#123—28no—
734#123—24no—
735#123—24no—
736#123—28no—
737#123—28no—
738#123—28no—
739#123—28no—
740#123C2×D418yes—
741#123C2×D418yes—
742C22⋊Q8—24no—
743C22⋊Q8—24no—
744C22⋊Q8—24no—
745C22⋊Q8—28no—
746C22⋊Q8—24no—
747C22⋊Q8—24no—
748C22⋊Q8—24no—
749C22⋊Q8—24no—
750C22⋊Q8—28no—
751C22⋊Q8—24no—
752C22⋊Q8—22no—
753C22⋊Q8—22no—
754C22⋊Q8—24no—
755C22⋊Q8—22no—
756C22⋊Q8—22no—
757C22⋊Q8—24no—
758C22⋊Q8—24no—
759C22⋊Q8—24no—
760C22⋊Q8—24no—
761C22⋊Q8—28no—
762C22⋊Q8—28no—
763C22⋊Q8—28no—
764C22⋊Q8—28no—
765C22⋊Q8—28no—
766C22⋊Q8C2×D414yes—
767C22⋊Q8C2×D414yes—
768C22⋊Q8C2×D414yes—
769C22⋊Q8C2418yes—
770C22⋊Q8C2418yes—
771#121—24no—
772#121—24no—
773#121—28no—
774#121—28no—
775#121—24no—
776#121—24no—
777#121—24no—
778#121—28no—
779#121—24no—
780#121—28no—
781#121—24no—
782#121—28no—
783#121—28no—
784#121—28no—
785#121—28no—
786#121—28no—
787#121—24no—
788#121—24no—
789#121—24no—
790#121—24no—
791#121—24no—
792#121—24no—
793#121—24no—
794#121—22no—
795#121—22no—
796#121—24no—
797#121—24no—
798#121—24no—
799#121—22no—
800#121—22no—
801#121—24no—
802#121—24no—
803#121—22no—
804#121—22no—
805#121—24no—
806#121—24no—
807#121—24no—
808#121—24no—
809#121—24no—
810#121—24no—
811#121—28no—
812#121—28no—
813#121—28no—
814#121—28no—
815#121—28no—
816#121—28no—
817#121—28no—
818#121C2×D414yes—
819#121C2×D414yes—
820#121C2×D414yes—
821#121C2×D414yes—
822#121C2×D414yes—
823#121C2×D418yes—
824#121C2414yes—
825#121C2414yes—
826#121C2418yes—
827#121C2418yes—
828#121C2418yes—
829#121C2414yes—
830#121C2414yes—
831#121C2418yes—
832#121C2414yes—
833#121C2414yes—
834#120—28no—
835#120—28no—
836#120—28no—
837#120—28no—
838#120—28no—
839#120—24no—
840#120—24no—
841#120—24no—
842#120—28no—
843#120—24no—
844#120—24no—
845#120—24no—
846#120—28no—
847#120—28no—
848#120—28no—
849#120—28no—
850#120C2×D418yes—
851C4×Q8—24no—
852C4×Q8—24no—
853C4×Q8—24no—
854C4×Q8—24no—
855C4×Q8C2×D412yes—
856C4×Q8C2418yes—
857C4×Q8C2412yes—
858C4×D4—24no—
859C4×D4—28no—
860C4×D4—28no—
861C4×D4—24no—
862C4×D4—24no—
863C4×D4—28no—
864C4×D4—28no—
865C4×D4—28no—
866C4×D4—28no—
867C4×D4—28no—
868C4×D4—28no—
869C4×D4—24no—
870C4×D4—22no—
871C4×D4—22no—
872C4×D4—24no—
873C4×D4—24no—
874C4×D4—24no—
875C4×D4—24no—
876C4×D4—24no—
877C4×D4—24no—
878C4×D4—22no—
879C4×D4—22no—
880C4×D4—24no—
881C4×D4—24no—
882C4×D4C2×D414yes—
883C4×D4C2×D414yes—
884C4×D4C2×D412yes—
885C4×D4C2412yes—
886C4×D4C2412yes—
887C4×D4C2414yes—
888C4×D4C2414yes—
889C4×D4C2414yes—
890C4×D4C2414yes—
891C4×D4C2412yes—
892C4×D4C2412yes—
893C4×D4C2414yes—
894C4×D4C2414yes—
895C4×D4C2418yes—
896C4×D4C2414yes—
897C4×D4C2414yes—
898C4×D4C2412yes—
899C4×D4C2418yes—
900#117—24no—
901#117—24no—
902#117—24no—
903#117—24no—
904#117—24no—
905#117—24no—
906#117—24no—
