Finite Group Databasebeta

← #10585395

Subgroups — #10585395

Order 512.

6356 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63037C211yesmaximal, characteristic, complemented
2#63014C211yesmaximal, characteristic, complemented
3#62552C216yesmaximal, complemented
4#62529C213yesmaximal, complemented
5#62525C211yesmaximal, characteristic, complemented
6#62381C213yesmaximal, complemented
7#62363C212yesmaximal, complemented
8#62200C216yesmaximal, complemented
9#62149C211yesmaximal, characteristic, complemented
10#62128C213yesmaximal, complemented
11#62057C216yesmaximal, complemented
12#62001C211yesmaximal, characteristic, complemented
13#61983C213yesmaximal, complemented
14#61937C213yesmaximal, complemented
15#61907C212yesmaximal, complemented
16#61868C213yesmaximal, complemented
17#61844C212yesmaximal, complemented
18#61498C216yesmaximal, complemented
19#61436C211yesmaximal, characteristic, complemented
20#61432C213yesmaximal, complemented
21#61329C213yesmaximal, complemented
22C2×#3362C212yesmaximal, complemented
23#60331C211yesmaximal, characteristic, complemented
24#3550—23no—
25#3550C2213yescomplemented
26#3548C2213yes—
27#3546—23no—
28#3544—26no—
29#3544C2216yescomplemented
30#3543C2216yes—
31#3542—26no—
32#3522—22no—
33#3522C2212yes—
34#3522C2212yescomplemented
35#3522C2216yescomplemented
36#3519C2216yes—
37#3517—21no—
38#3508C2213yes—
39#3503—21no—
40#3503C2211yescharacteristic, complemented
41#3503C2213yescomplemented
42#3499—23no—
43#3499C2213yescomplemented
44#3498C2213yes—
45#3498C2211yescharacteristic
46#3496—23no—
47#3488—22no—
48#3483C2211yescharacteristic
49#3483C2211yescharacteristic, complemented
50#3482—21no—
51#3482C2211yescharacteristic
52#3482C2213yescomplemented
53#3481C2213yes—
54C2×Q82C2212yescomplemented
55D4×#41—21no—
56C2×#550C2212yes—
57#3399C2216yescomplemented
58#3399C2216yescomplemented
59#3397C2216yescomplemented
60#3396C2216yescomplemented
61#3394C2213yescomplemented
62#3391C2212yescomplemented
63#3391C2211yescharacteristic, complemented
64#3385C2216yescomplemented
65#3385C2216yescomplemented
66#3384C2216yescomplemented
67Q8×Q16C2211yescharacteristic, complemented
68Q8×Q16C2212yescomplemented
69#3381C2213yescomplemented
70#3380C2216yescomplemented
71#3375C2216yescomplemented
72#3375C2216yescomplemented
73#3373C2216yescomplemented
74#3368C2216yescomplemented
75#3366C2216yescomplemented
76#3366C2216yescomplemented
77#3365C2213yescomplemented
78#3362C2212yescomplemented
79#3362C2216yescomplemented
80#3362C2212yescomplemented
81#3362C2212yescomplemented
82#3362C2216yescomplemented
83#3362C2216yescomplemented
84#3362C2211yescharacteristic, complemented
85#3362C2212yescomplemented
86#3362C2216yescomplemented
87#3362C2211yescharacteristic, complemented
88#3361C2216yescomplemented
89#3361C2216yescomplemented
90#3360C2213yescomplemented
91#3358C2216yescomplemented
92#3358C2216yescomplemented
93#3357C2216yescomplemented
94#3345C22112yescomplemented
95#3341C2213yescomplemented
96#3337C2216yescomplemented
97#3335C2213yescomplemented
98#3333C2216yescomplemented
99#3325C2216yescomplemented
100#3310C22112yescomplemented
101#3306C22112yescomplemented
102#3305C2213yescomplemented
103#3305C2213yescomplemented
104#3301C2216yescomplemented
105#3299C2211yescharacteristic, complemented
106#3296C2216yescomplemented
107#3295C2216yescomplemented
108#3295C2216yescomplemented
109#3294C2216yescomplemented
