Finite Group Databasebeta

← #10584994

Subgroups — #10584994

Order 512.

6173 conjugacy classes of subgroups.

The subgroup lattice has 1219 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63009C211yesmaximal, characteristic, complemented
2#63000C211yesmaximal, characteristic, complemented
3#62533C216yesmaximal, complemented
4#62532C213yesmaximal, complemented
5#62530C211yesmaximal, characteristic, complemented
6#62362C212yesmaximal, complemented
7#62361C213yesmaximal, complemented
8#62104C216yesmaximal, complemented
9#62098C213yesmaximal, complemented
10#62096C211yesmaximal, characteristic, complemented
11#61955C216yesmaximal, complemented
12#61950C213yesmaximal, complemented
13#61948C211yesmaximal, characteristic, complemented
14#61886C212yesmaximal, complemented
15#61882C213yesmaximal, complemented
16#61824C212yesmaximal, complemented
17#61819C213yesmaximal, complemented
18#61432C216yesmaximal, complemented
19#61427C213yesmaximal, complemented
20D8×#41C211yesmaximal, characteristic, complemented
21#61303C212yesmaximal, complemented
22C2×#3360C213yesmaximal, complemented
23C8×2−1+4C211yesmaximal, characteristic, complemented
24#3523C2212yescomplemented
25#3522C2212yescomplemented
26#3521—26no—
27#3520—26no—
28#3518—22no—
29#3516—22no—
30#3515C2216yescomplemented
31#3514C2216yescomplemented
32#3511C2213yescomplemented
33#3511C2213yescomplemented
34#3507C2213yescomplemented
35#3507C2213yescomplemented
36#3503C2211yescharacteristic
37#3503C2211yescharacteristic
38#3495—23no—
39#3495—23no—
40#3493—23no—
41#3492—23no—
42#3489—21no—
43#3489—21no—
44#3482C2216yescomplemented
45#3481C2216yescomplemented
46#3480C2212yescomplemented
47Q8×#41C2212yescomplemented
48#3475C2213yescomplemented
49#3475C2213yescomplemented
50C2×#556C2213yescomplemented
51C2×#554C2213yescomplemented
52D4×#41C2211yescharacteristic
53D4×#41C2211yescharacteristic
54C4×2−1+4C2211yescharacteristic
55#3428—21no—
56C2×#520—21no—
57#3396C2216yescomplemented
58#3394C2216yescomplemented
59#3394C2216yescomplemented
60#3393C2216yescomplemented
61#3393C2213yescomplemented
62#3392C2212yescomplemented
63#3391C2211yescharacteristic
64#3383C2216yescomplemented
65#3381C2216yescomplemented
66#3381C2216yescomplemented
67#3380C2213yescomplemented
68#3380C2216yescomplemented
69Q8×SD16C2212yescomplemented
70Q8×D8C2211yescharacteristic
71#3365C2216yescomplemented
72#3365C2216yescomplemented
73#3364C2216yescomplemented
74#3364C2216yescomplemented
75#3363C2212yescomplemented
76#3363C2212yescomplemented
77#3362C2212yescomplemented
78#3361C2216yescomplemented
79#3361C2216yescomplemented
80#3360C2216yes—
81#3360C2213yes—
82#3360C2216yescomplemented
83#3360C2216yescomplemented
84#3360C2216yescomplemented
85#3360C2216yescomplemented
86#3360C2216yescomplemented
87#3360C2216yescomplemented
88#3360C2216yescomplemented
89#3360C2213yescomplemented
90#3359C2212yescomplemented
91#3358C2211yescharacteristic
92#3358C2211yescharacteristic
93#3341C2213yescomplemented
94#3337C22112yescomplemented
95#3336C2216yescomplemented
96#3335C2216yescomplemented
97#3334C2213yes—
98#3303C2211yescharacteristic
99#3303C2213yescomplemented
100#3303C2216yescomplemented
101#3301C22112yescomplemented
102#3301C22112yescomplemented
103#3300C22112yescomplemented
104#3299C2216yescomplemented
105#3299C2216yescomplemented
106#3298C2216yescomplemented