907#117—28no—
908#117C2×D412yes—
909#117C2×D414yes—
910#117C2414yes—
911#117C2414yes—
912#117C2418yes—
913#117C2414yes—
914C2×C4⋊C4—21no—
915C2×C4⋊C4—22no—
916C2×C4⋊C4—21no—
917C2×C4⋊C4—21no—
918C2×C4⋊C4—24no—
919C2×C4⋊C4—24no—
920C2×C4⋊C4—24no—
921C2×C4⋊C4—24no—
922C2×C4⋊C4—24no—
923C2×C4⋊C4C2×D411yescharacteristic
924C2×C4⋊C4C2411yescharacteristic
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2411yescharacteristic
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C22⋊C4—22no—
932C2×C22⋊C4—22no—
933C2×C22⋊C4—22no—
934C2×C22⋊C4—21no—
935C2×C22⋊C4—21no—
936C2×C22⋊C4—24no—
937C2×C22⋊C4—24no—
938C2×C22⋊C4—24no—
939C2×C22⋊C4—24no—
940C2×C22⋊C4—28no—
941C2×C22⋊C4—28no—
942C2×C22⋊C4—28no—
943C2×C22⋊C4C2×D412yes—
944C2×C42—22no—
945C2×C42C2411yescharacteristic
946C2×C42C2414yes—
947#107C2412yes—
948#107C2414yes—
949#107C2414yes—
950#107C2418yes—
951#107C2412yes—
952#107C2414yes—
953#107C2414yes—
954#107C2414yes—
955#107C2414yes—
956#106C2418yes—
957#106C2418yes—
958#106C2418yes—
959C4⋊C8C2414yes—
960C4⋊C8C2412yes—
961C4⋊C8C2418yes—
962C4⋊C8C2414yes—
963C4⋊C8C2412yes—
964C4⋊C8C2414yes—
965#103C2414yes—
966#103C2414yes—
967#103C2414yes—
968#103C2414yes—
969#103C2418yes—
970#103C2418yes—
971#103C2418yes—
972#102C2411yescharacteristic
973#102C2414yes—
974#102C2412yes—
975#102C2414yes—
976#102C2411yescharacteristic
977#102C2411yescharacteristic
978#102C2411yescharacteristic
979#102C2414yes—
980#102C2414yes—
981#102C2414yes—
982#102C2414yes—
983#102C2418yes—
984#102C2412yes—
985#102C2414yes—
986#102C2414yes—
987#102C2418yes—
988#102C2414yes—
989#102C2418yes—
990#102C2418yes—
991#102C2414yes—
992#102C2414yes—
993#102C2414yes—
994#102C2414yes—
995#102C2414yes—
996C22⋊C8C2418yes—
997C22⋊C8C2414yes—
998C22⋊C8C2418yes—
999C22⋊C8C2414yes—
1000C22⋊C8C2414yes—
1001C22⋊C8C2418yes—
1002#97C2418yes—
1003C4×C8C2412yes—
1004C4×C8C2414yes—
1005C4×C8C2412yes—
1006C4×C8C2414yes—
1007C4×C8C2414yes—
1008C24—21no—
1009C24—24no—
1010C24—21no—
1011C24—24no—
1012C24—24no—
1013C24—24no—
1014C24C22×D412yes—
1015#41—28no—
1016#41—28no—
1017#41—44no—
1018#41—44no—
1019#41—44no—
1020#41—44no—
1021#41—48no—
1022#41—44no—
1023#41—48no—
1024#41—48no—
1025#41—48no—
1026#41—88no—
1027#41—88no—
1028#41—88no—
1029#41—88no—
1030#41—88no—
1031#41—84no—
1032#41—84no—
1033#41—88no—
1034#41—88no—
1035#41—88no—
1036#41—84no—
1037#41—84no—
1038#41—164no—
1039C2×Q8—22no—
1040C2×Q8—22no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—22no—
1044C2×Q8—24no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—84no—
1048C2×Q8—84no—
1049C2×Q8—161no—
1050C2×Q8C22×D412yes—
1051C2×Q8C22×D414yes—
1052C2×Q8C2514yes—
1053C2×D4—22no—
1054C2×D4—28no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—28no—
