Finite Group Databasebeta

← #10585209

Subgroups — #10585209

Order 512.

6068 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62962C211yesmaximal, characteristic, complemented
2#62944C211yesmaximal, characteristic, complemented
3#62562C214yesmaximal, complemented
4#62557C214yesmaximal, complemented
5#62527C212yesmaximal, complemented
6#62381C214yesmaximal, complemented
7#62357C211yesmaximal, characteristic, complemented
8#62194C214yesmaximal, complemented
9#62166C214yesmaximal, complemented
10#62114C212yesmaximal, complemented
11#62039C214yesmaximal, complemented
12#62016C214yesmaximal, complemented
13#61961C212yesmaximal, complemented
14#61914C214yesmaximal, complemented
15#61891C211yesmaximal, characteristic, complemented
16#61850C214yesmaximal, complemented
17#61826C211yesmaximal, characteristic, complemented
18#61498C214yesmaximal, complemented
19#61496C214yesmaximal, complemented
20SD16×#41C212yesmaximal, complemented
21#61326C214yesmaximal, complemented
22C2×#3361C211yesmaximal, characteristic, complemented
23#60330C211yesmaximal, characteristic, complemented
24#3561C2214yescomplemented
25#3559C2214yes—
26#3557—24no—
27#3554—24no—
28#3554C2214yescomplemented
29#3550C2214yescomplemented
30#3548C2214yescomplemented
31#3547C2214yescomplemented
32#3541—24no—
33#3536—24no—
34#3536—24no—
35#3535—24no—
36#3522C2214yescomplemented
37#3520C2214yescomplemented
38#3519C2214yes—
39#3519C2214yescomplemented
40#3511C2212yes—
41#3510—22no—
42#3508C2212yescomplemented
43#3507C2214yescomplemented
44#3502C2211yescharacteristic, complemented
45#3501—21no—
46#3501C2214yescomplemented
47#3497C2211yescharacteristic
48#3492—21no—
49#3489—22no—
50C2×#559C2211yescharacteristic, complemented
51Q8×#41C2212yescomplemented
52C2×#554C2211yescharacteristic
53D4×#41C2212yes—
54#3461C2211yescharacteristic
55#3460—21no—
56C2×#537—21no—
57#3399C2214yescomplemented
58#3399C2214yescomplemented
59#3399C2214yescomplemented
60#3397C2214yescomplemented
61#3397C2218yescomplemented
62#3392C2214yescomplemented
63#3392C2212yescomplemented
64#3385C2214yescomplemented
65#3385C2214yescomplemented
66#3385C2214yescomplemented
67#3384C2214yescomplemented
68#3384C2218yescomplemented
69Q8×SD16C2214yescomplemented
70Q8×SD16C2212yescomplemented
71#3376C2218yescomplemented
72#3376C2218yescomplemented
73#3376C2218yescomplemented
74#3373C2214yes—
75#3373C2214yescomplemented
76#3373C2214yescomplemented
77#3372C2214yescomplemented
78#3372C2214yescomplemented
79#3372C2214yescomplemented
80#3362C2214yescomplemented
81#3362C2212yescomplemented
82#3361C2214yes—
83#3361C2214yes—
84#3361C2214yescomplemented
85#3361C2214yescomplemented
86#3361C2214yescomplemented
87#3361C2214yescomplemented
88#3360C2214yescomplemented
89#3360C2218yescomplemented
90#3359C2214yescomplemented
91#3359C2212yescomplemented
92#3358C2214yescomplemented
93#3357C2214yescomplemented
94#3354C2214yescomplemented
95#3346C2218yescomplemented
96#3345C2218yescomplemented
97#3335C2214yescomplemented
98#3335C2212yescomplemented
99#3332C2214yescomplemented
100#3329C2214yescomplemented
101#3326C2218yescomplemented
102#3321C2218yescomplemented
103#3320C2218yescomplemented
104#3307C2218yescomplemented
105#3306C2218yescomplemented
106#3305C2214yescomplemented
107#3305C2214yescomplemented
108#3303C2214yescomplemented
109#3301C2218yescomplemented
110#3298C2214yescomplemented
111#3298C2212yescomplemented
112#3297C2218yescomplemented
113#3297C2218yescomplemented
114#3295C2214yes—
115#3295C2212yescomplemented
116#3294C2214yescomplemented
117D4×SD16C2214yes—
118D4×SD16C2212yescomplemented
119#3274C2214yes—
120#3272C2214yescomplemented
121#3265C2218yescomplemented
122#3264C2218yes—