107#3297C22112yescomplemented
108#3296C2216yescomplemented
109#3296C2216yescomplemented
110#3295C2216yescomplemented
111#3294C2213yes—
112#3294C2213yes—
113#3283C2213yescomplemented
114#3282C22112yescomplemented
115D4×SD16C2216yescomplemented
116#3280C2216yes—
117D4×D8C2213yes—
118#3250C22112yescomplemented
119#3248C2216yescomplemented
120#3247C2216yescomplemented
121#3246C2213yescomplemented
122#3246C2213yescomplemented
123#3233C2216yescomplemented
124#3232C22112yescomplemented
125#3231C2216yescomplemented
126#3230C2213yescomplemented
127#3227C2213yescomplemented
128#3212C2216yescomplemented
129#3211C22112yescomplemented
130#3209C2213yescomplemented
131#3207C2216yescomplemented
132#3206C2213yescomplemented
133#3170C2213yescomplemented
134#3169C2213yes—
135#3168C22112yescomplemented
136#3168C2216yescomplemented
137#3167C2216yescomplemented
138#3131C2216yescomplemented
139C2×#488C2216yescomplemented
140C2×#487C2213yescomplemented
141#3108C22112yescomplemented
142#3107C2216yescomplemented
143#3106C2216yescomplemented
144#3105C22112yescomplemented
145#3102C2216yes—
146#3102C2216yescomplemented
147#3101C2213yescomplemented
148#3101C2213yescomplemented
149#3100C2213yes—
150#3100C2213yes—
151#3076C2216yescomplemented
152C2×#479C2216yescomplemented
153C2×#476C2213yescomplemented
154#3035C2216yescomplemented
155C2×#463C2216yes—
156C2×#461C2213yescomplemented
157#2988C2211yescharacteristic
158#2988C2216yescomplemented
159#2988C2213yescomplemented
160#2982C2213yescomplemented
161#2982C2212yescomplemented
162C8×#41C2211yescharacteristic
163C8×#41C2213yescomplemented
164C8×#41C2216yescomplemented
165C2×C8×Q8C2213yescomplemented
166C2×C8×Q8C2212yescomplemented
167C4×#135C2216yescomplemented
168C2×C4×SD16C2216yescomplemented
169C2×C4×D8C2213yes—
170C2×2−1+4D411yescharacteristic
171C22×#41—21no—
172C22×#41—21no—
173C2×#135C2316yes—
174C22×SD16C2316yes—
175C22×D8C2313yes—
176#559C2316yes—
177#559C2316yes—
178Q82—21no—
179Q82C2312yes—
180#557—21no—
181#557C2312yes—
182#557C2316yes—
183#557C2316yes—
184#556—26no—
185#556—26no—
186#556—23no—
187#556—26no—
188#556—26no—
189#556—26no—
190#556C2313yes—
191#556C2316yes—
192#556C2316yes—
193#556C2316yes—
194#556C2313yes—
195#555—23no—
196#555—26no—
197#555C2311yescharacteristic
198#555C2313yes—
199#554—26no—
200#554—26no—
201#554—23no—
202#554—23no—
203#554—26no—
204#554C2313yes—
205#554C2316yes—
206#554C2316yes—
207#554C2316yes—
208#554C2313yes—
209#554C2316yes—
210#553—23no—
211#553—23no—
212#553—26no—
213#553—26no—
214#553—26no—
215#553C23112yes—
216#552—23no—
217#552—23no—
218#552—26no—
219#552—26no—
220#552—212no—
221#552—26no—
222#552—212no—
223#552—26no—
224#552C2316yes—
225#552C2316yes—
226#551—26no—
227#551—26no—
228#551—212no—
229#551—212no—
230#550C2311yescharacteristic
231#550C2311yescharacteristic
232D4×Q8—22no—
233D4×Q8—22no—
234D4×Q8—23no—
235D4×Q8C2316yes—
236D4×Q8C2311yescharacteristic
237D4×Q8C2311yescharacteristic
238#548—22no—
239#548—22no—
240#548—21no—
241#548—21no—
242#548—26no—
243#548C23112yes—
244#547—26no—
245#547—26no—
246#547—23no—
247#547—26no—
248#547C2311yescharacteristic
249#547C2313yes—
250#547C2313yes—
251#547C2313yes—
252#546—26no—
253#546—26no—
254#546—23no—
255#546—23no—
256#546C2316yes—
257#546C2316yes—
258D42C2313yes—
259D42C2313yes—
260#544—23no—
261#544—23no—
262#542—26no—
263#542—26no—