1059C2×D4—28no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—28no—
1065C2×D4—28no—
1066C2×D4—28no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—21no—
1070C2×D4—24no—
1071C2×D4—22no—
1072C2×D4—22no—
1073C2×D4—22no—
1074C2×D4—24no—
1075C2×D4—21no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—22no—
1079C2×D4—24no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—24no—
1083C2×D4—41no—
1084C2×D4—44no—
1085C2×D4—41no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—41no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—84no—
1094C2×D4—84no—
1095C2×D4—88no—
1096C2×D4—88no—
1097C2×D4—88no—
1098C2×D4—88no—
1099C2×D4—88no—
1100C2×D4—816no—
1101C2×D4—88no—
1102C2×D4—88no—
1103C2×D4—84no—
1104C2×D4—168no—
1105C2×D4—162no—
1106C2×D4C22×D414yes—
1107C2×D4C22×D414yes—
1108C2×D4C22×D412yes—
1109C2×D4C22×D418yes—
1110C2×D4C22×D418yes—
1111C2×D4C22×D414yes—
1112C2×D4C2514yes—
1113C2×D4C2511yescharacteristic
1114C2×D4C2512yes—
1115C2×D4C2514yes—
1116C2×D4C2511yescharacteristic
1117C22×C4—21no—
1118C22×C4—21no—
1119C22×C4—22no—
1120C22×C4—22no—
1121C22×C4—24no—
1122C22×C4—24no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—22no—
1127C22×C4—22no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—22no—
1131C22×C4—22no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—28no—
1136C22×C4—28no—
1137C22×C4—24no—
1138C22×C4—24no—
1139C22×C4—42no—
1140C22×C4—42no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—88no—
1144C22×C4—88no—
1145C22×C4—84no—
1146C22×C4C22×D414yes—
1147C22×C4C22×D412yes—
1148C22×C4C22×D411yescharacteristic
1149C22×C4C22×D414yes—
1150C22×C4C22×D414yes—
1151C22×C4C22×D411yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2514yes—
1154C22×C4C2514yes—
1155SD16—48no—
1156SD16—48no—
1157SD16—48no—
1158D8—24no—
1159D8—28no—
1160D8—42no—
1161D8—44no—
1162D8—44no—
1163D8—44no—
1164D8—48no—
1165D8—44no—
1166D8—44no—
1167M16—48no—
1168M16—44no—
1169M16—44no—
1170C2×C8—41no—
1171C2×C8—44no—
1172C2×C8—44no—
1173C2×C8—42no—
1174C2×C8—44no—
1175C2×C8—41no—
1176C2×C8—44no—
1177C2×C8C2511yescharacteristic
1178C2×C8C2512yes—
1179C2×C8C2514yes—
1180C2×C8C2514yes—
1181C2×C8C2511yescharacteristic
1182C2×C8C2514yes—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—28no—
1191C4⋊C4—21no—
1192C4⋊C4—22no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—21no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—22no—
1199C4⋊C4—24no—
1200C4⋊C4—28no—
1201C4⋊C4—22no—
1202C4⋊C4C22×D414yes—
1203C4⋊C4C22×D412yes—
1204C4⋊C4C22×D412yes—
1205C4⋊C4C22×D414yes—
1206C4⋊C4C22×D414yes—
1207C4⋊C4C22×D418yes—
1208C4⋊C4C22×D414yes—
1209C4⋊C4C22×D414yes—
1210C4⋊C4C2514yes—
1211C4⋊C4C2511yescharacteristic
1212C4⋊C4C2514yes—
1213C4⋊C4C2511yescharacteristic