123#3257C2218yescomplemented
124#3257C2218yescomplemented
125#3254C2214yescomplemented
126#3253C2214yescomplemented
127#3246C2212yescomplemented
128#3246C2214yescomplemented
129#3244C2218yescomplemented
130#3244C2218yescomplemented
131#3237C2214yescomplemented
132#3236C2214yescomplemented
133#3230C2212yescomplemented
134#3228C2214yescomplemented
135#3221C2218yescomplemented
136#3221C2218yescomplemented
137#3214C2214yescomplemented
138#3213C2214yescomplemented
139#3207C2214yescomplemented
140#3205C2212yescomplemented
141#3179C2218yescomplemented
142#3179C2218yescomplemented
143#3169C2214yescomplemented
144#3167C2214yescomplemented
145#3167C2212yescomplemented
146#3167C2214yescomplemented
147#3137C2218yescomplemented
148#3131C2214yescomplemented
149C2×#488C2212yescomplemented
150C2×#486C2211yescharacteristic, complemented
151#3119C2218yescomplemented
152#3119C2218yescomplemented
153#3118C2218yescomplemented
154#3118C2218yescomplemented
155#3112C2214yescomplemented
156#3110C2214yes—
157#3109C2214yes—
158#3109C2214yescomplemented
159#3103C2212yescomplemented
160#3103C2214yescomplemented
161#3101C2212yes—
162#3101C2214yescomplemented
163#3084C2218yescomplemented
164#3078C2214yescomplemented
165C2×#477C2211yescharacteristic, complemented
166C2×#478C2212yescomplemented
167#3042C2218yescomplemented
168#3036C2214yes—
169C2×#463C2212yes—
170C2×#459C2211yescharacteristic
171#2993C2214yescomplemented
172#2992C2214yescomplemented
173#2989C2212yescomplemented
174#2985C2214yescomplemented
175#2983C2211yescharacteristic, complemented
176#2966C2214yescomplemented
177#2966C2214yescomplemented
178C8×#41C2212yescomplemented
179#2960C2214yescomplemented
180C2×C8×Q8C2211yescharacteristic, complemented
181#2946C2218yescomplemented
182C2×C4×SD16C2211yescharacteristic
183C2×C4×SD16C2214yescomplemented
184C2×C4×D8C2212yes—
185C2×2−1+4—21no—
186C22×#41—22no—
187C2×AGL(1,ℤ/8)C2318yes—
188C22×SD16C2311yescharacteristic
189C22×SD16C2314yes—
190C22×D8C2312yes—
191#563—28no—
192#563—24no—
193#563—24no—
194#562—28no—
195#562—24no—
196#562—24no—
197#562—28no—
198#562—28no—
199#559—24no—
200#559—24no—
201#559—24no—
202#559—22no—
203#559C2314yes—
204#559C2314yes—
205#559C2314yes—
206Q82C2312yes—
207Q82C2314yes—
208#557—22no—
209#557—24no—
210#557C2312yes—
211#557C2314yes—
212#556—24no—
213#556—24no—
214#556—22no—
215#556C2314yes—
216#556C2318yes—
217#555C2314yes—
218#555C2314yes—
219#554—24no—
220#554—24no—
221#554—24no—
222#554—24no—
223#554—28no—
224#554—24no—
225#554—24no—
226#554—22no—
227#554C2314yes—
228#554C2318yes—
229#554C2314yes—
230#554C2314yes—
231#554C2314yes—
232#554C2314yes—
233#554C2312yes—
234#553—24no—
235#553—24no—
236#553C2318yes—
237#553C2318yes—
238#552—24no—
239#552—28no—
240#552—24no—
241#551—28no—
242#551—28no—
243#550—22no—
244#550C2314yes—
245#550C2314yes—
246#550C2312yes—
247#550C2314yes—
248D4×Q8—24no—
249D4×Q8—24no—
250D4×Q8C2312yes—
251D4×Q8C2314yes—
252D4×Q8C2314yes—
253D4×Q8C2312yes—
254D4×Q8C2314yes—
255#548—24no—
256#548—24no—
257#548—22no—
258#548—24no—
259#548—24no—
260#548C2318yes—
261#547—24no—
262#547—24no—
263#547—28no—
264#547—28no—
265#547—22no—
266#547C2314yes—
267#547C2312yes—
268#547C2314yes—
269#547C2314yes—
270#546—24no—
271#546—24no—
272#546—28no—
273#546—28no—
274#546—24no—
275#546—22no—
276#546—24no—
277#546C2318yes—
278D42C2314yes—
279D42C2312yes—
280D42C2314yes—
281#544—21no—
282#544—22no—
283#544D411yescharacteristic
284#544C2318yes—
285#543—24no—
286#543—28no—
287#542—28no—
288#542—28no—
289#542—28no—
290#542—24no—
291#542—24no—
292#542—24no—
293#542—24no—
294#542D414yes—
295#542C2318yes—
296#542C2318yes—
297#541D414yes—
298#540—24no—
299#540—24no—
300#540C2318yes—