264#542—26no—
265#542—26no—
266#541—26no—
267#541—26no—
268#539—212no—
269#539—26no—
270#539—26no—
271#538—212no—
272#537—23no—
273#537—23no—
274#536—23no—
275#536—23no—
276#533—26no—
277#533—26no—
278#533C2313yes—
279#533C2313yes—
280#533C2316yes—
281#533C2316yes—
282#532C2316yes—
283#532C2313yes—
284#532C2313yes—
285#532C2316yes—
286C2×C4⋊Q8C2313yes—
287C2×C4⋊Q8C2313yes—
288#529—26no—
289#529—26no—
290#529—212no—
291#529—26no—
292#529—26no—
293#529C2316yes—
294#529C2316yes—
295#529C23112yes—
296#529C23112yes—
297C2×#126—26no—
298C2×#125C2316yes—
299C2×#124C2316yes—
300#525—23no—
301#525—23no—
302#525—212no—
303#525—23no—
304#525—23no—
305C2×C22⋊Q8—23no—
306C2×C22⋊Q8—23no—
307C2×C22⋊Q8—26no—
308#520—21no—
309#520—21no—
310#520—22no—
311#520—26no—
312#520—23no—
313#520—23no—
314#520—23no—
315#520—23no—
316#520D411yescharacteristic
317#520D413yes—
318#520D416yes—
319#519—22no—
320#519D413yes—
321#519D412yes—
322#518—26no—
323C4×#41—22no—
324C4×#41—26no—
325C4×#41C2316yes—
326C4×#41C2316yes—
327C4×#41C2311yescharacteristic
328C4×#41C2313yes—
329C4×#41C2316yes—
330C2×C4×Q8—22no—
331C2×C4×Q8C2316yes—
332C2×C4×Q8C2313yes—
333C2×C4×Q8C2312yes—
334C2×C4×D4—26no—
335C2×C4×D4C2313yes—
336C2×C4×D4C2313yes—
337C2×C4×D4C2316yes—
338C2×#117—23no—
339C2×#117—23no—
340C2×#117—23no—
341C22×C4⋊C4—23no—
342#500C2313yes—
343#500C2313yes—
344#499C2316yes—
345#499C23112yes—
346#498C2316yes—
347#495C2316yes—
348#495C23112yes—
349#494C2313yes—
350#493C2313yes—
351#492C2316yes—
352#488C2316yes—
353#488C23112yes—
354#488C23112yes—
355#488C23112yes—
356#488C23112yes—
357#488C2316yes—
358#487C2316yes—
359#487C2313yes—
360#487C2316yes—
361#487C2316yes—
362#487C2311yescharacteristic
363#487C2316yes—
364#486C2313yes—
365#486C2313yes—
366#486C2316yes—
367#485C2312yes—
368#485C2316yes—
369#485C23112yes—
370#484C23112yes—
371#483C2316yes—
372#483C2316yes—
373#482C2316yes—
374#482C2316yes—
375#481C23112yes—
376#480C2316yes—
377#480C2316yes—
378#479C2316yes—
379#479C23112yes—
380#479C23112yes—
381#479C23112yes—
382#479C2316yes—
383#479C23112yes—
384#478C23112yes—
385#478C23112yes—
386#478C2316yes—
387#478C2316yes—
388#477C2316yes—
389#477C2316yes—
390#476C2316yes—
391#476C2313yes—
392#476C2313yes—
393#476C2311yescharacteristic
394#476C2313yes—
395#476C2316yes—
396#476C2316yes—
397#475C2316yes—
398#475C2316yes—
399#474C2313yes—
400#474C2313yes—
401#474C2313yes—
402#474C2313yes—
403#467C2316yes—
404#467C2316yes—
405#467C2316yes—
406#466C2316yes—
407#466C2316yes—
408#466C2316yes—
409#465C23112yes—
410#465C23112yes—
411#465C23112yes—
412#465C2316yes—
413#465C2312yes—
414#464C2316yes—
415#464C2316yes—
416#464C23112yes—
417#464C23112yes—
418#463C2316yes—
419#463C2316yes—
420#463C23112yes—
421#463C23112yes—
422#463C23112yes—
423#463C23112yes—
424#462C2316yes—
425#462C2316yes—
426#461C2311yescharacteristic
427#461C2313yes—
428#461C2313yes—
429#461C2313yes—
430#461C2316yes—
431#461C2316yes—
432#461C2316yes—
433#460C2316yes—
434#460C2316yes—
435#459C2313yes—
436#459C2313yes—
437#459C2313yes—
438#459C2313yes—
439#452C2316yes—
440#452C2316yes—
441#451C23112yes—
442#450C2316yes—
443#450C2316yes—
444#449C2312yes—
445#449C2316yes—
446#449C23112yes—
447#448C23112yes—
448#447C2316yes—
449#447C2316yes—
450C8×Q8C2311yescharacteristic
451C8×Q8C2312yes—
452C8×Q8C2313yes—
453C8×Q8C2316yes—
454C8×Q8C2316yes—
455C8×Q8C2316yes—