1214C4⋊C4C2512yes—
1215C4⋊C4C2514yes—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—24no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—22no—
1222C22⋊C4—24no—
1223C22⋊C4—22no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—24no—
1233C22⋊C4—28no—
1234C22⋊C4—24no—
1235C22⋊C4—22no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—22no—
1239C22⋊C4—24no—
1240C22⋊C4—28no—
1241C22⋊C4—28no—
1242C22⋊C4—24no—
1243C22⋊C4—24no—
1244C22⋊C4C22×D418yes—
1245C22⋊C4C22×D418yes—
1246C22⋊C4C22×D418yes—
1247C22⋊C4C22×D418yes—
1248C22⋊C4C22×D414yes—
1249C22⋊C4C22×D414yes—
1250C22⋊C4C22×D414yes—
1251C42—24no—
1252C42—24no—
1253C42—28no—
1254C42—28no—
1255C42C22×D414yes—
1256C42C22×D412yes—
1257C42C22×D414yes—
1258C42C2512yes—
1259C42C2514yes—
1260C23—21no—
1261C23—24no—
1262C23—24no—
1263C23—22no—
1264C23—24no—
1265C23—21no—
1266C23—42no—
1267C23—42no—
1268C23—42no—
1269C23—48no—
1270C23—42no—
1271C23—42no—
1272C23—81no—
1273C23—84no—
1274C23—84no—
1275C23—81no—
1276C23—84no—
1277C23—81no—
1278C23—84no—
1279C23—84no—
1280C23—84no—
1281C23—84no—
1282C23—84no—
1283C23—84no—
1284C23—84no—
1285C23—84no—
1286C23C23×D414yes—
1287C23C23×D414yes—
1288C23C23×D411yescharacteristic
1289Q8—24no—
1290Q8—24no—
1291Q8—24no—
1292Q8—44no—
1293Q8—44no—
1294Q8—44no—
1295Q8—82no—
1296Q8—84no—
1297Q8—84no—
1298Q8—84no—
1299D4—28no—
1300D4—22no—
1301D4—24no—
1302D4—24no—
1303D4—21no—
1304D4—21no—
1305D4—24no—
1306D4—24no—
1307D4—21no—
1308D4—22no—
1309D4—28no—
1310D4—24no—
1311D4—44no—
1312D4—48no—
1313D4—48no—
1314D4—48no—
1315D4—42no—
1316D4—48no—
1317D4—48no—
1318D4—48no—
1319D4—44no—
1320D4—44no—
1321D4—82no—
1322D4—84no—
1323D4—84no—
1324D4—81no—
1325D4—84no—
1326D4—84no—
1327D4—84no—
1328D4—84no—
1329D4—84no—
1330D4—82no—
1331D4—88no—
1332D4—88no—
1333D4—88no—
1334D4—84no—
1335D4—84no—
1336D4—84no—
1337D4—84no—
1338D4—84no—
1339D4—88no—
1340D4—88no—
1341D4#58512yes—
1342C2×C4—21no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—21no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—28no—
1349C2×C4—24no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—42no—
1357C2×C4—44no—
1358C2×C4—41no—
1359C2×C4—44no—
1360C2×C4—48no—
1361C2×C4—42no—
1362C2×C4—42no—
1363C2×C4—44no—
1364C2×C4—44no—
1365C2×C4—44no—
1366C2×C4—44no—
1367C2×C4—48no—
1368C2×C4—48no—
1369C2×C4—84no—
1370C2×C4—84no—
1371C2×C4—84no—
1372C2×C4—84no—
1373C2×C4—84no—
1374C2×C4—88no—
1375C2×C4—88no—
1376C2×C4—82no—
1377C2×C4—84no—
1378C2×C4—84no—
1379C2×C4—84no—
1380C2×C4—84no—
1381C2×C4—82no—
1382C2×C4#57614yes—
1383C2×C4C23×D414yes—
1384C2×C4C23×D414yes—
1385C2×C4C23×D414yes—
1386C2×C4C23×D412yes—
1387C2×C4C23×D411yescharacteristic
1388C2×C4C23×D414yes—
1389C2×C4C23×D412yes—
1390C2×C4C2611yescharacteristic