301#540C2318yes—
302#539—28no—
303#539—28no—
304#539—28no—
305#539—24no—
306#539—28no—
307#539D414yes—
308#538—28no—
309#538—28no—
310#538—24no—
311#537—22no—
312#537—24no—
313#537—24no—
314#537—28no—
315#537—24no—
316#537—24no—
317#537—21no—
318#537—22no—
319#537D411yescharacteristic
320#536—24no—
321#536—28no—
322#536D412yes—
323#536C2318yes—
324#535—22no—
325#533—22no—
326#533—24no—
327#533C2312yes—
328#533C2314yes—
329#533C2314yes—
330#533C2314yes—
331#533C2314yes—
332#532—24no—
333#532C2314yes—
334#532C2312yes—
335#532C2314yes—
336#532C2314yes—
337#532C2314yes—
338#532C2314yes—
339C2×C4⋊Q8C2311yescharacteristic
340C2×#127C2311yescharacteristic
341#529—24no—
342#529—24no—
343#529—24no—
344#529C2314yes—
345#529C2314yes—
346C2×#125C2312yes—
347C2×#124—21no—
348C2×#124C2312yes—
349#525—24no—
350#525—24no—
351#525—24no—
352#525—22no—
353#525—24no—
354C2×#123—22no—
355C2×C22⋊Q8—21no—
356C2×C22⋊Q8—24no—
357C2×C22⋊Q8—24no—
358C2×C22⋊Q8—24no—
359C2×C22⋊Q8—22no—
360C2×#121—24no—
361C2×#121—24no—
362#520—22no—
363#520C2318yes—
364#519—21no—
365#518—22no—
366#518C2318yes—
367C4×#41—22no—
368C4×#41C2312yes—
369C2×C4×Q8C2311yescharacteristic
370C2×C4×Q8C2314yes—
371C2×C4×Q8C2311yescharacteristic
372C2×C4×D4—21no—
373C2×C4×D4C2312yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2314yes—
376C2×C4×D4C2312yes—
377C22×C4⋊C4—21no—
378#501C2318yes—
379#501C2318yes—
380#500C2314yes—
381#498C2312yes—
382#498C2314yes—
383#498C2314yes—
384#496C2318yes—
385#496C2318yes—
386#493C2314yes—
387#492C2312yes—
388#492C2314yes—
389#492C2314yes—
390#491C2318yes—
391#491C2318yes—
392#489C2318yes—
393#489C2318yes—
394#488C2318yes—
395#488C2318yes—
396#488C2318yes—
397#488C2318yes—
398#487C2314yes—
399#487C2312yes—
400#487C2314yes—
401#487C2314yes—
402#486C2314yes—
403#486C2314yes—
404#486C2314yes—
405#486C2314yes—
406#486C2314yes—
407#486C2312yes—
408#485C2318yes—
409#485C2318yes—
410#484C2318yes—
411#483C2314yes—
412#483C2314yes—
413#483C2314yes—
414#482C2318yes—
415#482C2318yes—
416#481C2318yes—
417#481C2314yes—
418#481C2314yes—
419#481C2314yes—
420#480C2318yes—
421#479C2318yes—
422#479C2318yes—
423#479C2318yes—
424#479C2318yes—
425#478C2318yes—
426#478C2318yes—
427#478C2318yes—
428#478C2318yes—
429#477C2314yes—
430#477C2314yes—
431#477C2314yes—
432#477C2314yes—
433#476C2312yes—
434#476C2314yes—
435#476C2314yes—
436#476C2318yes—
437#476C2318yes—
438#476C2312yes—
439#476C2314yes—
440#476C2314yes—
441#476C2314yes—
442#475C2314yes—
443#475C2312yes—
444#475C2314yes—
445#475C2318yes—
446#475C2312yes—
447#475C2314yes—
448#474C2318yes—
449#474C2314yes—
450#474C2314yes—
451#469C2318yes—
452#469C2318yes—
453#468C2318yes—
454#468C2318yes—
455#466C2318yes—
456#466C2318yes—
457#465C2314yes—
458#465C2314yes—
459#465C2314yes—
460#465C2318yes—
461#465C2314yes—
462#465C2314yes—
463#465C2314yes—
464#463C2318yes—
465#463C2318yes—
466#463C2318yes—
467#463C2318yes—
468#463C2318yes—
469#463C2318yes—
470#463C2318yes—
471#463C2318yes—
472#461C2314yes—
473#461C2312yes—
474#461C2312yes—
475#461C2314yes—
476#461C2314yes—
477#461C2318yes—
478#461C2314yes—
479#461C2318yes—
480#461C2314yes—
481#460C2314yes—
482#460C2312yes—
483#460C2312yes—
484#460C2314yes—
485#460C2314yes—
486#460C2318yes—
487#459C2314yes—
488#459C2314yes—
489#459C2318yes—
490#459C2314yes—
491#459C2314yes—
492#459C2314yes—
493#459C2314yes—
494#450C2314yes—
495#450C2314yes—
496#450C2314yes—
497#449C2318yes—
498#449C2318yes—
499#449C2318yes—
500#449C2318yes—
501#448C2318yes—
502#448C2314yes—
503#448C2314yes—
504#448C2314yes—
505#447C2318yes—
506#447C2318yes—
507#446C2314yes—
508#446C2314yes—
509#446C2314yes—
510#446C2318yes—
511#446C2314yes—
512C8×Q8C2314yes—
513C8×Q8C2314yes—