110#3294C22112yescomplemented
111#3294C2213yescomplemented
112#3294C22112yescomplemented
113#3287C2213yescomplemented
114#3282C2216yescomplemented
115D4×SD16C2213yescomplemented
116#3274C2216yescomplemented
117#3265C22112yescomplemented
118#3257C22112yescomplemented
119#3254C2213yescomplemented
120#3253C2213yescomplemented
121#3247C2216yescomplemented
122#3247C2216yescomplemented
123#3241C22112yescomplemented
124#3238C2216yescomplemented
125#3227C2213yescomplemented
126#3226C2216yescomplemented
127#3226C2213yescomplemented
128#3224C22112yescomplemented
129#3217C2216yescomplemented
130#3208C2213yescomplemented
131#3205C2213yescomplemented
132#3205C2216yescomplemented
133#3179C22112yescomplemented
134#3169C2216yescomplemented
135#3169C2213yescomplemented
136#3168C2216yescomplemented
137#3167C2213yescomplemented
138#3136C2216yescomplemented
139C2×#486C2213yescomplemented
140C2×#486C2216yescomplemented
141#3119C22112yescomplemented
142#3118C22112yescomplemented
143#3112C2216yescomplemented
144#3109C2216yescomplemented
145#3108C2216yescomplemented
146#3107C2213yescomplemented
147#3106C2213yescomplemented
148#3106C2213yescomplemented
149#3106C2213yescomplemented
150#3105C2216yescomplemented
151#3081C2216yescomplemented
152#3079C2213yescomplemented
153C2×#476C2216yescomplemented
154#3045C2216yescomplemented
155#3038C2213yescomplemented
156C2×#460C2216yescomplemented
157#2994C2216yescomplemented
158#2991C2211yescharacteristic, complemented
159#2990C2213yescomplemented
160#2986C2213yescomplemented
161#2984C2212yescomplemented
162#2966C2216yescomplemented
163C8×#41C2211yescharacteristic, complemented
164C8×#41C2213yescomplemented
165#2960C2213yescomplemented
166C2×C8×Q8C2212yescomplemented
167#2946C2216yescomplemented
168C4×#135C2213yescomplemented
169C2×C4×SD16C2216yescomplemented
170C2×2−1+4—23no—
171C2×H(5,𝔽2)—21no—
172C2×H(5,𝔽2)—23no—
173C22×#41—22no—
174C2×AGL(1,ℤ/8)C2316yes—
175C2×#135C2313yes—
176C22×SD16C2316yes—
177#563—212no—
178#563—26no—
179#562—26no—
180#560—212no—
181#559—26no—
182#559C2316yes—
183#559C2316yes—
184#559C2313yes—
185Q82—22no—
186Q82—26no—
187Q82C2311yescharacteristic
188Q82C2312yes—
189Q82C2316yes—
190Q82C2316yes—
191Q82C2311yescharacteristic
192#557—21no—
193#557D411yescharacteristic
194#557C2313yes—
195#556—23no—
196#556—23no—
197#556D413yes—
198#556C2313yes—
199#555—23no—
200#555—23no—
201#555C2313yes—
202#555C2313yes—
203#554—26no—
204#554—26no—
205#554C2313yes—
206#554C2316yes—
207#554C2316yes—
208#554C2316yes—
209#554C2311yescharacteristic
210#553—26no—
211#553—23no—
212#553C2316yes—
213#552—26no—
214#552—26no—
215#552D416yes—
216#552C2316yes—
217#551—26no—
218#550—21no—
219#550—21no—
220#550—22no—
221#550—26no—
222#550—21no—
223#550—23no—
224#550C2313yes—
225#550C2313yes—
226#550C2316yes—
227#550C2311yescharacteristic
228#550C2312yes—
229#550C2316yes—
230#550C2316yes—
231#550C2311yescharacteristic
232D4×Q8—23no—
233D4×Q8—26no—
234D4×Q8—23no—
235D4×Q8—23no—
236D4×Q8D411yescharacteristic
237D4×Q8C2311yescharacteristic
238D4×Q8C2316yes—
239#548—22no—
240#548—22no—
241#548D412yes—
242#548C2316yes—
243#547—23no—
244#547—23no—
245#547—23no—
246#547—212no—
247#547—26no—
248#547—23no—
249#547—26no—
250#547—26no—
251#547—26no—
252#547D413yes—
253#547C2313yes—
254#547C23112yes—
255#546—23no—
256#546—26no—
257#546—212no—
258#546—26no—
259#546—26no—
260#546—26no—
261#546C2316yes—
262D42—26no—
