Finite Group Databasebeta

← #10583882

Subgroups — #10583882

Order 512.

6057 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62929C211yesmaximal, characteristic, complemented
2#62915C211yesmaximal, characteristic, complemented
3#62551C214yesmaximal, complemented
4#62530C212yesmaximal, complemented
5#62341C214yesmaximal, complemented
6#62281C214yesmaximal, complemented
7#62246C211yesmaximal, characteristic, complemented
8#62181C214yesmaximal, complemented
9#62108C212yesmaximal, complemented
10#62036C214yesmaximal, complemented
11#61960C212yesmaximal, complemented
12#61816C214yesmaximal, complemented
13#61757C214yesmaximal, complemented
14#61721C211yesmaximal, characteristic, complemented
15#61693C214yesmaximal, complemented
16#61619C214yesmaximal, complemented
17#61586C211yesmaximal, characteristic, complemented
18#61492C214yesmaximal, complemented
19#61427C212yesmaximal, complemented
20#61217C214yesmaximal, complemented
21#61173C214yesmaximal, complemented
22C2×#3303C211yesmaximal, characteristic, complemented
23#60306C211yesmaximal, characteristic, complemented
24#3565—24no—
25#3561—24no—
26#3559—24no—
27#3552C2214yescomplemented
28#3547—24no—
29#3547C2214yescomplemented
30#3547C2214yescomplemented
31#3544—24no—
32#3544C2214yescomplemented
33#3538C2214yes—
34#3536C2214yes—
35#3535—24no—
36#3518C2214yescomplemented
37#3515C2214yescomplemented
38#3511C2214yescomplemented
39#3503C2212yes—
40#3503C2212yes—
41#3501C2211yescharacteristic
42#3501C2211yescharacteristic
43#3499C2214yescomplemented
44#3495C2214yes—
45#3494—22no—
46#3494—22no—
47#3493—21no—
48#3492—21no—
49#3489C2214yes—
50#3475C2212yes—
51#3475C2212yes—
52C2×#555C2211yescharacteristic
53C2×#547C2211yescharacteristic
54#3460C2211yescharacteristic
55#3458—21no—
56C2×#544—21no—
57#3398C2214yescomplemented
58#3393C2212yescomplemented
59#3385C2214yescomplemented
60#3380C2212yescomplemented
61#3372C2214yescomplemented
62#3369C2214yescomplemented
63#3363C2214yescomplemented
64#3363C2214yescomplemented
65#3360C2212yescomplemented
66#3360C2212yescomplemented
67#3357C2214yescomplemented
68#3357C2214yescomplemented
69#3357C2214yescomplemented
70#3352C2218yescomplemented
71#3349C2218yescomplemented
72#3344C2218yes—
73#3343C2218yescomplemented
74#3341C2212yescomplemented
75#3338C2214yescomplemented
76#3336C2214yes—
77#3331C2214yescomplemented
78#3331C2214yescomplemented
79#3331C2214yescomplemented
80#3330C2218yescomplemented
81#3329C2214yescomplemented
82#3329C2214yescomplemented
83#3329C2214yescomplemented
84#3328C2218yescomplemented
85#3315C2218yescomplemented
86#3314C2218yes—
87#3313C2218yescomplemented
88#3312C2218yes—
89#3312C2218yescomplemented
90#3308C2218yescomplemented
91#3303C2214yes—
92#3303C2214yes—
93#3303C2214yes—
94#3303C2214yes—
95#3303C2212yescomplemented
96#3303C2212yescomplemented
97#3302C2218yescomplemented
98#3300C2218yescomplemented
99#3300C2218yescomplemented
100#3299C2218yes—
101#3299C2218yes—
102#3299C2214yescomplemented
103#3299C2214yescomplemented
104#3299C2214yescomplemented
105#3299C2214yescomplemented
106#3298C2218yescomplemented
107#3296C2214yes—
108#3296C2214yes—
109D4×Q16C2214yescomplemented
110#3283C2212yescomplemented
111#3280C2214yes—
112#3277C2218yescomplemented
113#3276C2214yescomplemented
114#3276C2214yescomplemented
115#3276C2214yescomplemented
116#3270C2218yescomplemented
117#3269C2218yescomplemented
118#3266C2218yes—
119#3258C2218yescomplemented
120#3252C2214yescomplemented
121#3252C2214yescomplemented