514C8×Q8C2312yes—
515C8×Q8C2314yes—
516C8×Q8C2312yes—
517#442C2318yes—
518#442C2318yes—
519#442C2318yes—
520#442C2318yes—
521#440C2318yes—
522#440C2318yes—
523#440C2318yes—
524#440C2318yes—
525C4×SD16C2314yes—
526C4×SD16C2314yes—
527C4×SD16C2312yes—
528C4×SD16C2314yes—
529C4×SD16C2314yes—
530C4×SD16C2312yes—
531C4×SD16C2314yes—
532C4×SD16C2314yes—
533C4×SD16C2314yes—
534C4×SD16C2318yes—
535C4×SD16C2312yes—
536C4×SD16C2314yes—
537C4×SD16C2314yes—
538C4×SD16C2312yes—
539C4×SD16C2314yes—
540C4×SD16C2318yes—
541C4×D8C2314yes—
542C4×D8C2318yes—
543C4×D8C2314yes—
544C4×D8C2314yes—
545C4×D8C2314yes—
546C4×D8C2318yes—
547#436C2314yes—
548#436C2314yes—
549#435C2318yes—
550#435C2318yes—
551C8×D4C2314yes—
552C8×D4C2312yes—
553C8×D4C2314yes—
554C8×D4C2312yes—
555C8×D4C2314yes—
556#433C2318yes—
557#433C2318yes—
558#432C2314yes—
559#432C2314yes—
560#431C2312yes—
561#431C2314yes—
562#428C2318yes—
563C2×#107C2312yes—
564C2×#106C2311yescharacteristic
565C2×#106C2314yes—
566#424C2318yes—
567#423C2314yes—
568C2×C4⋊C8C2312yes—
569C2×C4⋊C8C2311yescharacteristic
570#419C2318yes—
571#417C2318yes—
572#416C2318yes—
573#416C2318yes—
574C2×#103C2312yes—
575C2×#103C2311yescharacteristic
576C2×#103C2314yes—
577C2×#102C2312yes—
578C2×#102C2312yes—
579C2×#102C2312yes—
580C2×#102C2311yescharacteristic
581C2×#102C2314yes—
582#405C2318yes—
583C2×C4×C8C2311yescharacteristic
584C2×C4×C8C2312yes—
585C2×C4×C8C2314yes—
5862−1+4—84no—
587C2×#41—24no—
588C2×#41—22no—
589C2×#41—24no—
590C2×#41—24no—
591C2×#41—22no—
592C2×#41—24no—
593C2×#41—22no—
594C2×#41—24no—
595C2×#41—24no—
596C2×#41—24no—
597C2×#41—24no—
598C2×#41—88no—
599C2×#41C2×D412yes—
600C2×#41C2418yes—
601C22×Q8—22no—
602C22×Q8—24no—
603C22×Q8—24no—
604C22×Q8—21no—
605C22×Q8C2×D411yescharacteristic
606C22×Q8C2411yescharacteristic
607C22×Q8C2414yes—
608C22×D4—22no—
609C22×D4—24no—
610C22×D4—24no—
611C22×D4—21no—
612C22×D4—21no—
613C22×D4C2411yescharacteristic
614C22×D4C2414yes—
615C22×D4C2412yes—
616C23×C4—21no—
617C23×C4—24no—
618C23×C4—22no—
619C23×C4—22no—
620AGL(1,ℤ/8)—416no—
621C2×SD16—42no—
622C2×SD16—48no—
623C2×SD16C2412yes—
624C2×SD16C2414yes—
625C2×SD16C2414yes—
626C2×SD16C2412yes—
627C2×SD16C2414yes—
628C2×SD16C2418yes—
629C2×SD16C2414yes—
630C2×SD16C2414yes—
631C2×SD16C2414yes—
632C2×D8—44no—
633C2×D8C2414yes—
634C2×D8C2414yes—
635C2×D8C2418yes—
636C2×D8C2418yes—
637C2×M16C2418yes—
638C22×C8C2412yes—
639C22×C8C2411yescharacteristic
640C22×C8C2414yes—
641C22×C8C2411yescharacteristic
642C22×C8C2414yes—
643C4⋊Q8—24no—
644C4⋊Q8—24no—
645C4⋊Q8—22no—
646C4⋊Q8—22no—
647C4⋊Q8—24no—
648C4⋊Q8—28no—
649C4⋊Q8—28no—
650C4⋊Q8—22no—
651C4⋊Q8C2×D414yes—
652C4⋊Q8C2×D414yes—
653C4⋊Q8C2412yes—
654C4⋊Q8C2414yes—
655C4⋊Q8C2414yes—
656C4⋊Q8C2414yes—
657C4⋊Q8C2412yes—
658C4⋊Q8C2412yes—
659C4⋊Q8C2414yes—
660C4⋊Q8C2414yes—
661C4⋊Q8C2414yes—
662C4⋊Q8C2414yes—
663#127—24no—
664#127—22no—
665#127C2414yes—
666#127C2412yes—
667#127C2414yes—
668#127C2414yes—
669#126—28no—
670#126—28no—
671#126—28no—
672#126—28no—
673#126—28no—
674#126—28no—
675#126—28no—
676#126C2×D418yes—
677#126C2×D418yes—
678#125—22no—
679#125—22no—
680#125—24no—
681#125—24no—
682#125—24no—
683#125—28no—
684#125—28no—
685#125—24no—
686#125—24no—
687#125—24no—
688#125—22no—
689#125C2×D414yes—
690#125C2×D414yes—
691#125C2×D418yes—
692#125C2418yes—
693#125C2418yes—
694#124—24no—
695#124—24no—
696#124—24no—
697#124—28no—
698#124—28no—
699#124—28no—
700#124—28no—
701#124—28no—
702#124—24no—
703#124—24no—
704#124—24no—
705#124—22no—
706#124—24no—
707#124—24no—
708#124C2×D414yes—
709#124C2×D414yes—
710#124C2418yes—
711#124C2418yes—
712#123—28no—
713#123—28no—
714#123—28no—
715#123—28no—
716#123—28no—
717#123—28no—