263D42—23no—
264D42—26no—
265D42—23no—
266D42C2313yes—
267D42C23112yes—
268D42C2316yes—
269#544—26no—
270#544—26no—
271#544—23no—
272#544C2316yes—
273#542—212no—
274#542—26no—
275#542—26no—
276#542—26no—
277#542—26no—
278#542C23112yes—
279#540—26no—
280#540—26no—
281#540C23112yes—
282#538—212no—
283#537—26no—
284#537—26no—
285#536—212no—
286#536—26no—
287#536—26no—
288#536—23no—
289#535—26no—
290#535—26no—
291#535—23no—
292#535—23no—
293#535C2316yes—
294#534—212no—
295#533—23no—
296#533—23no—
297#533C2313yes—
298#533C2313yes—
299#532—23no—
300#532—23no—
301#532—26no—
302#532—23no—
303#532—23no—
304#532C2313yes—
305#532C2313yes—
306#532C2313yes—
307#532C2316yes—
308#532C2316yes—
309C2×C4⋊Q8—23no—
310C2×C4⋊Q8—26no—
311C2×C4⋊Q8C2313yes—
312C2×C4⋊Q8C2316yes—
313C2×#127C2313yes—
314C2×#127C2316yes—
315#529—26no—
316#529—23no—
317#529—26no—
318#529C2316yes—
319#529C2316yes—
320#529C2316yes—
321#525—26no—
322#525—26no—
323C2×#121—26no—
324C2×#121—26no—
325#520—21no—
326#520—22no—
327#520—22no—
328#520C2316yes—
329#518C2316yes—
330C4×#41—21no—
331C4×#41—21no—
332C4×#41—23no—
333C4×#41C2313yes—
334C4×#41C2313yes—
335C4×#41C2313yes—
336C4×#41C2311yescharacteristic
337C2×C4×Q8—22no—
338C2×C4×Q8C2316yes—
339C2×C4×Q8C2312yes—
340C2×C4×D4—23no—
341C2×C4×D4C2316yes—
342#501C23112yes—
343#500C2313yes—
344#500C2316yes—
345#499C2316yes—
346#498C2313yes—
347#496C23112yes—
348#495C2316yes—
349#493C2316yes—
350#493C2313yes—
351#492C2313yes—
352#490C23112yes—
353#489C23112yes—
354#488C2316yes—
355#488C2316yes—
356#487C2311yescharacteristic
357#486C2316yes—
358#486C2313yes—
359#486C23112yes—
360#486C23112yes—
361#486C2316yes—
362#486C2313yes—
363#486C2316yes—
364#486C2313yes—
365#486C2316yes—
366#486C2316yes—
367#485C2316yes—
368#484C2312yes—
369#483C2316yes—
370#482C2316yes—
371#482C2316yes—
372#482C2316yes—
373#481C2316yes—
374#481C23112yes—
375#480C23112yes—
376#480C2316yes—
377#480C23112yes—
378#479C2316yes—
379#479C2316yes—
380#478C2316yes—
381#478C23112yes—
382#478C23112yes—
383#478C2316yes—
384#477C2316yes—
385#477C2316yes—
386#477C2311yescharacteristic
387#477C2313yes—
388#477C2313yes—
389#476C2316yes—
390#476C2313yes—
391#476C23112yes—
392#476C2313yes—
393#476C2313yes—
394#476C2316yes—
395#476C23112yes—
396#476C2316yes—
397#476C2316yes—
398#475C2313yes—
399#474C2316yes—
400#474C23112yes—
401#474C2313yes—
402#474C23112yes—
403#469C23112yes—
404#468C23112yes—
405#467C2312yes—
406#466C2316yes—
407#466C23112yes—
408#466C2316yes—
409#466C2316yes—
410#465C2316yes—
411#465C2316yes—
412#465C2316yes—
413#465C2316yes—
414#464C2316yes—
415#464C2316yes—
416#463C2316yes—
417#463C2316yes—
418#463C23112yes—
419#463C23112yes—
420#462C2311yescharacteristic
421#461C2313yes—
422#460C2316yes—
423#460C2313yes—
424#460C2313yes—
425#460C2313yes—
426#460C2316yes—
427#460C23112yes—
428#460C2316yes—
429#460C23112yes—
430#460C2316yes—
431#459C2313yes—
432#459C23112yes—
433#459C23112yes—
434#459C2316yes—
435#459C2316yes—
436#459C2316yes—
437#459C2313yes—
438#459C2313yes—
439#452C2316yes—
440#451C2312yes—
441#450C2316yes—
442#450C23112yes—
443#449C2316yes—
444#449C2316yes—
445#449C2316yes—
446#448C2316yes—
447#447C2316yes—
448#447C23112yes—
449#447C23112yes—
450#446C2316yes—
451#446C2316yes—
452#446C2316yes—
453C8×Q8C2313yes—
454C8×Q8C2313yes—
455C8×Q8C2316yes—
456C8×Q8C2311yescharacteristic
457C8×Q8C2316yes—
458C8×Q8C2312yes—
459C8×Q8C2311yescharacteristic