122#3249C2212yes—
123#3242C2218yescomplemented
124#3238C2214yescomplemented
125#3230C2212yes—
126#3230C2214yescomplemented
127#3225C2218yescomplemented
128#3218C2214yescomplemented
129#3209C2212yes—
130#3209C2214yescomplemented
131#3203C2218yescomplemented
132#3202C2218yescomplemented
133#3201C2218yescomplemented
134#3195C2214yes—
135#3193C2214yes—
136#3189C2214yes—
137#3178C2218yescomplemented
138#3170C2212yes—
139#3170C2214yescomplemented
140#3168C2214yescomplemented
141#3137C2214yescomplemented
142C2×#487C2211yescharacteristic
143C2×#487C2214yescomplemented
144#3127C2218yescomplemented
145#3124C2218yescomplemented
146#3116C2214yescomplemented
147#3116C2214yescomplemented
148#3102C2214yescomplemented
149#3102C2214yescomplemented
150#3101C2212yes—
151#3101C2212yes—
152#3098C2214yescomplemented
153#3097C2218yescomplemented
154#3095C2214yes—
155C2×#485C2212yes—
156#3083C2214yescomplemented
157#3079C2214yescomplemented
158C2×#476C2211yescharacteristic
159#3063C2218yescomplemented
160#3063C2214yescomplemented
161C2×#467C2214yes—
162C2×#465C2212yes—
163#3044C2214yescomplemented
164#3039C2214yescomplemented
165C2×#461C2211yescharacteristic
166#3013C2218yescomplemented
167#3011C2214yescomplemented
168#3007C2214yes—
169C2×#449C2212yes—
170#2993C2214yescomplemented
171#2989C2212yes—
172#2981C2214yescomplemented
173#2976C2214yes—
174#2975C2211yescharacteristic
175#2966C2214yescomplemented
176C8×#41C2212yes—
177#2947C2214yescomplemented
178C4×#135C2214yescomplemented
179C2×C4×D8C2211yescharacteristic
180#2931C2214yescomplemented
181#2929C2214yes—
182C2×C8×D4C2211yescharacteristic
183#2898C2214yescomplemented
184C2×#416C2212yes—
185C2×2−1+4C2314yes—
186C22×#41C2312yes—
187C2×#137C2314yes—
188C2×#137C2314yes—
189C2×#137C2318yes—
190C2×#135C2314yes—
191C22×Q16C2314yes—
192C22×SD16C2312yes—
193C22×D8C2311yescharacteristic
194C2×#131C2314yes—
195C23×C8C2312yes—
196#563—28no—
197#563—28no—
198#563—28no—
199#562—28no—
200#562—28no—
201#562—28no—
202Q82—22no—
203Q82C2314yes—
204#557—22no—
205#557C2314yes—
206#556—28no—
207#556—24no—
208#556C2312yes—
209#556C2312yes—
210#556C2318yes—
211#555—24no—
212#555—24no—
213#555—24no—
214#555—24no—
215#555C2312yes—
216#555C2314yes—
217#555C2314yes—
218#555C2312yes—
219#554—24no—
220#554—24no—
221#554—24no—
222#554—24no—
223#554—22no—
224#554C2312yes—
225#554C2312yes—
226#554C2314yes—
227#554C2314yes—
228#554C2314yes—
229#554C2318yes—
230#553—24no—
231#553—24no—
232#553—24no—
233#553—24no—
234#553—24no—
235#553—24no—
236#553—22no—
237#553—22no—
238#552—28no—
239#552—28no—
240#552—24no—
241#552—24no—
242#552—22no—
243#552—22no—
244#552C2314yes—
245#552C2314yes—
246#552C2318yes—
247#552C2318yes—
248#551—28no—
249#551—28no—
250#551—24no—
251#551—24no—
252D4×Q8—22no—
253D4×Q8—24no—
254D4×Q8C2318yes—
255D4×Q8C2314yes—
256D4×Q8C2314yes—
257D4×Q8C2318yes—
258D4×Q8C2314yes—
259#548—28no—
260#548C2318yes—
261#548C2318yes—
262#547—28no—
263#547—24no—
264#547—24no—
265#547—24no—
266#547—28no—
267#547—24no—
268#547C2318yes—
269#547C2312yes—
270#547C2314yes—
271#547C2314yes—
272#547C2312yes—
273#547C2318yes—
274#546—28no—
275#546—28no—
276#546C2314yes—
277#546C2314yes—
278#544—24no—
279#544—24no—
280#544—24no—
281#544—24no—
282#544—24no—
283#544—24no—
284#544—22no—
285#544—22no—
286#544—24no—
287#544—24no—
288#544—21no—
289#544—21no—
290#544D411yescharacteristic
291#544C2314yes—
292#543—24no—
293#543—22no—
294#543—22no—
295#542—24no—
296#542—24no—
297#542—28no—