718#123—28no—
719#123—28no—
720#123—28no—
721#123—24no—
722#123—24no—
723#123—24no—
724#123—28no—
725#123—28no—
726#123—28no—
727#123—28no—
728#123—28no—
729#123—28no—
730#123—28no—
731#123C2×D418yes—
732#123C2×D418yes—
733C22⋊Q8—24no—
734C22⋊Q8—24no—
735C22⋊Q8—24no—
736C22⋊Q8—24no—
737C22⋊Q8—24no—
738C22⋊Q8—28no—
739C22⋊Q8—28no—
740C22⋊Q8—24no—
741C22⋊Q8—24no—
742C22⋊Q8—24no—
743C22⋊Q8—24no—
744C22⋊Q8—22no—
745C22⋊Q8—22no—
746C22⋊Q8—24no—
747C22⋊Q8—28no—
748C22⋊Q8—28no—
749C22⋊Q8—28no—
750C22⋊Q8—28no—
751C22⋊Q8—28no—
752C22⋊Q8—24no—
753C22⋊Q8—22no—
754C22⋊Q8—24no—
755C22⋊Q8—24no—
756C22⋊Q8—24no—
757C22⋊Q8—28no—
758C22⋊Q8—28no—
759C22⋊Q8—28no—
760C22⋊Q8—28no—
761C22⋊Q8—28no—
762C22⋊Q8—28no—
763C22⋊Q8—28no—
764C22⋊Q8—28no—
765C22⋊Q8—24no—
766C22⋊Q8—28no—
767C22⋊Q8—28no—
768C22⋊Q8—24no—
769C22⋊Q8—24no—
770C22⋊Q8—24no—
771C22⋊Q8—24no—
772C22⋊Q8—24no—
773C22⋊Q8C2×D414yes—
774C22⋊Q8C2×D414yes—
775C22⋊Q8C2×D414yes—
776C22⋊Q8C2×D414yes—
777C22⋊Q8C2×D418yes—
778C22⋊Q8C2414yes—
779C22⋊Q8C2414yes—
780C22⋊Q8C2414yes—
781#121—28no—
782#121—24no—
783#121—28no—
784#121—24no—
785#121—24no—
786#121—28no—
787#121—24no—
788#121—24no—
789#121—24no—
790#121—24no—
791#121—22no—
792#121—24no—
793#121—24no—
794#121—24no—
795#121—24no—
796#121—22no—
797#121—22no—
798#121—24no—
799#121—24no—
800#121—24no—
801#121—28no—
802#121—28no—
803#121—28no—
804#121—28no—
805#121—28no—
806#121—28no—
807#121—28no—
808#121—28no—
809#121C2×D414yes—
810#121C2×D414yes—
811#121C2414yes—
812#121C2414yes—
813#121C2414yes—
814#121C2418yes—
815#121C2418yes—
816#120—28no—
817#120—24no—
818#120—28no—
819#120—24no—
820#120—24no—
821C4×Q8—22no—
822C4×Q8—22no—
823C4×Q8—24no—
824C4×Q8—24no—
825C4×Q8—24no—
826C4×Q8—22no—
827C4×Q8—24no—
828C4×Q8—24no—
829C4×Q8—24no—
830C4×Q8—22no—
831C4×Q8—24no—
832C4×Q8—24no—
833C4×Q8C2×D414yes—
834C4×Q8C2×D412yes—
835C4×Q8C2412yes—
836C4×Q8C2414yes—
837C4×Q8C2412yes—
838C4×Q8C2414yes—
839C4×Q8C2414yes—
840C4×Q8C2418yes—
841C4×Q8C2414yes—
842C4×Q8C2412yes—
843C4×Q8C2414yes—
844C4×D4—24no—
845C4×D4—22no—
846C4×D4—24no—
847C4×D4—22no—
848C4×D4—24no—
849C4×D4—24no—
850C4×D4—24no—
851C4×D4—24no—
852C4×D4—28no—
853C4×D4—28no—
854C4×D4—28no—
855C4×D4—28no—
856C4×D4—28no—
857C4×D4—28no—
858C4×D4—28no—
859C4×D4—22no—
860C4×D4—24no—
861C4×D4—24no—
862C4×D4—24no—
863C4×D4—24no—
864C4×D4—24no—
865C4×D4—24no—
866C4×D4—24no—
867C4×D4—24no—
868C4×D4—22no—
869C4×D4—24no—
870C4×D4—24no—
871C4×D4C2×D414yes—
872C4×D4C2×D412yes—
873C4×D4C2412yes—
874C4×D4C2414yes—
875C4×D4C2414yes—
876C4×D4C2414yes—
877C4×D4C2412yes—
878C4×D4C2414yes—
879C4×D4C2414yes—
880C4×D4C2414yes—
881C4×D4C2414yes—
882C4×D4C2418yes—
883C4×D4C2418yes—
884C4×D4C2418yes—
885C4×D4C2414yes—
886C4×D4C2412yes—
887C4×D4C2414yes—
888#117—22no—
889#117—24no—
890#117—24no—
891#117—24no—
892#117—28no—
893#117—24no—
894#117—24no—
895#117—28no—
896#117C2×D412yes—
897#117C2×D414yes—
898#117C2418yes—
899#117C2418yes—
900C2×C4⋊C4—21no—
901C2×C4⋊C4—22no—
902C2×C4⋊C4—21no—
903C2×C4⋊C4—24no—
904C2×C4⋊C4—22no—
905C2×C4⋊C4—24no—
906C2×C4⋊C4—24no—
907C2×C4⋊C4—24no—
908C2×C4⋊C4—28no—
909C2×C4⋊C4—24no—
910C2×C4⋊C4—28no—
911C2×C4⋊C4—24no—
912C2×C4⋊C4C2×D411yescharacteristic
913C2×C4⋊C4C2×D412yes—
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C22⋊C4—22no—
920C2×C22⋊C4—21no—
921C2×C22⋊C4—22no—
922C2×C22⋊C4—22no—
923C2×C22⋊C4—24no—
924C2×C22⋊C4—22no—
925C2×C22⋊C4—28no—
926C2×C22⋊C4—28no—
927C2×C22⋊C4—28no—
928C2×C42—21no—
929C2×C42—24no—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2414yes—
933#107C2414yes—
934#107C2414yes—
935#107C2418yes—
936#107C2418yes—
937#106C2412yes—
938#106C2414yes—
939#106C2414yes—
940#106C2412yes—
941#106C2414yes—
942#106C2418yes—
943#106C2414yes—