1391C8—22no—
1392C8—24no—
1393C8—21no—
1394C8—21no—
1395C8—24no—
1396C8—24no—
1397C22—21no—
1398C22—21no—
1399C22—24no—
1400C22—24no—
1401C22—22no—
1402C22—24no—
1403C22—24no—
1404C22—24no—
1405C22—24no—
1406C22—41no—
1407C22—41no—
1408C22—41no—
1409C22—44no—
1410C22—42no—
1411C22—44no—
1412C22—42no—
1413C22—41no—
1414C22—44no—
1415C22—44no—
1416C22—44no—
1417C22—42no—
1418C22—41no—
1419C22—44no—
1420C22—84no—
1421C22—84no—
1422C22—162no—
1423C22—168no—
1424C22—168no—
1425C22—324no—
1426C22—324no—
1427C22C2×#57612yes—
1428C22C24×D411yescharacteristic
1429C4—24no—
1430C4—21no—
1431C4—24no—
1432C4—24no—
1433C4—22no—
1434C4—24no—
1435C4—44no—
1436C4—41no—
1437C4—42no—
1438C4—41no—
1439C4—44no—
1440C4—44no—
1441C4—44no—
1442C4C2×#57614yes—
1443C4C2×#58511yescharacteristic
1444C4H(7,𝔽2)11yescharacteristic
1445C2—22no—
1446C2—44no—
1447C2—44no—
1448C2—42no—
1449C2—81no—
1450C2—82no—
1451C2—84no—
1452C2—84no—
1453C2#6298711yescharacteristic
1454C2C22×#57611yescharacteristic
1455C2#6309211yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3460 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62930C2semidirect
2. #62914C2semidirect
3. #62561C2semidirect
4. #62532C2semidirect
5. #62342C2semidirect
6. #62280C2semidirect
7. #62245C2semidirect
8. #62190C2semidirect
9. #62110C2semidirect
10. #62040C2semidirect
11. #61962C2semidirect
12. #61807C2semidirect
13. #61759C2semidirect
14. #61720C2semidirect
15. #61679C2semidirect
16. #61617C2semidirect
17. #61585C2semidirect
18. #61496C2semidirect
19. D8×#41C2semidirect
20. #61211C2semidirect
21. #61171C2semidirect
22. C2×#3303C2semidirect
23. #60306C2semidirect
25. #3549C22semidirect
26. #3548C22semidirect
27. #3547C22semidirect
28. #3546C22semidirect
32. #3537C22semidirect
34. #3536C22semidirect
36. #3520C22semidirect
37. #3519C22semidirect
38. #3511C22semidirect
39. #3511C22semidirect
40. #3506C22semidirect
41. #3496C22semidirect
42. #3496C22semidirect
43. #3496C22semidirect
44. #3494C22semidirect
49. #3488C22semidirect
50. C2×#555C22semidirect
51. D4×#41C22semidirect
52. D4×#41C22semidirect
53. C2×#547C22semidirect
57. #3397C22semidirect
58. #3391C22semidirect
59. #3384C22semidirect
60. Q8×D8C22semidirect
61. #3367C22semidirect
62. #3366C22semidirect
63. #3360C22semidirect
64. #3360C22semidirect
65. #3358C22semidirect
66. #3358C22semidirect
67. #3357C22semidirect
68. #3354C22semidirect
69. #3354C22semidirect
70. #3354C22semidirect
71. #3346C22semidirect
72. #3346C22semidirect
73. #3345C22semidirect
74. #3334C22semidirect
75. #3334C22semidirect
76. #3334C22semidirect
77. #3330C22semidirect
78. #3330C22semidirect
79. #3330C22semidirect
80. #3325C22semidirect
81. #3325C22semidirect
82. #3325C22semidirect
83. #3322C22semidirect