298#542—28no—
299#542—28no—
300#542—28no—
301#542—24no—
302#542D414yes—
303#542C2318yes—
304#541—24no—
305#541C2318yes—
306#540—24no—
307#540—24no—
308#540D414yes—
309#539—28no—
310#539—28no—
311#539—24no—
312#539—24no—
313#539—24no—
314#538—24no—
315#538D414yes—
316#537—24no—
317#537—24no—
318#537D411yescharacteristic
319#537C2314yes—
320#537C2318yes—
321#536—28no—
322#536—28no—
323#536—24no—
324#536C2314yes—
325#536C2318yes—
326#536C2314yes—
327#535D412yes—
328#533—24no—
329#533—24no—
330#533—24no—
331#533C2312yes—
332#533C2312yes—
333#533C2314yes—
334#533C2314yes—
335#532—24no—
336#532—24no—
337#532C2314yes—
338C2×C4⋊Q8—24no—
339C2×C4⋊Q8C2311yescharacteristic
340C2×C4⋊Q8C2314yes—
341C2×C4⋊Q8C2314yes—
342C2×C4⋊Q8C2311yescharacteristic
343#529—24no—
344#529—24no—
345#529—24no—
346#529—24no—
347#529—24no—
348#529C2314yes—
349#529C2314yes—
350#529C2314yes—
351C2×#125—24no—
352C2×#124—22no—
353#525—22no—
354#525—22no—
355#525—24no—
356#525C2314yes—
357C2×#123—22no—
358C2×C22⋊Q8—24no—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2314yes—
361C2×C22⋊Q8C2314yes—
362C2×#121—21no—
363C2×#121—21no—
364C2×#121C2312yes—
365#520—22no—
366#520—22no—
367#520C2314yes—
368#520C2314yes—
369#519C2314yes—
370#518—21no—
371#518—21no—
372C4×#41C2314yes—
373C4×#41C2314yes—
374C4×#41C2312yes—
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×#117—22no—
379C2×#117—22no—
380C2×#117—21no—
381C2×#117C2312yes—
382C22×C4⋊C4—21no—
383#501C2318yes—
384#500C2312yes—
385#500C2314yes—
386#499C2314yes—
387#497C2318yes—
388#495C2314yes—
389#494C2312yes—
390#494C2314yes—
391#491C2318yes—
392#489C2318yes—
393#488C2314yes—
394#488C2314yes—
395#487C2318yes—
396#487C2314yes—
397#487C2314yes—
398#487C2312yes—
399#487C2312yes—
400#487C2314yes—
401#487C2314yes—
402#487C2318yes—
403#485C2314yes—
404#485C2318yes—
405#485C2318yes—
406#485C2318yes—
407#485C2318yes—
408#485C2314yes—
409#485C2318yes—
410#485C2318yes—
411#484C2318yes—
412#484C2318yes—
413#484C2318yes—
414#484C2318yes—
415#484C2318yes—
416#483C2318yes—
417#483C2318yes—
418#483C2314yes—
419#483C2314yes—
420#482C2314yes—
421#482C2314yes—
422#480C2318yes—
423#480C2318yes—
424#479C2314yes—
425#479C2314yes—
426#479C2318yes—
427#479C2318yes—
428#478C2314yes—
429#478C2314yes—
430#477C2314yes—
431#477C2314yes—
432#477C2314yes—
433#477C2314yes—
434#477C2318yes—
435#477C2318yes—
436#476C2312yes—
437#476C2312yes—
438#476C2314yes—
439#476C2312yes—
440#476C2312yes—
441#476C2314yes—
442#475C2318yes—
443#474C2318yes—
444#470C2318yes—
445#470C2318yes—
446#470C2318yes—
447#470C2318yes—
448#468C2318yes—
449#468C2318yes—
450#468C2318yes—
451#468C2318yes—
452#467C2314yes—
453#467C2314yes—
454#467C2318yes—
455#467C2318yes—
456#467C2318yes—
457#467C2314yes—
458#467C2318yes—
459#467C2318yes—
460#466C2314yes—
461#465C2318yes—
462#465C2314yes—
463#465C2314yes—
464#465C2318yes—
465#464C2314yes—
466#464C2314yes—
467#464C2318yes—
468#464C2318yes—
469#463C2314yes—
470#463C2314yes—
471#462C2318yes—
472#462C2314yes—
473#462C2314yes—
474#462C2314yes—
475#462C2318yes—
476#462C2318yes—
477#462C2314yes—
478#461C2312yes—
479#461C2312yes—
480#461C2314yes—
481#461C2318yes—
482#461C2312yes—
483#461C2312yes—
484#461C2314yes—
485#452C2318yes—
486#452C2318yes—
487#452C2318yes—
488#452C2314yes—
489#452C2314yes—
490#452C2318yes—
491#451C2318yes—
492#451C2318yes—
493#451C2318yes—
494#451C2318yes—
495#451C2318yes—
496#451C2318yes—
497#451C2318yes—
498#450C2314yes—
499#450C2314yes—
500#449C2314yes—
501#449C2318yes—