944#106C2414yes—
945#106C2414yes—
946C4⋊C8C2414yes—
947C4⋊C8C2418yes—
948C4⋊C8C2412yes—
949C4⋊C8C2418yes—
950C4⋊C8C2414yes—
951C4⋊C8C2414yes—
952C4⋊C8C2412yes—
953C4⋊C8C2414yes—
954C4⋊C8C2414yes—
955#103C2412yes—
956#103C2414yes—
957#103C2418yes—
958#103C2412yes—
959#103C2414yes—
960#103C2414yes—
961#103C2414yes—
962#103C2418yes—
963#103C2418yes—
964#103C2414yes—
965#103C2418yes—
966#103C2414yes—
967#102C2411yescharacteristic
968#102C2414yes—
969#102C2418yes—
970#102C2418yes—
971#102C2411yescharacteristic
972#102C2411yescharacteristic
973#102C2411yescharacteristic
974#102C2414yes—
975#102C2414yes—
976#102C2414yes—
977#102C2414yes—
978#102C2418yes—
979#102C2418yes—
980#102C2414yes—
981#102C2414yes—
982#102C2418yes—
983#102C2414yes—
984C22⋊C8C2414yes—
985C22⋊C8C2414yes—
986C22⋊C8C2414yes—
987C22⋊C8C2418yes—
988#97C2418yes—
989#97C2418yes—
990C4×C8C2412yes—
991C4×C8C2414yes—
992C4×C8C2414yes—
993C4×C8C2412yes—
994C4×C8C2414yes—
995C4×C8C2414yes—
996C4×C8C2414yes—
997C24—21no—
998C24—22no—
999C24—24no—
1000#41—28no—
1001#41—48no—
1002#41—48no—
1003#41—48no—
1004#41—88no—
1005#41—88no—
1006#41—88no—
1007#41—84no—
1008#41—84no—
1009#41—88no—
1010#41—164no—
1011#41—164no—
1012#41—164no—
1013#41—164no—
1014C2×Q8—24no—
1015C2×Q8—22no—
1016C2×Q8—24no—
1017C2×Q8—21no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—22no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—41no—
1025C2×Q8—44no—
1026C2×Q8—41no—
1027C2×Q8—44no—
1028C2×Q8—84no—
1029C2×Q8—88no—
1030C2×Q8—161no—
1031C2×Q8—164no—
1032C2×Q8C22×D414yes—
1033C2×Q8C22×D412yes—
1034C2×Q8C22×D414yes—
1035C2×Q8C2512yes—
1036C2×Q8C2514yes—
1037C2×D4—22no—
1038C2×D4—28no—
1039C2×D4—24no—
1040C2×D4—28no—
1041C2×D4—28no—
1042C2×D4—28no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—21no—
1047C2×D4—24no—
1048C2×D4—22no—
1049C2×D4—22no—
1050C2×D4—24no—
1051C2×D4—22no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—41no—
1057C2×D4—44no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—44no—
1061C2×D4—84no—
1062C2×D4—88no—
1063C2×D4—161no—
1064C2×D4—164no—
1065C2×D4C22×D414yes—
1066C2×D4C22×D412yes—
1067C2×D4C22×D414yes—
1068C2×D4C2514yes—
1069C2×D4C2511yescharacteristic
1070C2×D4C2514yes—
1071C2×D4C2511yescharacteristic
1072C22×C4—21no—
1073C22×C4—21no—
1074C22×C4—21no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—24no—
1079C22×C4—22no—
1080C22×C4—22no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—24no—
1084C22×C4—28no—
1085C22×C4—28no—
1086C22×C4—28no—
1087C22×C4—28no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—44no—
1093C22×C4—88no—
1094C22×C4—162no—
1095C22×C4—162no—
1096C22×C4C22×D414yes—
1097C22×C4C22×D412yes—
1098C22×C4C22×D411yescharacteristic
1099C22×C4C22×D412yes—
1100C22×C4C22×D414yes—
1101C22×C4C22×D411yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2514yes—
1104SD16—24no—
1105SD16—28no—
1106SD16—42no—
1107SD16—44no—
1108SD16—44no—
1109SD16—44no—
1110SD16—44no—
1111SD16—44no—
1112SD16—48no—
1113D8—28no—
1114D8—44no—
1115D8—48no—
1116D8—48no—
1117M16—48no—
1118C2×C8—44no—
1119C2×C8—41no—
1120C2×C8—42no—
1121C2×C8—41no—
1122C2×C8—44no—
1123C2×C8C2511yescharacteristic
1124C2×C8C2511yescharacteristic
1125C2×C8C2512yes—
1126C2×C8C2514yes—
1127C2×C8C2514yes—
1128C2×C8C2514yes—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—22no—
1132C4⋊C4—28no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—22no—
1145C4⋊C4—21no—
1146C4⋊C4—21no—
1147C4⋊C4—24no—
1148C4⋊C4—22no—
1149C4⋊C4—24no—
1150C4⋊C4—22no—
1151C4⋊C4—22no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—22no—
1157C4⋊C4—24no—
1158C4⋊C4—22no—
1159C4⋊C4—24no—
1160C4⋊C4C22×D414yes—
1161C4⋊C4C22×D412yes—
1162C4⋊C4C22×D414yes—