84. #3322C22semidirect
85. #3319C22semidirect
86. #3319C22semidirect
87. #3318C22semidirect
88. #3309C22semidirect
89. #3309C22semidirect
90. #3308C22semidirect
91. #3305C22semidirect
92. #3303C22semidirect
93. #3303C22semidirect
94. #3303C22semidirect
95. #3303C22semidirect
96. #3303C22semidirect
97. #3303C22semidirect
98. #3301C22semidirect
99. #3301C22semidirect
100. #3297C22semidirect
101. #3297C22semidirect
102. #3295C22semidirect
103. #3294C22semidirect
104. #3294C22semidirect
105. #3294C22semidirect
106. #3294C22semidirect
107. #3294C22semidirect
108. #3294C22semidirect
109. D4×D8C22semidirect
110. D4×D8C22semidirect
111. D4×D8C22semidirect
112. #3274C22semidirect
113. #3272C22semidirect
114. #3272C22semidirect
115. #3272C22semidirect
116. #3265C22semidirect
117. #3264C22semidirect
118. #3264C22semidirect
119. #3257C22semidirect
120. #3254C22semidirect
121. #3253C22semidirect
122. #3245C22semidirect
123. #3243C22semidirect
124. #3235C22semidirect
125. #3231C22semidirect
126. #3227C22semidirect
127. #3220C22semidirect
128. #3214C22semidirect
129. #3207C22semidirect
130. #3206C22semidirect
131. #3198C22semidirect
132. #3198C22semidirect
133. #3198C22semidirect
134. #3193C22semidirect
135. #3192C22semidirect
136. #3186C22semidirect
137. #3179C22semidirect
138. #3169C22semidirect
139. #3169C22semidirect
140. #3167C22semidirect
141. #3136C22semidirect
142. #3131C22semidirect
143. C2×#487C22semidirect
144. #3119C22semidirect
145. #3118C22semidirect
146. #3110C22semidirect
147. #3109C22semidirect
148. #3100C22semidirect
149. #3100C22semidirect
150. #3100C22semidirect
151. #3100C22semidirect
152. #3098C22semidirect
153. #3098C22semidirect
154. #3094C22semidirect
155. C2×#485C22semidirect
156. #3083C22semidirect
157. #3077C22semidirect
158. C2×#476C22semidirect
159. #3062C22semidirect
160. #3062C22semidirect
161. C2×#466C22semidirect
162. C2×#465C22semidirect
163. #3041C22semidirect
164. #3036C22semidirect
165. C2×#461C22semidirect
166. #3008C22semidirect
167. #3008C22semidirect
168. #3006C22semidirect
169. C2×#449C22semidirect
170. #2993C22semidirect
171. #2989C22semidirect
172. #2981C22semidirect
173. #2976C22semidirect
174. #2975C22semidirect
175. #2966C22semidirect
176. C8×#41C22semidirect
177. #2946C22semidirect
178. C2×C4×D8C22semidirect
179. C2×C4×D8C22semidirect
180. #2931C22semidirect
181. #2929C22semidirect
182. C2×C8×D4C22semidirect
183. #2897C22semidirect
184. C2×#416C22semidirect

Maximal subgroups

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

subgroupindex
#629302
#629142
#625612
#625322
#623422
#622802
#622452
#621902
#621102
#620402
#619622
#618072
#617592
#617202
#616792
#616172
#615852
#614962
D8×#412
#612112
#611712
C2×#33032
#603062