502#449C2314yes—
503#449C2318yes—
504#448C2318yes—
505#448C2318yes—
506#446C2314yes—
507C8×Q8C2312yes—
508C8×Q8C2312yes—
509#441C2318yes—
510#441C2318yes—
511#440C2318yes—
512#440C2318yes—
513C4×Q16C2314yes—
514C4×Q16C2314yes—
515C4×Q16C2318yes—
516C4×Q16C2314yes—
517C4×Q16C2318yes—
518C4×SD16C2314yes—
519C4×SD16C2314yes—
520C4×SD16C2314yes—
521C4×SD16C2314yes—
522C4×SD16C2314yes—
523C4×SD16C2314yes—
524C4×D8C2314yes—
525C4×D8C2312yes—
526C4×D8C2312yes—
527C4×D8C2312yes—
528C4×D8C2312yes—
529#436C2318yes—
530#436C2314yes—
531#436C2314yes—
532#436C2314yes—
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—
550#427C2314yes—
551C2×#107C2311yescharacteristic
552C2×#107C2314yes—
553C2×#106C2312yes—
554#424C2314yes—
555#423C2314yes—
556C2×C4⋊C8C2311yescharacteristic
557#419C2314yes—
558#419C2318yes—
559#419C2314yes—
560#417C2314yes—
561#417C2318yes—
562#417C2314yes—
563#416C2314yes—
564#416C2314yes—
565#416C2314yes—
566#416C2314yes—
567#416C2314yes—
568#416C2314yes—
569C2×#103C2312yes—
570C2×#103C2312yes—
571C2×#103C2318yes—
572C2×#103C2312yes—
573C2×#103C2318yes—
574C2×#103C2314yes—
575C2×#103C2314yes—
576C2×#102C2311yescharacteristic
577C2×#102C2312yes—
578C2×#102C2311yescharacteristic
579#408C2318yes—
580#408C2314yes—
581#407C2314yes—
582C2×C22⋊C8C2312yes—
583#405C2314yes—
584C2×C4×C8C2311yescharacteristic
585C2×C4×C8C2314yes—
5862−1+4—48no—
5872−1+4—84no—
588C2×#41—24no—
589C2×#41—28no—
590C2×#41—28no—
591C2×#41—24no—
592C2×#41—44no—
593C2×#41—82no—
594C2×#41C2×D412yes—
595C2×#41C2414yes—
596C2×#41C2414yes—
597C2×#41C2414yes—
598C2×#41C2414yes—
599C2×#41C2414yes—
600C22×Q8—24no—
601C22×Q8—21no—
602C22×Q8—24no—
603C22×Q8C2414yes—
604C22×Q8C2412yes—
605C22×Q8C2414yes—
606C22×Q8C2418yes—
607C22×D4—22no—
608C22×D4—22no—
609C22×D4C2×D411yescharacteristic
610C22×D4C2411yescharacteristic
611C22×D4C2411yescharacteristic
612C23×C4—21no—
613C23×C4—21no—
614C23×C4—22no—
615C23×C4C2412yes—
616#137—48no—
617#137—88no—
618#137—84no—
619#135—48no—
620C2×Q16—84no—
621C2×Q16C2414yes—
622C2×Q16C2418yes—
623C2×Q16C2414yes—
624C2×Q16C2418yes—
625C2×Q16C2418yes—
626C2×SD16—82no—
627C2×SD16C2414yes—
628C2×SD16C2418yes—
629C2×SD16C2414yes—
630C2×SD16C2414yes—
631C2×SD16C2414yes—
632C2×D8—42no—
633C2×D8C2412yes—
634C2×D8C2412yes—
635#131—84no—
636C2×M16C2414yes—
637C2×M16C2418yes—
638C2×M16C2414yes—
639C22×C8—82no—
640C22×C8C2411yescharacteristic
641C22×C8C2414yes—
642C22×C8C2412yes—
643C22×C8C2414yes—
644C22×C8C2414yes—
645C22×C8C2411yescharacteristic
646C22×C8C2414yes—
647C4⋊Q8—28no—
648C4⋊Q8—24no—
649C4⋊Q8—24no—
650C4⋊Q8—24no—
651C4⋊Q8—28no—
652C4⋊Q8—24no—
653C4⋊Q8—24no—
654C4⋊Q8—24no—
655C4⋊Q8—28no—
656C4⋊Q8—28no—
657C4⋊Q8—24no—
658C4⋊Q8—24no—
659C4⋊Q8—24no—
660C4⋊Q8—24no—
661C4⋊Q8—22no—
662C4⋊Q8—22no—
663C4⋊Q8C2×D414yes—
664C4⋊Q8C2414yes—
665C4⋊Q8C2412yes—
666C4⋊Q8C2418yes—
667C4⋊Q8C2412yes—
668C4⋊Q8C2412yes—
669C4⋊Q8C2414yes—
670C4⋊Q8C2418yes—
671C4⋊Q8C2412yes—
672#127C2×D414yes—
673#126—24no—
674#126—24no—
675#126—28no—
676#126—24no—
677#126—28no—
678#126—28no—
679#126—24no—
680#126—28no—
681#126—28no—
682#126—28no—
683#126—28no—
684#126—24no—
685#126—24no—
686#126C2×D418yes—
687#125—28no—
688#125—28no—
689#125—24no—
690#125—24no—
691#125—24no—
692#125—24no—
693#125—24no—
694#125—28no—
695#125—24no—
696#125—24no—
697#125—28no—
698#125—28no—
699#125—28no—
700#125—24no—
701#125—24no—
702#125—22no—
703#125—22no—
704#125C2×D414yes—
705#125C2414yes—
706#125C2414yes—
707#124—24no—
708#124—28no—
709#124—28no—