456C8×Q8C2313yes—
457C8×Q8C2316yes—
458C8×Q8C2316yes—
459C8×Q8C2311yescharacteristic
460C4×Q16C2316yes—
461C4×Q16C2316yes—
462C4×Q16C23112yes—
463C4×Q16C2316yes—
464C4×SD16C2316yes—
465C4×SD16C23112yes—
466C4×SD16C2316yes—
467C4×SD16C2316yes—
468C4×SD16C2316yes—
469C4×SD16C2316yes—
470C4×SD16C23112yes—
471C4×SD16C23112yes—
472C4×SD16C23112yes—
473C4×SD16C2316yes—
474C4×D8C2313yes—
475C4×D8C2313yes—
476C4×D8C2313yes—
477C4×D8C2316yes—
478C4×D8C2313yes—
479C4×D8C2313yes—
480C4×D8C2313yes—
481C4×D8C2311yescharacteristic
482C4×D8C2313yes—
483C4×D8C2316yes—
484C4×D8C23112yes—
485C8×D4C2313yes—
486C8×D4C2316yes—
487C8×D4C2316yes—
488C8×D4C23112yes—
489C8×D4C2313yes—
490C8×D4C2313yes—
491C8×D4C2316yes—
492C8×D4C2311yescharacteristic
493#431C2313yes—
494#431C2313yes—
495#431C2316yes—
496#431C23112yes—
497#431C2316yes—
498#427C2316yes—
499C2×#107C2313yes—
500C2×#106C2316yes—
501C2×C4⋊C8C2316yes—
502C2×C4⋊C8C2316yes—
503C2×C4⋊C8C2313yes—
504#416C23112yes—
505#416C2316yes—
506#416C2312yes—
507C2×#103C2316yes—
508C2×#103C2316yes—
509C2×#103C2316yes—
510C2×#102C2313yes—
511C2×#102C2316yes—
512C2×#102C2313yes—
513C2×C4×C8C2313yes—
514C2×C4×C8C2316yes—
515C2×C4×C8C2316yes—
5162−1+4—28no—
517C2×#41—21no—
518C2×#41—21no—
519C2×#41—23no—
520C2×#41—23no—
521C2×#41—23no—
522C2×#41—23no—
523C2×#41—26no—
524C2×#41—48no—
525C2×#41—48no—
526C2×#41C2×D413yes—
527C2×#41C2×D416yes—
528C2×#41C2×D411yescharacteristic
529C2×#41C2412yes—
530C2×#41C2416yes—
531C22×Q8—21no—
532C22×Q8—21no—
533C22×Q8—23no—
534C22×Q8C2×D413yes—
535C22×Q8C2×D412yes—
536C22×Q8C2416yes—
537C22×D4—23no—
538C22×D4—23no—
539C22×D4C2413yes—
540C22×D4C2413yes—
541C23×C4—23no—
542C23×C4—23no—
543C23×C4—26no—
544#135—412no—
545C2×Q16C2416yes—
546C2×Q16C2416yes—
547C2×SD16—412no—
548C2×SD16C2416yes—
549C2×SD16C24112yes—
550C2×SD16C2416yes—
551C2×SD16C2416yes—
552C2×SD16C2412yes—
553C2×D8—46no—
554C2×D8C2411yescharacteristic
555C2×D8C2413yes—
556C2×D8C2413yes—
557C2×D8C2413yes—
558C2×D8C2416yes—
559C22×C8C2413yes—
560C22×C8C2416yes—
561C22×C8C2416yes—
562C22×C8C2413yes—
563C22×C8C2412yes—
564C4⋊Q8—26no—
565C4⋊Q8—26no—
566C4⋊Q8—26no—
567C4⋊Q8—26no—
568C4⋊Q8—23no—
569C4⋊Q8—23no—
570C4⋊Q8—23no—
571C4⋊Q8—23no—
572C4⋊Q8C2413yes—
573C4⋊Q8C2416yes—
574C4⋊Q8C2411yescharacteristic
575C4⋊Q8C2413yes—
576C4⋊Q8C2416yes—
577C4⋊Q8C2413yes—
578C4⋊Q8C2413yes—
579C4⋊Q8C2411yescharacteristic
580#127C2413yes—
581#127C2413yes—
582#126—26no—
583#126—212no—
584#126—212no—
585#126—212no—
586#126—26no—
587#126—212no—
588#126—26no—
589#126—26no—
590#126—212no—
591#126—212no—
592#126—26no—
593#126—26no—
594#125—26no—
595#125—212no—
596#125—26no—
597#125—26no—
598#125—26no—
599#125—212no—
600#125—212no—
601#125—26no—
602#125—23no—
603#125—23no—
604#125C2416yes—
605#125C24112yes—
606#125C2416yes—
607#124—26no—
608#124—26no—
609#124—22no—
610#124—212no—
611#124—26no—
612#124—212no—
613#124—23no—
614#124—23no—
615#124—26no—
616#124C2416yes—
617#124C24112yes—
618#124C2416yes—
619#123—26no—
620#123—26no—
621#123—212no—
622#123—212no—
623#123—26no—
624#123—26no—
625#123—212no—
626#123—26no—
627#123—212no—
628#123—26no—
629#123—26no—
630#123—26no—
631#123—212no—
632#123—22no—
633#123—26no—
634C22⋊Q8—23no—
635C22⋊Q8—23no—
636C22⋊Q8—26no—
637C22⋊Q8—26no—
638C22⋊Q8—26no—
639C22⋊Q8—26no—
640C22⋊Q8—26no—
641C22⋊Q8—26no—
642C22⋊Q8—23no—
643C22⋊Q8—23no—