1163C4⋊C4C22×D414yes—
1164C4⋊C4C22×D418yes—
1165C4⋊C4C22×D418yes—
1166C4⋊C4C22×D418yes—
1167C4⋊C4C22×D412yes—
1168C4⋊C4C22×D418yes—
1169C4⋊C4C22×D414yes—
1170C4⋊C4C22×D414yes—
1171C4⋊C4C2511yescharacteristic
1172C4⋊C4C2511yescharacteristic
1173C4⋊C4C2514yes—
1174C4⋊C4C2512yes—
1175C4⋊C4C2514yes—
1176C4⋊C4C2514yes—
1177C22⋊C4—24no—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—22no—
1184C22⋊C4—24no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—22no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—28no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4C22×D414yes—
1203C22⋊C4C22×D418yes—
1204C22⋊C4C22×D418yes—
1205C22⋊C4C22×D414yes—
1206C22⋊C4C22×D414yes—
1207C22⋊C4C22×D418yes—
1208C42—22no—
1209C42—24no—
1210C42—22no—
1211C42—24no—
1212C42—24no—
1213C42—28no—
1214C42—28no—
1215C42C22×D414yes—
1216C42C22×D412yes—
1217C42C22×D414yes—
1218C42C22×D414yes—
1219C42C2512yes—
1220C42C2514yes—
1221C42C2514yes—
1222C23—21no—
1223C23—24no—
1224C23—21no—
1225C23—24no—
1226C23—42no—
1227C23—48no—
1228C23—42no—
1229C23—44no—
1230C23—81no—
1231C23—84no—
1232C23—82no—
1233C23—82no—
1234C23—84no—
1235C23C23×D414yes—
1236C23C23×D411yescharacteristic
1237Q8—28no—
1238Q8—24no—
1239Q8—22no—
1240Q8—24no—
1241Q8—22no—
1242Q8—24no—
1243Q8—44no—
1244Q8—44no—
1245Q8—84no—
1246Q8—81no—
1247Q8—84no—
1248Q8—84no—
1249Q8—84no—
1250Q8—84no—
1251Q8—84no—
1252Q8—82no—
1253D4—28no—
1254D4—24no—
1255D4—21no—
1256D4—24no—
1257D4—21no—
1258D4—24no—
1259D4—24no—
1260D4—21no—
1261D4—24no—
1262D4—44no—
1263D4—48no—
1264D4—42no—
1265D4—48no—
1266D4—48no—
1267D4—44no—
1268D4—82no—
1269D4—84no—
1270D4—84no—
1271D4—84no—
1272D4—84no—
1273D4—82no—
1274D4—84no—
1275D4—84no—
1276D4—84no—
1277D4—88no—
1278D4—88no—
1279D4—88no—
1280D4#58512yes—
1281C2×C4—24no—
1282C2×C4—21no—
1283C2×C4—24no—
1284C2×C4—21no—
1285C2×C4—24no—
1286C2×C4—28no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—21no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—42no—
1296C2×C4—41no—
1297C2×C4—44no—
1298C2×C4—42no—
1299C2×C4—44no—
1300C2×C4—44no—
1301C2×C4—48no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—84no—
1307C2×C4—84no—
1308C2×C4—88no—
1309C2×C4—88no—
1310C2×C4—88no—
1311C2×C4—88no—
1312C2×C4—84no—
1313C2×C4—81no—
1314C2×C4—82no—
1315C2×C4—84no—
1316C2×C4—81no—
1317C2×C4—84no—
1318C2×C4#57714yes—
1319C2×C4C23×D414yes—
1320C2×C4C23×D414yes—
1321C2×C4C23×D414yes—
1322C2×C4C23×D411yescharacteristic
1323C2×C4C23×D412yes—
1324C2×C4C23×D414yes—
1325C2×C4C23×D414yes—
1326C2×C4C23×D412yes—
1327C2×C4C2611yescharacteristic
1328C8—22no—
1329C8—24no—
1330C8—24no—
1331C8—21no—
1332C8—24no—
1333C8—21no—
1334C22—21no—
1335C22—21no—
1336C22—24no—
1337C22—22no—
1338C22—24no—
1339C22—24no—
1340C22—41no—
1341C22—41no—
1342C22—44no—
1343C22—41no—
1344C22—44no—
1345C22—41no—
1346C22—44no—
1347C22—44no—
1348C22—41no—
1349C22—44no—
1350C22—44no—
1351C22—84no—
1352C22—164no—
1353C22—168no—
1354C22C2×#57712yes—
1355C22C24×D411yescharacteristic
1356C4—24no—
1357C4—21no—
1358C4—24no—
1359C4—24no—
1360C4—22no—
1361C4—24no—
1362C4—24no—
1363C4—44no—
1364C4—42no—
1365C4—42no—
1366C4—44no—
1367C4—41no—
1368C4—44no—
1369C4—41no—
1370C4—44no—
1371C4C2×#57714yes—
1372C4C2×#58511yescharacteristic
1373C42−1+611yescharacteristic
1374C2—22no—
1375C2—44no—
1376C2—42no—
1377C2—81no—
1378C2—84no—
1379C2—84no—
1380C2#6300211yescharacteristic
1381C2C22×#57711yescharacteristic
1382C2#6309111yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3461 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62962C2semidirect
2. #62944C2semidirect
3. #62562C2semidirect
4. #62557C2semidirect
5. #62527C2semidirect
6. #62381C2semidirect
7. #62357C2semidirect
8. #62194C2semidirect