710#124—28no—
711#124—28no—
712#124—24no—
713#124—24no—
714#124—28no—
715#124—28no—
716#124—28no—
717#124C2×D414yes—
718#124C2×D418yes—
719#124C2414yes—
720#124C2414yes—
721#123—24no—
722#123—24no—
723#123—28no—
724#123—28no—
725#123—28no—
726#123—28no—
727#123—28no—
728#123—24no—
729#123—24no—
730#123—24no—
731#123—24no—
732#123—28no—
733#123—28no—
734#123—28no—
735#123—28no—
736#123—24no—
737#123—24no—
738#123—28no—
739#123—28no—
740#123—28no—
741#123—28no—
742#123C2×D418yes—
743#123C2×D418yes—
744C22⋊Q8—24no—
745C22⋊Q8—22no—
746C22⋊Q8—22no—
747C22⋊Q8—22no—
748C22⋊Q8—22no—
749C22⋊Q8—28no—
750C22⋊Q8—24no—
751C22⋊Q8—24no—
752C22⋊Q8—24no—
753C22⋊Q8—24no—
754C22⋊Q8—24no—
755C22⋊Q8—24no—
756C22⋊Q8—24no—
757C22⋊Q8—22no—
758C22⋊Q8—22no—
759C22⋊Q8—24no—
760C22⋊Q8—28no—
761C22⋊Q8—24no—
762C22⋊Q8—24no—
763C22⋊Q8—24no—
764C22⋊Q8—28no—
765C22⋊Q8—28no—
766C22⋊Q8—28no—
767C22⋊Q8—28no—
768C22⋊Q8—28no—
769C22⋊Q8—28no—
770C22⋊Q8—28no—
771C22⋊Q8—28no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—28no—
777C22⋊Q8—28no—
778C22⋊Q8—28no—
779C22⋊Q8—28no—
780C22⋊Q8C2×D414yes—
781C22⋊Q8C2×D414yes—
782C22⋊Q8C2×D414yes—
783C22⋊Q8C2414yes—
784C22⋊Q8C2414yes—
785C22⋊Q8C2418yes—
786C22⋊Q8C2418yes—
787C22⋊Q8C2418yes—
788C22⋊Q8C2414yes—
789C22⋊Q8C2414yes—
790C22⋊Q8C2418yes—
791C22⋊Q8C2418yes—
792#121—24no—
793#121—24no—
794#121—24no—
795#121—24no—
796#121—22no—
797#121—22no—
798#121—24no—
799#121—22no—
800#121—22no—
801#121—28no—
802#121—28no—
803#121—28no—
804#121—28no—
805#121—28no—
806#121—28no—
807#121—28no—
808#121—24no—
809#121—24no—
810#121—24no—
811#121C2×D414yes—
812#121C2×D414yes—
813#121C2×D414yes—
814#121C2×D414yes—
815#121C2×D414yes—
816#121C2×D418yes—
817#121C2418yes—
818#121C2414yes—
819#121C2414yes—
820#120—24no—
821#120—24no—
822#120C2×D418yes—
823C4×Q8—24no—
824C4×Q8—24no—
825C4×Q8—24no—
826C4×Q8—24no—
827C4×Q8—24no—
828C4×Q8—28no—
829C4×Q8—22no—
830C4×Q8—22no—
831C4×Q8—24no—
832C4×Q8—24no—
833C4×Q8C2×D412yes—
834C4×Q8C2414yes—
835C4×Q8C2414yes—
836C4×Q8C2414yes—
837C4×Q8C2414yes—
838C4×Q8C2418yes—
839C4×Q8C2418yes—
840C4×Q8C2412yes—
841C4×D4—24no—
842C4×D4—24no—
843C4×D4—24no—
844C4×D4—24no—
845C4×D4—28no—
846C4×D4—28no—
847C4×D4—24no—
848C4×D4—24no—
849C4×D4—24no—
850C4×D4—28no—
851C4×D4—28no—
852C4×D4—24no—
853C4×D4—24no—
854C4×D4—24no—
855C4×D4—24no—
856C4×D4—24no—
857C4×D4—24no—
858C4×D4—28no—
859C4×D4—28no—
860C4×D4—28no—
861C4×D4—22no—
862C4×D4—22no—
863C4×D4C2×D414yes—
864C4×D4C2×D414yes—
865C4×D4C2×D412yes—
866C4×D4C2412yes—
867C4×D4C2412yes—
868C4×D4C2412yes—
869C4×D4C2412yes—
870C4×D4C2414yes—
871C4×D4C2414yes—
872C4×D4C2414yes—
873C4×D4C2414yes—
874C4×D4C2412yes—
875C4×D4C2418yes—
876#117—22no—
877#117—22no—
878#117—24no—
879#117—24no—
880#117—24no—
881#117—22no—
882#117—22no—
883#117—24no—
884#117—24no—
885#117—22no—
886#117—22no—
887#117—24no—
888#117—24no—
889#117—24no—
890#117—28no—
891#117—28no—
892#117—28no—
893#117—24no—
894#117—24no—
895#117—24no—
896#117—24no—
897#117C2×D412yes—
898#117C2×D414yes—
899#117C2414yes—
900#117C2414yes—
901#117C2414yes—
902#117C2414yes—
903#117C2414yes—
904C2×C4⋊C4—21no—
905C2×C4⋊C4—22no—
906C2×C4⋊C4—21no—
907C2×C4⋊C4—24no—
908C2×C4⋊C4—24no—
909C2×C4⋊C4—24no—
910C2×C4⋊C4—24no—
911C2×C4⋊C4—21no—
912C2×C4⋊C4—24no—
913C2×C4⋊C4—24no—
914C2×C4⋊C4—24no—
915C2×C4⋊C4—22no—
916C2×C4⋊C4—22no—
917C2×C4⋊C4—22no—
918C2×C4⋊C4—22no—
919C2×C4⋊C4—24no—
920C2×C4⋊C4—28no—
921C2×C4⋊C4C2×D411yescharacteristic
922C2×C4⋊C4C2411yescharacteristic