644C22⋊Q8—26no—
645C22⋊Q8—26no—
646C22⋊Q8—26no—
647C22⋊Q8—23no—
648C22⋊Q8—23no—
649C22⋊Q8—26no—
650C22⋊Q8—212no—
651C22⋊Q8—212no—
652C22⋊Q8—212no—
653C22⋊Q8—23no—
654C22⋊Q8—23no—
655C22⋊Q8—23no—
656C22⋊Q8—23no—
657C22⋊Q8—26no—
658C22⋊Q8—212no—
659C22⋊Q8—212no—
660C22⋊Q8—212no—
661C22⋊Q8C2412yes—
662C22⋊Q8C2416yes—
663C22⋊Q8C2416yes—
664C22⋊Q8C2416yes—
665#121—21no—
666#121—21no—
667#121—23no—
668#121—23no—
669#121—212no—
670#121—212no—
671#121—26no—
672#121—26no—
673#121—26no—
674#121—23no—
675#121—23no—
676#121—23no—
677#121—23no—
678#121—23no—
679#121—23no—
680#121—26no—
681#121—26no—
682#121C2412yes—
683#121C2416yes—
684#121C2416yes—
685#121C2416yes—
686#120—26no—
687#120—26no—
688#120—26no—
689#120—26no—
690C4×Q8—22no—
691C4×Q8—22no—
692C4×Q8—26no—
693C4×Q8—26no—
694C4×Q8—26no—
695C4×Q8—212no—
696C4×Q8—26no—
697C4×Q8—23no—
698C4×Q8—23no—
699C4×Q8—26no—
700C4×Q8C2×D412yes—
701C4×Q8C2×D416yes—
702C4×Q8C2×D416yes—
703C4×Q8C2×D416yes—
704C4×Q8C2×D416yes—
705C4×Q8C2×D411yescharacteristic
706C4×Q8C2×D413yes—
707C4×Q8C2416yes—
708C4×Q8C24112yes—
709C4×Q8C2416yes—
710C4×Q8C2416yes—
711C4×Q8C2416yes—
712C4×Q8C2411yescharacteristic
713C4×Q8C2413yes—
714C4×Q8C2416yes—
715C4×D4—26no—
716C4×D4—26no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—26no—
720C4×D4—26no—
721C4×D4—26no—
722C4×D4—26no—
723C4×D4—26no—
724C4×D4—26no—
725C4×D4—26no—
726C4×D4—26no—
727C4×D4—212no—
728C4×D4—212no—
729C4×D4—26no—
730C4×D4—23no—
731C4×D4—23no—
732C4×D4—212no—
733C4×D4—23no—
734C4×D4—23no—
735C4×D4—26no—
736C4×D4—23no—
737C4×D4—23no—
738C4×D4—26no—
739C4×D4C2×D416yes—
740C4×D4C2×D4112yes—
741C4×D4C2×D413yes—
742C4×D4C2×D413yes—
743C4×D4C2×D416yes—
744C4×D4C2411yescharacteristic
745C4×D4C2411yescharacteristic
746C4×D4C2416yes—
747C4×D4C2413yes—
748C4×D4C2413yes—
749C4×D4C2413yes—
750C4×D4C2413yes—
751C4×D4C24112yes—
752C4×D4C2413yes—
753C4×D4C2413yes—
754C4×D4C2416yes—
755C4×D4C2413yes—
756C4×D4C2416yes—
757C4×D4C2411yescharacteristic
758#117—23no—
759#117—23no—
760#117—26no—
761#117—21no—
762#117—23no—
763#117—26no—
764#117—26no—
765#117—23no—
766#117—26no—
767#117—23no—
768#117—26no—
769#117—26no—
770#117—26no—
771#117—26no—
772#117—26no—
773#117—26no—
774#117—212no—
775#117—212no—
776#117C2×D413yes—
777#117C2×D413yes—
778#117C2×D416yes—
779#117C2×D4112yes—
780#117C2×D416yes—
781#117C2412yes—
782#117C2416yes—
783C2×C4⋊C4—26no—
784C2×C4⋊C4—23no—
785C2×C4⋊C4—23no—
786C2×C4⋊C4—26no—
787C2×C4⋊C4—26no—
788C2×C4⋊C4—23no—
789C2×C4⋊C4—23no—
790C2×C4⋊C4—26no—
791C2×C4⋊C4—26no—
792C2×C4⋊C4—26no—
793C2×C4⋊C4—21no—
794C2×C4⋊C4—23no—
795C2×C4⋊C4—23no—
796C2×C4⋊C4C2×D413yes—
797C2×C4⋊C4C2×D416yes—
798C2×C4⋊C4C2×D416yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2416yes—
802C2×C22⋊C4—26no—
803C2×C22⋊C4—23no—
804C2×C22⋊C4—26no—
805C2×C22⋊C4—23no—
806C2×C22⋊C4—26no—
807C2×C22⋊C4—26no—
808C2×C22⋊C4—26no—
809C2×C42—26no—
810C2×C42—26no—
811C2×C42—26no—
812C2×C42C2413yes—
813C2×C42C2416yes—
814C2×C42C2416yes—
815#107C2411yescharacteristic
816#107C2413yes—
817#107C2413yes—
818#107C2413yes—
819#107C2416yes—
820#107C2416yes—
821#107C2416yes—
822#106C2416yes—
823#106C24112yes—
824#106C2416yes—
825#106C2412yes—
826#106C2416yes—
827C4⋊C8C2413yes—
828C4⋊C8C2416yes—
829C4⋊C8C2413yes—
830C4⋊C8C2416yes—
831C4⋊C8C24112yes—
832C4⋊C8C2413yes—
833C4⋊C8C2411yescharacteristic
834C4⋊C8C2416yes—
835#103C2416yes—