9. #62166C2semidirect
10. #62114C2semidirect
11. #62039C2semidirect
12. #62016C2semidirect
13. #61961C2semidirect
14. #61914C2semidirect
15. #61891C2semidirect
16. #61850C2semidirect
17. #61826C2semidirect
18. #61498C2semidirect
19. #61496C2semidirect
20. SD16×#41C2semidirect
21. #61326C2semidirect
22. C2×#3361C2semidirect
23. #60330C2semidirect
24. #3561C22semidirect
28. #3554C22semidirect
29. #3550C22semidirect
30. #3548C22semidirect
31. #3547C22semidirect
36. #3522C22semidirect
37. #3520C22semidirect
39. #3519C22semidirect
42. #3508C22semidirect
43. #3507C22semidirect
44. #3502C22semidirect
46. #3501C22semidirect
50. C2×#559C22semidirect
51. Q8×#41C22semidirect
57. #3399C22semidirect
58. #3399C22semidirect
59. #3399C22semidirect
60. #3397C22semidirect
61. #3397C22semidirect
62. #3392C22semidirect
63. #3392C22semidirect
64. #3385C22semidirect
65. #3385C22semidirect
66. #3385C22semidirect
67. #3384C22semidirect
68. #3384C22semidirect
69. Q8×SD16C22semidirect
70. Q8×SD16C22semidirect
71. #3376C22semidirect
72. #3376C22semidirect
73. #3376C22semidirect
75. #3373C22semidirect
76. #3373C22semidirect
77. #3372C22semidirect
78. #3372C22semidirect
79. #3372C22semidirect
80. #3362C22semidirect
81. #3362C22semidirect
84. #3361C22semidirect
85. #3361C22semidirect
86. #3361C22semidirect
87. #3361C22semidirect
88. #3360C22semidirect
89. #3360C22semidirect
90. #3359C22semidirect
91. #3359C22semidirect
92. #3358C22semidirect
93. #3357C22semidirect
94. #3354C22semidirect
95. #3346C22semidirect
96. #3345C22semidirect
97. #3335C22semidirect
98. #3335C22semidirect
99. #3332C22semidirect
100. #3329C22semidirect
101. #3326C22semidirect
102. #3321C22semidirect
103. #3320C22semidirect
104. #3307C22semidirect
105. #3306C22semidirect
106. #3305C22semidirect
107. #3305C22semidirect
108. #3303C22semidirect
109. #3301C22semidirect
110. #3298C22semidirect
111. #3298C22semidirect
112. #3297C22semidirect
113. #3297C22semidirect
115. #3295C22semidirect
116. #3294C22semidirect
118. D4×SD16C22semidirect
120. #3272C22semidirect
121. #3265C22semidirect
123. #3257C22semidirect
124. #3257C22semidirect
125. #3254C22semidirect
126. #3253C22semidirect
127. #3246C22semidirect
128. #3246C22semidirect
129. #3244C22semidirect
130. #3244C22semidirect
131. #3237C22semidirect
132. #3236C22semidirect
133. #3230C22semidirect
134. #3228C22semidirect
135. #3221C22semidirect
136. #3221C22semidirect
137. #3214C22semidirect
138. #3213C22semidirect
139. #3207C22semidirect
140. #3205C22semidirect
141. #3179C22semidirect
142. #3179C22semidirect
143. #3169C22semidirect
144. #3167C22semidirect
145. #3167C22semidirect
146. #3167C22semidirect
147. #3137C22semidirect
148. #3131C22semidirect
149. C2×#488C22semidirect
150. C2×#486C22semidirect
151. #3119C22semidirect
152. #3119C22semidirect
153. #3118C22semidirect
154. #3118C22semidirect
155. #3112C22semidirect
158. #3109C22semidirect
159. #3103C22semidirect
160. #3103C22semidirect
162. #3101C22semidirect
163. #3084C22semidirect
164. #3078C22semidirect
165. C2×#477C22semidirect
166. C2×#478C22semidirect
167. #3042C22semidirect
171. #2993C22semidirect
172. #2992C22semidirect
173. #2989C22semidirect
174. #2985C22semidirect
175. #2983C22semidirect
176. #2966C22semidirect
177. #2966C22semidirect
178. C8×#41C22semidirect
179. #2960C22semidirect
180. C2×C8×Q8C22semidirect
181. #2946C22semidirect
183. C2×C4×SD16C22semidirect

Maximal subgroups

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

subgroupindex
#629622
#629442
#625622
#625572
#625272
#623812
#623572
#621942
#621662
#621142
#620392
#620162
#619612
#619142
#618912
#618502
#618262
#614982
#614962
SD16×#412
#613262
C2×#33612
#603302