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2411yescharacteristic
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2418yes—
928C2×C22⋊C4—22no—
929C2×C22⋊C4—24no—
930C2×C22⋊C4—24no—
931C2×C22⋊C4—22no—
932C2×C22⋊C4—22no—
933C2×C22⋊C4—21no—
934C2×C22⋊C4—21no—
935C2×C22⋊C4—24no—
936C2×C22⋊C4—24no—
937C2×C22⋊C4C2×D412yes—
938C2×C42—22no—
939C2×C42—24no—
940C2×C42—24no—
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943#107C2414yes—
944#107C2412yes—
945#107C2418yes—
946#107C2412yes—
947#107C2414yes—
948#107C2418yes—
949#107C2418yes—
950#106C2418yes—
951#106C2414yes—
952#106C2414yes—
953#106C2414yes—
954#106C2414yes—
955C4⋊C8C2414yes—
956C4⋊C8C2412yes—
957C4⋊C8C2418yes—
958C4⋊C8C2414yes—
959C4⋊C8C2412yes—
960C4⋊C8C2414yes—
961#103C2414yes—
962#103C2414yes—
963#103C2414yes—
964#103C2418yes—
965#103C2414yes—
966#103C2414yes—
967#103C2414yes—
968#103C2414yes—
969#103C2418yes—
970#103C2418yes—
971#103C2418yes—
972#103C2418yes—
973#103C2418yes—
974#103C2418yes—
975#103C2414yes—
976#103C2414yes—
977#103C2414yes—
978#103C2414yes—
979#103C2414yes—
980#102C2411yescharacteristic
981#102C2411yescharacteristic
982#102C2411yescharacteristic
983#102C2411yescharacteristic
984#102C2414yes—
985#102C2412yes—
986#102C2414yes—
987#102C2412yes—
988#102C2414yes—
989#102C2414yes—
990#102C2414yes—
991#102C2414yes—
992C22⋊C8C2418yes—
993C22⋊C8C2414yes—
994C22⋊C8C2418yes—
995C22⋊C8C2414yes—
996C22⋊C8C2414yes—
997C22⋊C8C2418yes—
998#97C2418yes—
999C4×C8C2412yes—
1000C4×C8C2414yes—
1001C4×C8C2412yes—
1002C4×C8C2414yes—
1003C4×C8C2414yes—
1004C24—21no—
1005C24—21no—
1006C24C22×D412yes—
1007#41—28no—
1008#41—28no—
1009#41—28no—
1010#41—44no—
1011#41—44no—
1012#41—44no—
1013#41—44no—
1014#41—44no—
1015#41—44no—
1016#41—44no—
1017#41—44no—
1018#41—88no—
1019#41—88no—
1020#41—816no—
1021#41—168no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—22no—
1025C2×Q8—28no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—22no—
1029C2×Q8—28no—
1030C2×Q8—42no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—48no—
1035C2×Q8—42no—
1036C2×Q8—48no—
1037C2×Q8—44no—
1038C2×Q8—88no—
1039C2×Q8—161no—
1040C2×Q8—164no—
1041C2×Q8C22×D412yes—
1042C2×Q8C22×D414yes—
1043C2×Q8C2514yes—
1044C2×Q8C2514yes—
1045C2×Q8C2514yes—
1046C2×D4—22no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—28no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—21no—
1056C2×D4—21no—
1057C2×D4—41no—
1058C2×D4—41no—
1059C2×D4—41no—
1060C2×D4—84no—
1061C2×D4—162no—
1062C2×D4C22×D414yes—
1063C2×D4C22×D414yes—
1064C2×D4C22×D412yes—
1065C2×D4C22×D418yes—
1066C2×D4C22×D418yes—
1067C2×D4C22×D414yes—
1068C2×D4C2511yescharacteristic
1069C2×D4C2512yes—
1070C2×D4C2511yescharacteristic
1071C22×C4—21no—
1072C22×C4—21no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—28no—
1080C22×C4—28no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—22no—
1086C22×C4—22no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—84no—
1096C22×C4C22×D414yes—
1097C22×C4C22×D412yes—
1098C22×C4C22×D411yescharacteristic
1099C22×C4C22×D414yes—
1100C22×C4C22×D414yes—
1101C22×C4C22×D411yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105Q16—44no—
1106Q16—48no—
1107Q16—44no—
1108Q16—48no—
1109Q16—48no—
1110SD16—28no—
1111SD16—48no—
1112SD16—44no—
1113SD16—44no—
1114SD16—44no—
1115D8—24no—
1116D8—42no—
1117M16—48no—
1118M16—44no—
1119M16—44no—
1120C2×C8—41no—
1121C2×C8—44no—
1122C2×C8—42no—
1123C2×C8—44no—
1124C2×C8—44no—
1125C2×C8—41no—
1126C2×C8—44no—
1127C2×C8C2511yescharacteristic