460#442C23112yes—
461#442C23112yes—
462#440C23112yes—
463#440C23112yes—
464C4×Q16C2316yes—
465C4×Q16C2313yes—
466C4×Q16C2311yescharacteristic
467C4×SD16C2313yes—
468C4×SD16C2316yes—
469C4×SD16C2316yes—
470C4×SD16C2316yes—
471C4×SD16C2316yes—
472C4×SD16C2313yes—
473C4×SD16C2316yes—
474C4×SD16C2313yes—
475C4×SD16C2316yes—
476C4×SD16C2313yes—
477C4×SD16C2316yes—
478C4×SD16C2316yes—
479C4×D8C2313yes—
480C4×D8C2313yes—
481C4×D8C23112yes—
482C4×D8C2316yes—
483C4×D8C23112yes—
484C4×D8C2316yes—
485#436C2316yes—
486#435C23112yes—
487C8×D4C2313yes—
488C8×D4C2316yes—
489C8×D4C2313yes—
490C8×D4C2311yescharacteristic
491C8×D4C2316yes—
492C8×D4C2313yes—
493#433C23112yes—
494#432C2316yes—
495#431C2316yes—
496#431C2313yes—
497#431C2313yes—
498#428C2316yes—
499#427C2313yes—
500C2×#106C2316yes—
501#424C2316yes—
502#423C2313yes—
503C2×C4⋊C8C2316yes—
504#418C2316yes—
505#417C2316yes—
506#416C2313yes—
507#416C2313yes—
508C2×#103C2312yes—
509C2×#102C2316yes—
510C2×#102C2316yes—
511C2×#102C2316yes—
512C2×#102C23112yes—
513#405C2316yes—
514C2×C4×C8C2313yes—
515C2×C4×C8C2316yes—
5162−1+4—812no—
517H(5,𝔽2)—812no—
518H(5,𝔽2)—84no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—22no—
522C2×#41—26no—
523C2×#41—26no—
524C2×#41—26no—
525C2×#41—23no—
526C2×#41—212no—
527C2×#41—23no—
528C2×#41—23no—
529C2×#41—23no—
530C2×#41—26no—
531C2×#41—26no—
532C2×#41—88no—
533C2×#41C2×D411yescharacteristic
534C2×#41C2×D413yes—
535C2×#41C2413yes—
536C2×#41C2413yes—
537C22×Q8—26no—
538C22×Q8—26no—
539C22×Q8—23no—
540C22×Q8C2×D412yes—
541C22×Q8C2412yes—
542C22×D4—23no—
543C22×D4—212no—
544C22×D4—26no—
545C22×D4—26no—
546C22×D4—26no—
547C22×D4—23no—
548C22×D4—23no—
549C22×D4C2416yes—
550C22×D4C2416yes—
551C23×C4—26no—
552AGL(1,ℤ/8)—412no—
553#135—46no—
554C2×Q16C2411yescharacteristic
555C2×Q16C2412yes—
556C2×SD16—412no—
557C2×SD16C2413yes—
558C2×SD16C2416yes—
559C2×SD16C2416yes—
560C2×SD16C2416yes—
561C2×SD16C2413yes—
562C2×SD16C2416yes—
563C2×D8C2413yes—
564C2×D8C24112yes—
565C2×D8C2416yes—
566C2×D8C2416yes—
567C2×M16C2416yes—
568C22×C8C2416yes—
569C22×C8C2413yes—
570C22×C8C2412yes—
571C22×C8C2413yes—
572C4⋊Q8—23no—
573C4⋊Q8—26no—
574C4⋊Q8—23no—
575C4⋊Q8—26no—
576C4⋊Q8—212no—
577C4⋊Q8—26no—
578C4⋊Q8—212no—
579C4⋊Q8—26no—
580C4⋊Q8—23no—
581C4⋊Q8—21no—
582C4⋊Q8—23no—
583C4⋊Q8—23no—
584C4⋊Q8—26no—
585C4⋊Q8—26no—
586C4⋊Q8C2×D413yes—
587C4⋊Q8C2×D413yes—
588C4⋊Q8C2411yescharacteristic
589C4⋊Q8C2416yes—
590C4⋊Q8C2413yes—
591C4⋊Q8C2413yes—
592C4⋊Q8C24112yes—
593C4⋊Q8C2411yescharacteristic
594C4⋊Q8C2413yes—
595#127—23no—
596#127—23no—
597#127—23no—
598#127—23no—
599#127—26no—
600#127—26no—
601#127C2413yes—
602#127C2416yes—
603#127C2413yes—
604#127C24112yes—
605#127C2413yes—
606#126—26no—
607#126—26no—
608#126—212no—
609#126—26no—
610#126—26no—
611#126—26no—
612#126C2×D4112yes—
613#125—21no—
614#125—26no—
615#125—26no—
616#125—26no—
617#125—26no—
618#125—23no—
619#125C2×D416yes—
620#125C2×D416yes—
621#125C2416yes—
622#125C2416yes—
623#124—23no—
624#124—26no—
625#124—26no—
626#124—26no—
627#124—212no—
628#124—26no—
629#124—26no—
630#124—26no—
631#124—23no—
632#124—23no—
633#124—26no—
634#124—23no—
635#124C2×D416yes—
636#124C2416yes—
637#124C2416yes—
638#123—26no—
639#123—26no—
640#123—26no—
641#123—212no—
642#123—26no—
643#123—26no—
644#123—212no—
645#123—212no—
646#123—212no—
647#123—26no—
648#123—212no—
649#123—26no—
650#123—212no—
651#123—212no—
652#123C2×D4112yes—