836#103C2416yes—
837#103C2416yes—
838#103C24112yes—
839#103C24112yes—
840#103C24112yes—
841#103C2412yes—
842#103C2412yes—
843#103C2416yes—
844#103C2416yes—
845#103C2412yes—
846#102C2411yescharacteristic
847#102C2411yescharacteristic
848#102C2416yes—
849#102C2413yes—
850#102C24112yes—
851#102C2413yes—
852#102C2413yes—
853#102C2413yes—
854#102C2413yes—
855#102C2413yes—
856#102C2416yes—
857#102C2412yes—
858#102C2416yes—
859#102C2416yes—
860#102C2416yes—
861C22⋊C8C2416yes—
862C22⋊C8C2416yes—
863C22⋊C8C2412yes—
864C22⋊C8C2416yes—
865C4×C8C2411yescharacteristic
866C4×C8C2413yes—
867C4×C8C2416yes—
868C4×C8C2413yes—
869C4×C8C2413yes—
870C4×C8C2416yes—
871C4×C8C24112yes—
872C4×C8C2416yes—
873C24—23no—
874C24—23no—
875#41—224no—
876#41—212no—
877#41—24no—
878#41—42no—
879#41—46no—
880#41—46no—
881#41—44no—
882#41—44no—
883#41—412no—
884#41—412no—
885#41—412no—
886#41—412no—
887#41—166no—
888#41#13518yescomplemented
889C2×Q8—28no—
890C2×Q8—212no—
891C2×Q8—23no—
892C2×Q8—23no—
893C2×Q8—21no—
894C2×Q8—26no—
895C2×Q8—23no—
896C2×Q8—26no—
897C2×Q8—46no—
898C2×Q8—46no—
899C2×Q8—44no—
900C2×Q8—44no—
901C2×Q8—163no—
902C2×Q8C22×D413yes—
903C2×Q8C22×D416yes—
904C2×Q8C22×D411yescharacteristic
905C2×Q8C2516yes—
906C2×Q8C2512yes—
907C2×D4—26no—
908C2×D4—22no—
909C2×D4—26no—
910C2×D4—26no—
911C2×D4—22no—
912C2×D4—26no—
913C2×D4—26no—
914C2×D4—23no—
915C2×D4—23no—
916C2×D4—23no—
917C2×D4—23no—
918C2×D4—23no—
919C2×D4—23no—
920C2×D4—43no—
921C2×D4—43no—
922C2×D4—43no—
923C2×D4—412no—
924C2×D4—412no—
925C2×D4C22×D416yes—
926C2×D4C22×D411yescharacteristic
927C2×D4C22×D413yes—
928C2×D4C2511yescharacteristic
929C2×D4C2513yes—
930C2×D4C2513yes—
931C2×D4C2511yescharacteristic
932C22×C4—23no—
933C22×C4—23no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—22no—
937C22×C4—23no—
938C22×C4—23no—
939C22×C4—21no—
940C22×C4—23no—
941C22×C4—23no—
942C22×C4—23no—
943C22×C4—21no—
944C22×C4—23no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—212no—
949C22×C4—412no—
950C22×C4—412no—
951C22×C4—166no—
952C22×C4C22×D416yes—
953C22×C4C22×D416yes—
954C22×C4C22×D416yes—
955C22×C4C22×D413yes—
956C22×C4C22×D416yes—
957C22×C4C22×D413yes—
958C22×C4C2513yes—
959C22×C4C2512yes—
960Q16—46no—
961Q16—46no—
962SD16—212no—
963SD16—412no—
964SD16—46no—
965SD16—42no—
966SD16—46no—
967D8—22no—
968D8—26no—
969D8—43no—
970D8—43no—
971D8—46no—
972C2×C8—43no—
973C2×C8—42no—
974C2×C8—43no—
975C2×C8—46no—
976C2×C8—46no—
977C2×C8C2511yescharacteristic
978C2×C8C2512yes—
979C2×C8C2513yes—
980C2×C8C2516yes—
981C2×C8C2513yes—
982C2×C8C2511yescharacteristic
983C4⋊C4—23no—
984C4⋊C4—26no—
985C4⋊C4—21no—
986C4⋊C4—23no—
987C4⋊C4—26no—
988C4⋊C4—212no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—23no—
992C4⋊C4—21no—
993C4⋊C4—22no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—212no—
999C4⋊C4—212no—
1000C4⋊C4—23no—
1001C4⋊C4—23no—
1002C4⋊C4—26no—
1003C4⋊C4—23no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—23no—
1011C4⋊C4—21no—
1012C4⋊C4C22×D413yes—
1013C4⋊C4C22×D411yescharacteristic
1014C4⋊C4C22×D416yes—
1015C4⋊C4C22×D413yes—
1016C4⋊C4C22×D416yes—
1017C4⋊C4C22×D4112yes—
1018C4⋊C4C22×D413yes—
1019C4⋊C4C22×D416yes—
1020C4⋊C4C2516yes—
1021C4⋊C4C2511yescharacteristic
1022C4⋊C4C2513yes—
1023C4⋊C4C2511yescharacteristic
1024C4⋊C4C2513yes—
1025C4⋊C4C2512yes—
1026C22⋊C4—26no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—22no—