1128C2×C8C2512yes—
1129C2×C8C2514yes—
1130C2×C8C2511yescharacteristic
1131C2×C8C2514yes—
1132C2×C8C2514yes—
1133C4⋊C4—24no—
1134C4⋊C4—22no—
1135C4⋊C4—22no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—22no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—22no—
1146C4⋊C4—22no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—28no—
1152C4⋊C4—28no—
1153C4⋊C4—28no—
1154C4⋊C4—28no—
1155C4⋊C4—28no—
1156C4⋊C4—21no—
1157C4⋊C4—22no—
1158C4⋊C4—21no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—28no—
1168C4⋊C4—28no—
1169C4⋊C4—22no—
1170C4⋊C4C22×D414yes—
1171C4⋊C4C22×D412yes—
1172C4⋊C4C22×D412yes—
1173C4⋊C4C22×D414yes—
1174C4⋊C4C22×D418yes—
1175C4⋊C4C22×D414yes—
1176C4⋊C4C22×D414yes—
1177C4⋊C4C22×D414yes—
1178C4⋊C4C2511yescharacteristic
1179C4⋊C4C2511yescharacteristic
1180C4⋊C4C2514yes—
1181C4⋊C4C2514yes—
1182C4⋊C4C2512yes—
1183C4⋊C4C2514yes—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—24no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—22no—
1198C22⋊C4—22no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—24no—
1203C22⋊C4—28no—
1204C22⋊C4—22no—
1205C22⋊C4—22no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4C22×D414yes—
1211C22⋊C4C22×D418yes—
1212C22⋊C4C22×D418yes—
1213C22⋊C4C22×D418yes—
1214C22⋊C4C22×D418yes—
1215C22⋊C4C22×D414yes—
1216C22⋊C4C22×D414yes—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—28no—
1226C42—28no—
1227C42C22×D414yes—
1228C42C22×D414yes—
1229C42C22×D412yes—
1230C42C2512yes—
1231C42C2514yes—
1232C23—21no—
1233C23—24no—
1234C23—21no—
1235C23—22no—
1236C23—42no—
1237C23—42no—
1238C23—42no—
1239C23—42no—
1240C23—42no—
1241C23—81no—
1242C23—81no—
1243C23—81no—
1244C23C23×D414yes—
1245C23C23×D414yes—
1246C23C23×D411yescharacteristic
1247Q8—24no—
1248Q8—24no—
1249Q8—24no—
1250Q8—24no—
1251Q8—24no—
1252Q8—24no—
1253Q8—24no—
1254Q8—44no—
1255Q8—82no—
1256Q8—84no—
1257Q8—84no—
1258Q8—88no—
1259Q8—82no—
1260Q8—82no—
1261Q8—84no—
1262Q8—88no—
1263D4—28no—
1264D4—22no—
1265D4—21no—
1266D4—21no—
1267D4—22no—
1268D4—21no—
1269D4—28no—
1270D4—24no—
1271D4—44no—
1272D4—48no—
1273D4—48no—
1274D4—42no—
1275D4—48no—
1276D4—48no—
1277D4—81no—
1278D4—84no—
1279D4—84no—
1280D4—88no—
1281D4—84no—
1282D4—84no—
1283D4#58512yes—
1284C2×C4—21no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—21no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—28no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—42no—
1301C2×C4—44no—
1302C2×C4—41no—
1303C2×C4—44no—
1304C2×C4—48no—
1305C2×C4—48no—
1306C2×C4—42no—
1307C2×C4—42no—
1308C2×C4—44no—
1309C2×C4—44no—
1310C2×C4—44no—
1311C2×C4—44no—
1312C2×C4—84no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—84no—
1317C2×C4—82no—
1318C2×C4—82no—
1319C2×C4—84no—
1320C2×C4—88no—
1321C2×C4—84no—
1322C2×C4—88no—
1323C2×C4—84no—
1324C2×C4#57814yes—
1325C2×C4C23×D414yes—
1326C2×C4C23×D414yes—
1327C2×C4C23×D414yes—
1328C2×C4C23×D414yes—
1329C2×C4C23×D412yes—
1330C2×C4C23×D411yescharacteristic
1331C2×C4C23×D412yes—
1332C2×C4C2611yescharacteristic
1333C8—22no—
1334C8—24no—
1335C8—21no—
1336C8—21no—
1337C8—24no—
1338C8—24no—
1339C22—21no—
1340C22—21no—
1341C22—24no—
1342C22—24no—
1343C22—22no—
1344C22—24no—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—42no—
1352C22—41no—
1353C22—42no—
1354C22—42no—
1355C22—41no—
1356C22—84no—
1357C22—84no—
1358C22—162no—
1359C22C2×#57812yes—
1360C22C24×D411yescharacteristic
1361C4—24no—
1362C4—21no—
1363C4—24no—
1364C4—24no—
1365C4—22no—
1366C4—24no—
1367C4—44no—