653C22⋊Q8—26no—
654C22⋊Q8—23no—
655C22⋊Q8—23no—
656C22⋊Q8—26no—
657C22⋊Q8—23no—
658C22⋊Q8—26no—
659C22⋊Q8—26no—
660C22⋊Q8—23no—
661C22⋊Q8—26no—
662C22⋊Q8—212no—
663C22⋊Q8—212no—
664C22⋊Q8—212no—
665C22⋊Q8—212no—
666C22⋊Q8—212no—
667C22⋊Q8—22no—
668C22⋊Q8—22no—
669C22⋊Q8—212no—
670C22⋊Q8—212no—
671C22⋊Q8C2×D416yes—
672C22⋊Q8C2×D416yes—
673C22⋊Q8C2×D416yes—
674C22⋊Q8C2412yes—
675C22⋊Q8C2412yes—
676C22⋊Q8C2416yes—
677#121—26no—
678#121—23no—
679#121—26no—
680#121—23no—
681#121—26no—
682#121—26no—
683#121—23no—
684#121—23no—
685#121—23no—
686#121—26no—
687#121—23no—
688#121—212no—
689#121—26no—
690#121—26no—
691#121—212no—
692#121—26no—
693#121—23no—
694#121—26no—
695#121—26no—
696#121—26no—
697#121—23no—
698#121—212no—
699#121—212no—
700#121—212no—
701#121—26no—
702#121—26no—
703#121—26no—
704#121—212no—
705#121C2×D416yes—
706#121C2416yes—
707#121C2416yes—
708#121C2416yes—
709#121C2416yes—
710#121C2416yes—
711#120—26no—
712#120—212no—
713#120—26no—
714#120—212no—
715#120—212no—
716#120—212no—
717C4×Q8—21no—
718C4×Q8—22no—
719C4×Q8—26no—
720C4×Q8—26no—
721C4×Q8—21no—
722C4×Q8—23no—
723C4×Q8—26no—
724C4×Q8—26no—
725C4×Q8—23no—
726C4×Q8C2×D412yes—
727C4×Q8C2×D416yes—
728C4×Q8C2×D411yescharacteristic
729C4×Q8C2×D413yes—
730C4×Q8C2413yes—
731C4×Q8C2416yes—
732C4×Q8C2416yes—
733C4×Q8C2416yes—
734C4×Q8C2411yescharacteristic
735C4×Q8C2411yescharacteristic
736C4×Q8C2413yes—
737C4×Q8C2411yescharacteristic
738C4×Q8C2416yes—
739C4×Q8C2413yes—
740C4×D4—21no—
741C4×D4—21no—
742C4×D4—26no—
743C4×D4—26no—
744C4×D4—26no—
745C4×D4—23no—
746C4×D4—23no—
747C4×D4—23no—
748C4×D4—23no—
749C4×D4—23no—
750C4×D4—23no—
751C4×D4—23no—
752C4×D4—26no—
753C4×D4—26no—
754C4×D4—26no—
755C4×D4—26no—
756C4×D4—26no—
757C4×D4—26no—
758C4×D4—212no—
759C4×D4—23no—
760C4×D4—26no—
761C4×D4—26no—
762C4×D4—23no—
763C4×D4—23no—
764C4×D4—26no—
765C4×D4—26no—
766C4×D4C2×D413yes—
767C4×D4C2×D416yes—
768C4×D4C2×D413yes—
769C4×D4C2413yes—
770C4×D4C2416yes—
771C4×D4C2416yes—
772C4×D4C2416yes—
773C4×D4C2413yes—
774C4×D4C2413yes—
775C4×D4C2413yes—
776C4×D4C24112yes—
777C4×D4C24112yes—
778C4×D4C2411yescharacteristic
779C4×D4C2416yes—
780C4×D4C2413yes—
781#117—23no—
782#117—23no—
783#117—23no—
784#117—23no—
785#117—26no—
786#117—26no—
787#117—23no—
788#117—23no—
789#117—26no—
790#117—26no—
791#117C2×D416yes—
792#117C2×D413yes—
793#117C2×D413yes—
794#117C2413yes—
795#117C2413yes—
796#117C2416yes—
797C2×C4⋊C4—26no—
798C2×C4⋊C4—26no—
799C2×C4⋊C4—23no—
800C2×C4⋊C4—23no—
801C2×C4⋊C4—26no—
802C2×C4⋊C4—26no—
803C2×C4⋊C4—26no—
804C2×C4⋊C4C2×D416yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2416yes—
807C2×C4⋊C4C2416yes—
808C2×C22⋊C4—26no—
809C2×C22⋊C4—26no—
810C2×C22⋊C4—212no—
811C2×C42—26no—
812C2×C42—23no—
813C2×C42—23no—
814C2×C42C2416yes—
815C2×C42C2413yes—
816#107C2411yescharacteristic
817#107C2413yes—
818#107C24112yes—
819#107C2412yes—
820#107C2416yes—
821#107C2416yes—
822#106C2413yes—
823#106C2416yes—
824#106C2416yes—
825#106C2416yes—
826#106C2413yes—
827#106C2416yes—
828C4⋊C8C2413yes—
829C4⋊C8C2416yes—
830C4⋊C8C24112yes—
831C4⋊C8C2413yes—
832C4⋊C8C2416yes—
833C4⋊C8C2411yescharacteristic
834C4⋊C8C2413yes—
835C4⋊C8C2416yes—
836#103C2411yescharacteristic
837#103C2412yes—
838#103C2412yes—
839#103C2412yes—
840#103C2411yescharacteristic
841#103C2413yes—
842#103C2413yes—
843#103C2416yes—
844#103C2412yes—
845#103C2416yes—
846#102C2416yes—
847#102C2413yes—
848#102C2416yes—