1030C22⋊C4—26no—
1031C22⋊C4—22no—
1032C22⋊C4—26no—
1033C22⋊C4—22no—
1034C22⋊C4—21no—
1035C22⋊C4—21no—
1036C22⋊C4—26no—
1037C22⋊C4—26no—
1038C22⋊C4—26no—
1039C22⋊C4—212no—
1040C22⋊C4—26no—
1041C22⋊C4—23no—
1042C22⋊C4—23no—
1043C22⋊C4—212no—
1044C22⋊C4—23no—
1045C22⋊C4—23no—
1046C22⋊C4—212no—
1047C22⋊C4—23no—
1048C22⋊C4—23no—
1049C22⋊C4—26no—
1050C22⋊C4—26no—
1051C22⋊C4—26no—
1052C22⋊C4—26no—
1053C22⋊C4C22×D416yes—
1054C22⋊C4C22×D416yes—
1055C22⋊C4C22×D416yes—
1056C22⋊C4C22×D412yes—
1057C42—22no—
1058C42—26no—
1059C42—26no—
1060C42—212no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42C22×D416yes—
1065C42C22×D416yes—
1066C42C22×D4112yes—
1067C42C22×D413yes—
1068C42C22×D413yes—
1069C42C2511yescharacteristic
1070C42C2516yes—
1071C42C2513yes—
1072C23—21no—
1073C23—21no—
1074C23—23no—
1075C23—23no—
1076C23—46no—
1077C23—46no—
1078C23—46no—
1079C23—83no—
1080C23—83no—
1081C23—83no—
1082C23C23×D412yes—
1083C23C23×D413yes—
1084Q8—212no—
1085Q8—26no—
1086Q8—26no—
1087Q8—22no—
1088Q8—22no—
1089Q8—26no—
1090Q8—46no—
1091Q8—46no—
1092Q8—81no—
1093Q8—86no—
1094Q8—83no—
1095Q8—86no—
1096Q8C2×#13514yes—
1097D4—212no—
1098D4—21no—
1099D4—23no—
1100D4—23no—
1101D4—21no—
1102D4—23no—
1103D4—23no—
1104D4—21no—
1105D4—22no—
1106D4—46no—
1107D4—44no—
1108D4—412no—
1109D4—412no—
1110D4—46no—
1111D4—46no—
1112D4—83no—
1113D4—83no—
1114D4—83no—
1115D4—82no—
1116D4—86no—
1117D4—86no—
1118D4C2×#135112yes—
1119D4#58512yes—
1120C2×C4—212no—
1121C2×C4—23no—
1122C2×C4—22no—
1123C2×C4—23no—
1124C2×C4—22no—
1125C2×C4—212no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—26no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—26no—
1133C2×C4—21no—
1134C2×C4—46no—
1135C2×C4—43no—
1136C2×C4—46no—
1137C2×C4—44no—
1138C2×C4—46no—
1139C2×C4—46no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—46no—
1143C2×C4—46no—
1144C2×C4—46no—
1145C2×C4—46no—
1146C2×C4—46no—
1147C2×C4—46no—
1148C2×C4—86no—
1149C2×C4—86no—
1150C2×C4—812no—
1151C2×C4—86no—
1152C2×C4—86no—
1153C2×C4—86no—
1154C2×C4C2×#135112yes—
1155C2×C4C23×D412yes—
1156C2×C4C23×D416yes—
1157C2×C4C23×D413yes—
1158C2×C4C23×D411yescharacteristic
1159C2×C4C23×D416yes—
1160C2×C4C23×D413yes—
1161C2×C4C23×D413yes—
1162C2×C4C23×D411yescharacteristic
1163C2×C4C2611yescharacteristic
1164C8—21no—
1165C8—23no—
1166C8—26no—
1167C8—21no—
1168C8—23no—
1169C8—22no—
1170C22—23no—
1171C22—23no—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—22no—
1176C22—41no—
1177C22—41no—
1178C22—43no—
1179C22—43no—
1180C22—41no—
1181C22—41no—
1182C22—43no—
1183C22—43no—
1184C22—43no—
1185C22—43no—
1186C22—41no—
1187C22—812no—
1188C22—166no—
1189C22C22×#13516yes—
1190C22C24×D411yescharacteristic
1191C4—22no—
1192C4—23no—
1193C4—26no—
1194C4—26no—
1195C4—23no—
1196C4—21no—
1197C4—42no—
1198C4—46no—
1199C4—41no—
1200C4—41no—
1201C4—43no—
1202C4—43no—
1203C4—46no—
1204C4—42no—
1205C4C22×#13516yes—
1206C4C22×#13512yes—
1207C4C2×#58511yescharacteristic
1208C42−1+611yescharacteristic
1209C2—26no—
1210C2—42no—
1211C2—42no—
1212C2—83no—
1213C2—83no—
1214C2—81no—
1215C2#6300211yescharacteristic
1216C2C23×#13511yescharacteristic
1217C2#6309211yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×2−1+4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63009C2semidirect
2. #63000C2semidirect
3. #62533C2semidirect
4. #62532C2semidirect
5. #62530C2semidirect