1368C4—44no—
1369C4—44no—
1370C4—41no—
1371C4—41no—
1372C4—42no—
1373C4—44no—
1374C4—44no—
1375C4—44no—
1376C4C2×#57814yes—
1377C4C2×#58511yescharacteristic
1378C4H(7,𝔽2)11yescharacteristic
1379C2—22no—
1380C2—44no—
1381C2—44no—
1382C2—42no—
1383C2—81no—
1384C2—82no—
1385C2#6298711yescharacteristic
1386C2C22×#57811yescharacteristic
1387C2#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. #62929C2semidirect
2. #62915C2semidirect
3. #62551C2semidirect
4. #62530C2semidirect
5. #62341C2semidirect
6. #62281C2semidirect
7. #62246C2semidirect
8. #62181C2semidirect
9. #62108C2semidirect
10. #62036C2semidirect
11. #61960C2semidirect
12. #61816C2semidirect
13. #61757C2semidirect
14. #61721C2semidirect
15. #61693C2semidirect
16. #61619C2semidirect
17. #61586C2semidirect
18. #61492C2semidirect
19. #61427C2semidirect
20. #61217C2semidirect
21. #61173C2semidirect
22. C2×#3303C2semidirect
23. #60306C2semidirect
27. #3552C22semidirect
29. #3547C22semidirect
30. #3547C22semidirect
32. #3544C22semidirect
36. #3518C22semidirect
37. #3515C22semidirect
38. #3511C22semidirect
43. #3499C22semidirect
57. #3398C22semidirect
58. #3393C22semidirect
59. #3385C22semidirect
60. #3380C22semidirect
61. #3372C22semidirect
62. #3369C22semidirect
63. #3363C22semidirect
64. #3363C22semidirect
65. #3360C22semidirect
66. #3360C22semidirect
67. #3357C22semidirect
68. #3357C22semidirect
69. #3357C22semidirect
70. #3352C22semidirect
71. #3349C22semidirect
73. #3343C22semidirect
74. #3341C22semidirect
75. #3338C22semidirect
77. #3331C22semidirect
78. #3331C22semidirect
79. #3331C22semidirect
80. #3330C22semidirect
81. #3329C22semidirect
82. #3329C22semidirect
83. #3329C22semidirect
84. #3328C22semidirect
85. #3315C22semidirect
87. #3313C22semidirect
89. #3312C22semidirect
90. #3308C22semidirect
95. #3303C22semidirect
96. #3303C22semidirect
97. #3302C22semidirect
98. #3300C22semidirect
99. #3300C22semidirect
102. #3299C22semidirect
103. #3299C22semidirect
104. #3299C22semidirect
105. #3299C22semidirect
106. #3298C22semidirect
109. D4×Q16C22semidirect
110. #3283C22semidirect
112. #3277C22semidirect
113. #3276C22semidirect
114. #3276C22semidirect
115. #3276C22semidirect
116. #3270C22semidirect
117. #3269C22semidirect
119. #3258C22semidirect
120. #3252C22semidirect
121. #3252C22semidirect
123. #3242C22semidirect
124. #3238C22semidirect
126. #3230C22semidirect
127. #3225C22semidirect
128. #3218C22semidirect
130. #3209C22semidirect
131. #3203C22semidirect
132. #3202C22semidirect
133. #3201C22semidirect
137. #3178C22semidirect
139. #3170C22semidirect
140. #3168C22semidirect
141. #3137C22semidirect
143. C2×#487C22semidirect
144. #3127C22semidirect
145. #3124C22semidirect
146. #3116C22semidirect
147. #3116C22semidirect
148. #3102C22semidirect
149. #3102C22semidirect
152. #3098C22semidirect
153. #3097C22semidirect
156. #3083C22semidirect
157. #3079C22semidirect
159. #3063C22semidirect
160. #3063C22semidirect
163. #3044C22semidirect
164. #3039C22semidirect
166. #3013C22semidirect
167. #3011C22semidirect
170. #2993C22semidirect
172. #2981C22semidirect
175. #2966C22semidirect
177. #2947C22semidirect
178. C4×#135C22semidirect
180. #2931C22semidirect
183. #2898C22semidirect

Maximal subgroups

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

subgroupindex
#629292
#629152
#625512
#625302
#623412
#622812
#622462
#621812
#621082
#620362
#619602
#618162
#617572
#617212
#616932
#616192
#615862
#614922
#614272
#612172
#611732
C2×#33032
#603062