849#102C24112yes—
850#102C2416yes—
851#102C24112yes—
852#102C24112yes—
853#102C2416yes—
854#102C2416yes—
855#102C24112yes—
856#102C2413yes—
857#102C2413yes—
858#102C2413yes—
859#102C2416yes—
860#102C2416yes—
861#102C2416yes—
862C22⋊C8C2412yes—
863C22⋊C8C2416yes—
864C22⋊C8C2416yes—
865C22⋊C8C2416yes—
866#97C24112yes—
867C4×C8C2411yescharacteristic
868C4×C8C2413yes—
869C4×C8C2416yes—
870C4×C8C2413yes—
871C4×C8C2413yes—
872C4×C8C2416yes—
873C4×C8C2416yes—
874C24—26no—
875C24—26no—
876#41—24no—
877#41—212no—
878#41—26no—
879#41—43no—
880#41—43no—
881#41—43no—
882#41—44no—
883#41—44no—
884#41—48no—
885#41—412no—
886#41—86no—
887#41—86no—
888#41—86no—
889#41—812no—
890#41—812no—
891#41—824no—
892#41—812no—
893#41—812no—
894#41—812no—
895C2×Q8—28no—
896C2×Q8—22no—
897C2×Q8—23no—
898C2×Q8—21no—
899C2×Q8—23no—
900C2×Q8—212no—
901C2×Q8—26no—
902C2×Q8—23no—
903C2×Q8—24no—
904C2×Q8—42no—
905C2×Q8—812no—
906C2×Q8—86no—
907C2×Q8—812no—
908C2×Q8C22×D416yes—
909C2×Q8C22×D413yes—
910C2×Q8C22×D411yescharacteristic
911C2×Q8C2511yescharacteristic
912C2×Q8C2512yes—
913C2×Q8C2511yescharacteristic
914C2×D4—23no—
915C2×D4—26no—
916C2×D4—26no—
917C2×D4—23no—
918C2×D4—26no—
919C2×D4—26no—
920C2×D4—26no—
921C2×D4—23no—
922C2×D4—23no—
923C2×D4—26no—
924C2×D4—23no—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—212no—
928C2×D4—23no—
929C2×D4—26no—
930C2×D4—212no—
931C2×D4—23no—
932C2×D4—23no—
933C2×D4—46no—
934C2×D4—46no—
935C2×D4—46no—
936C2×D4—46no—
937C2×D4—412no—
938C2×D4—812no—
939C2×D4—86no—
940C2×D4—86no—
941C2×D4—812no—
942C2×D4—812no—
943C2×D4—824no—
944C2×D4C22×D413yes—
945C2×D4C22×D416yes—
946C2×D4C22×D411yescharacteristic
947C2×D4C2516yes—
948C2×D4C2513yes—
949C2×D4C2513yes—
950C22×C4—22no—
951C22×C4—26no—
952C22×C4—22no—
953C22×C4—26no—
954C22×C4—23no—
955C22×C4—23no—
956C22×C4—23no—
957C22×C4—23no—
958C22×C4—23no—
959C22×C4—26no—
960C22×C4—23no—
961C22×C4—26no—
962C22×C4—212no—
963C22×C4—26no—
964C22×C4—212no—
965C22×C4—812no—
966C22×C4C22×D416yes—
967C22×C4C22×D416yes—
968C22×C4C22×D413yes—
969C22×C4C22×D413yes—
970C22×C4C2512yes—
971C22×C4C2513yes—
972Q16—22no—
973Q16—42no—
974SD16—26no—
975SD16—212no—
976SD16—46no—
977SD16—46no—
978SD16—46no—
979SD16—43no—
980D8—46no—
981D8—46no—
982D8—43no—
983D8—412no—
984M16—46no—
985C2×C8—42no—
986C2×C8—43no—
987C2×C8—46no—
988C2×C8—43no—
989C2×C8C2511yescharacteristic
990C2×C8C2512yes—
991C2×C8C2513yes—
992C2×C8C2511yescharacteristic
993C2×C8C2513yes—
994C2×C8C2516yes—
995C4⋊C4—21no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—23no—
999C4⋊C4—23no—
1000C4⋊C4—23no—
1001C4⋊C4—26no—
1002C4⋊C4—23no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—212no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—22no—
1010C4⋊C4—26no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—22no—
1015C4⋊C4—21no—
1016C4⋊C4—22no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—23no—
1020C4⋊C4C22×D416yes—
1021C4⋊C4C22×D413yes—
1022C4⋊C4C22×D416yes—
1023C4⋊C4C22×D413yes—
1024C4⋊C4C22×D4112yes—
1025C4⋊C4C22×D413yes—
1026C4⋊C4C22×D416yes—
1027C4⋊C4C22×D411yescharacteristic
1028C4⋊C4C22×D416yes—
1029C4⋊C4C22×D416yes—
1030C4⋊C4C2516yes—
1031C4⋊C4C2513yes—
1032C4⋊C4C2511yescharacteristic
1033C4⋊C4C2511yescharacteristic
1034C4⋊C4C2512yes—
1035C4⋊C4C2513yes—
1036C22⋊C4—23no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—26no—
1040C22⋊C4—23no—
1041C22⋊C4—26no—
1042C22⋊C4—23no—