6. #62362C2semidirect
7. #62361C2semidirect
8. #62104C2semidirect
9. #62098C2semidirect
10. #62096C2semidirect
11. #61955C2semidirect
12. #61950C2semidirect
13. #61948C2semidirect
14. #61886C2semidirect
15. #61882C2semidirect
16. #61824C2semidirect
17. #61819C2semidirect
18. #61432C2semidirect
19. #61427C2semidirect
20. D8×#41C2semidirect
21. #61303C2semidirect
22. C2×#3360C2semidirect
23. C8×2−1+4C2semidirect
24. #3523C22semidirect
25. #3522C22semidirect
30. #3515C22semidirect
31. #3514C22semidirect
32. #3511C22semidirect
33. #3511C22semidirect
34. #3507C22semidirect
35. #3507C22semidirect
44. #3482C22semidirect
45. #3481C22semidirect
46. #3480C22semidirect
47. Q8×#41C22semidirect
48. #3475C22semidirect
49. #3475C22semidirect
50. C2×#556C22semidirect
51. C2×#554C22semidirect
57. #3396C22semidirect
58. #3394C22semidirect
59. #3394C22semidirect
60. #3393C22semidirect
61. #3393C22semidirect
62. #3392C22semidirect
64. #3383C22semidirect
65. #3381C22semidirect
66. #3381C22semidirect
67. #3380C22semidirect
68. #3380C22semidirect
69. Q8×SD16C22semidirect
71. #3365C22semidirect
72. #3365C22semidirect
73. #3364C22semidirect
74. #3364C22semidirect
75. #3363C22semidirect
76. #3363C22semidirect
77. #3362C22semidirect
78. #3361C22semidirect
79. #3361C22semidirect
82. #3360C22semidirect
83. #3360C22semidirect
84. #3360C22semidirect
85. #3360C22semidirect
86. #3360C22semidirect
87. #3360C22semidirect
88. #3360C22semidirect
89. #3360C22semidirect
90. #3359C22semidirect
93. #3341C22semidirect
94. #3337C22semidirect
95. #3336C22semidirect
96. #3335C22semidirect
99. #3303C22semidirect
100. #3303C22semidirect
101. #3301C22semidirect
102. #3301C22semidirect
103. #3300C22semidirect
104. #3299C22semidirect
105. #3299C22semidirect
106. #3298C22semidirect
107. #3297C22semidirect
108. #3296C22semidirect
109. #3296C22semidirect
110. #3295C22semidirect
113. #3283C22semidirect
114. #3282C22semidirect
115. D4×SD16C22semidirect
118. #3250C22semidirect
119. #3248C22semidirect
120. #3247C22semidirect
121. #3246C22semidirect
122. #3246C22semidirect
123. #3233C22semidirect
124. #3232C22semidirect
125. #3231C22semidirect
126. #3230C22semidirect
127. #3227C22semidirect
128. #3212C22semidirect
129. #3211C22semidirect
130. #3209C22semidirect
131. #3207C22semidirect
132. #3206C22semidirect
133. #3170C22semidirect
135. #3168C22semidirect
136. #3168C22semidirect
137. #3167C22semidirect
138. #3131C22semidirect
139. C2×#488C22semidirect
140. C2×#487C22semidirect
141. #3108C22semidirect
142. #3107C22semidirect
143. #3106C22semidirect
144. #3105C22semidirect
146. #3102C22semidirect
147. #3101C22semidirect
148. #3101C22semidirect
151. #3076C22semidirect
152. C2×#479C22semidirect
153. C2×#476C22semidirect
154. #3035C22semidirect
156. C2×#461C22semidirect
158. #2988C22semidirect
159. #2988C22semidirect
160. #2982C22semidirect
161. #2982C22semidirect
163. C8×#41C22semidirect
164. C8×#41C22semidirect
165. C2×C8×Q8C22semidirect
166. C2×C8×Q8C22semidirect
167. C4×#135C22semidirect
168. C2×C4×SD16C22semidirect
888. #41#135semidirect

Maximal subgroups

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

subgroupindex
#630092
#630002
#625332
#625322
#625302
#623622
#623612
#621042
#620982
#620962
#619552
#619502
#619482
#618862
#618822
#618242
#618192
#614322
#614272
D8×#412
#613032
C2×#33602
C8×2−1+42