1043C22⋊C4—26no—
1044C22⋊C4—26no—
1045C22⋊C4—26no—
1046C22⋊C4—212no—
1047C22⋊C4—26no—
1048C22⋊C4—26no—
1049C22⋊C4—26no—
1050C22⋊C4—26no—
1051C22⋊C4—26no—
1052C22⋊C4—26no—
1053C22⋊C4—26no—
1054C22⋊C4—26no—
1055C22⋊C4—23no—
1056C22⋊C4—23no—
1057C22⋊C4—23no—
1058C22⋊C4—212no—
1059C22⋊C4C22×D416yes—
1060C22⋊C4C22×D4112yes—
1061C22⋊C4C22×D412yes—
1062C22⋊C4C22×D416yes—
1063C22⋊C4C22×D416yes—
1064C42—21no—
1065C42—21no—
1066C42—23no—
1067C42—23no—
1068C42—23no—
1069C42—23no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42C22×D413yes—
1074C42C22×D413yes—
1075C42C22×D416yes—
1076C42C22×D416yes—
1077C42C2511yescharacteristic
1078C42C2513yes—
1079C42C2516yes—
1080C23—23no—
1081C23—26no—
1082C23—23no—
1083C23—412no—
1084C23—86no—
1085C23—86no—
1086C23—86no—
1087C23—86no—
1088C23—86no—
1089C23C23×D413yes—
1090C23C23×D412yes—
1091Q8—21no—
1092Q8—26no—
1093Q8—212no—
1094Q8—22no—
1095Q8—21no—
1096Q8—22no—
1097Q8—21no—
1098Q8—44no—
1099Q8—46no—
1100Q8—83no—
1101Q8—86no—
1102Q8—812no—
1103Q8—83no—
1104Q8—81no—
1105Q8#57714yes—
1106Q8#58512yes—
1107D4—212no—
1108D4—23no—
1109D4—26no—
1110D4—23no—
1111D4—23no—
1112D4—23no—
1113D4—26no—
1114D4—26no—
1115D4—46no—
1116D4—412no—
1117D4—412no—
1118D4—46no—
1119D4—412no—
1120D4—46no—
1121D4—46no—
1122D4—86no—
1123D4—86no—
1124D4—83no—
1125D4—86no—
1126D4—812no—
1127D4—83no—
1128D4—812no—
1129D4—83no—
1130D4—86no—
1131D4—86no—
1132D4—83no—
1133D4—86no—
1134D4#57614yes—
1135C2×C4—21no—
1136C2×C4—212no—
1137C2×C4—22no—
1138C2×C4—23no—
1139C2×C4—22no—
1140C2×C4—23no—
1141C2×C4—26no—
1142C2×C4—212no—
1143C2×C4—26no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—26no—
1151C2×C4—22no—
1152C2×C4—46no—
1153C2×C4—44no—
1154C2×C4—412no—
1155C2×C4—46no—
1156C2×C4—46no—
1157C2×C4—46no—
1158C2×C4—412no—
1159C2×C4—46no—
1160C2×C4—86no—
1161C2×C4—86no—
1162C2×C4—812no—
1163C2×C4—812no—
1164C2×C4—83no—
1165C2×C4—82no—
1166C2×C4—86no—
1167C2×C4C23×D413yes—
1168C2×C4C23×D416yes—
1169C2×C4C23×D412yes—
1170C2×C4C23×D411yescharacteristic
1171C2×C4C23×D413yes—
1172C2×C4C23×D416yes—
1173C2×C4C23×D411yescharacteristic
1174C2×C4C23×D413yes—
1175C2×C4C2611yescharacteristic
1176C8—21no—
1177C8—23no—
1178C8—26no—
1179C8—21no—
1180C8—22no—
1181C8—23no—
1182C22—22no—
1183C22—22no—
1184C22—23no—
1185C22—23no—
1186C22—23no—
1187C22—43no—
1188C22—43no—
1189C22—46no—
1190C22—43no—
1191C22—43no—
1192C22—46no—
1193C22—43no—
1194C22—46no—
1195C22—43no—
1196C22—1612no—
1197C22—326no—
1198C22C2×#57614yes—
1199C22C24×D411yescharacteristic
1200C4—23no—
1201C4—22no—
1202C4—22no—
1203C4—23no—
1204C4—26no—
1205C4—21no—
1206C4—26no—
1207C4—42no—
1208C4—41no—
1209C4—43no—
1210C4—43no—
1211C4—46no—
1212C4—41no—
1213C4—41no—
1214C4—42no—
1215C4C2×#57612yes—
1216C4C2×#57716yes—
1217C4C2×#58511yescharacteristic
1218C42−1+611yescharacteristic
1219C2—24no—
1220C2—43no—
1221C2—83no—
1222C2—83no—
1223C2—86no—
1224C2#6300211yescharacteristic
1225C2C22×#57611yescharacteristic
1226C2C22×#57711yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3482 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63037C2semidirect
2. #63014C2semidirect
3. #62552C2semidirect
4. #62529C2semidirect
5. #62525C2semidirect
6. #62381C2semidirect
7. #62363C2semidirect
8. #62200C2semidirect
9. #62149C2semidirect
10. #62128C2semidirect
11. #62057C2semidirect
12. #62001C2semidirect
13. #61983C2semidirect
14. #61937C2semidirect
15. #61907C2semidirect
16. #61868C2semidirect
17. #61844C2semidirect
18. #61498C2semidirect
19. #61436C2semidirect
20. #61432C2semidirect
21. #61329C2semidirect
22. C2×#3362C2semidirect
23. #60331C2semidirect
25. #3550C22semidirect
29. #3544C22semidirect
34. #3522C22semidirect
35. #3522C22semidirect
40. #3503C22semidirect
41. #3503C22semidirect
43. #3499C22semidirect
49. #3483C22semidirect
52. #3482C22semidirect
54. C2×Q82C22semidirect
57. #3399C22semidirect
58. #3399C22semidirect
59. #3397C22semidirect
60. #3396C22semidirect
61. #3394C22semidirect
62. #3391C22semidirect
63. #3391C22semidirect
64. #3385C22semidirect
65. #3385C22semidirect
66. #3384C22semidirect
67. Q8×Q16C22semidirect
68. Q8×Q16C22semidirect
69. #3381C22semidirect
70. #3380C22semidirect
71. #3375C22semidirect
72. #3375C22semidirect
73. #3373C22semidirect
74. #3368C22semidirect
75. #3366C22semidirect
76. #3366C22semidirect
77. #3365C22semidirect
78. #3362C22semidirect
79. #3362C22semidirect
80. #3362C22semidirect
81. #3362C22semidirect
82. #3362C22semidirect
83. #3362C22semidirect
84. #3362C22semidirect
85. #3362C22semidirect
86. #3362C22semidirect
87. #3362C22semidirect
88. #3361C22semidirect
89. #3361C22semidirect
90. #3360C22semidirect
91. #3358C22semidirect
92. #3358C22semidirect
93. #3357C22semidirect
94. #3345C22semidirect
95. #3341C22semidirect
96. #3337C22semidirect
97. #3335C22semidirect
98. #3333C22semidirect
99. #3325C22semidirect
100. #3310C22semidirect
101. #3306C22semidirect
102. #3305C22semidirect
103. #3305C22semidirect
104. #3301C22semidirect
105. #3299C22semidirect
106. #3296C22semidirect
107. #3295C22semidirect
108. #3295C22semidirect
109. #3294C22semidirect
110. #3294C22semidirect
111. #3294C22semidirect
112. #3294C22semidirect
113. #3287C22semidirect
114. #3282C22semidirect
115. D4×SD16C22semidirect
116. #3274C22semidirect
117. #3265C22semidirect
118. #3257C22semidirect
119. #3254C22semidirect
120. #3253C22semidirect
121. #3247C22semidirect
122. #3247C22semidirect
123. #3241C22semidirect
124. #3238C22semidirect
125. #3227C22semidirect
126. #3226C22semidirect
127. #3226C22semidirect
128. #3224C22semidirect
129. #3217C22semidirect
130. #3208C22semidirect
131. #3205C22semidirect
132. #3205C22semidirect
133. #3179C22semidirect
134. #3169C22semidirect
135. #3169C22semidirect
136. #3168C22semidirect
137. #3167C22semidirect
138. #3136C22semidirect
139. C2×#486C22semidirect
140. C2×#486C22semidirect
141. #3119C22semidirect
142. #3118C22semidirect
143. #3112C22semidirect
144. #3109C22semidirect
145. #3108C22semidirect
146. #3107C22semidirect
147. #3106C22semidirect
148. #3106C22semidirect
149. #3106C22semidirect
150. #3105C22semidirect
151. #3081C22semidirect
152. #3079C22semidirect
153. C2×#476C22semidirect
154. #3045C22semidirect
155. #3038C22semidirect
156. C2×#460C22semidirect
157. #2994C22semidirect
158. #2991C22semidirect
159. #2990C22semidirect
160. #2986C22semidirect
161. #2984C22semidirect
162. #2966C22semidirect
163. C8×#41C22semidirect
164. C8×#41C22semidirect
165. #2960C22semidirect
166. C2×C8×Q8C22semidirect
167. #2946C22semidirect
168. C4×#135C22semidirect
169. C2×C4×SD16C22semidirect

Maximal subgroups

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

subgroupindex
#630372
#630142
#625522
#625292
#625252
#623812
#623632
#622002
#621492
#621282
#620572
#620012
#619832
#619372
#619072
#618682
#618442
#614982
#614362
#614322
#613292
C2×#33622
#603312