Finite Group Databasebeta

← #10583726

Subgroups — #10583726

Order 512.

6231 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63037C211yesmaximal, characteristic, complemented
2#63022C211yesmaximal, characteristic, complemented
3#62589C212yesmaximal, complemented
4#62540C213yesmaximal, complemented
5#62526C211yesmaximal, characteristic, complemented
6#62345C216yesmaximal, complemented
7#62326C213yesmaximal, complemented
8#62148C211yesmaximal, characteristic, complemented
9#62134C213yesmaximal, complemented
10#62105C212yesmaximal, complemented
11#62002C211yesmaximal, characteristic, complemented
12#61980C213yesmaximal, complemented
13#61948C212yesmaximal, complemented
14#61803C216yesmaximal, complemented
15#61789C213yesmaximal, complemented
16#61692C216yesmaximal, complemented
17#61664C213yesmaximal, complemented
18#61466C212yesmaximal, complemented
19#61448C213yesmaximal, complemented
20#61434C211yesmaximal, characteristic, complemented
21#61217C213yesmaximal, complemented
22#61209C216yesmaximal, complemented
23#60328C211yesmaximal, characteristic, complemented
24#3550C2213yescomplemented
25#3550C2216yescomplemented
26#3549C2213yes—
27#3546—23no—
28#3546C2216yes—
29#3544—23no—
30#3544—26no—
31#3540—26no—
32#3522—21no—
33#3522—22no—
34#3522—23no—
35#3518—21no—
36#3518C2212yes—
37#3511C2213yes—
38#3511C2213yes—
39#3506—23no—
40#3506C2216yes—
41#3503C2213yescomplemented
42#3503C2211yescharacteristic, complemented
43#3503C2212yescomplemented
44#3499C2211yescharacteristic
45#3499C2216yescomplemented
46#3499C2213yescomplemented
47#3487—22no—
48#3483C2211yescharacteristic
49#3483C2211yescharacteristic
50#3482C2213yescomplemented
51#3482C2212yescomplemented
52#3482C2211yescharacteristic, complemented
53#3481C2213yes—
54C2×Q82—21no—
55D4×#41—21no—
56D4×#41C2212yes—
57#3400C2213yes—
58#3392C2212yes—
59#3392C2211yescharacteristic
60#3384C2213yescomplemented
61Q8×SD16C2211yescharacteristic, complemented
62Q8×D8C2212yescomplemented
63#3373C2211yescharacteristic
64#3372C2213yescomplemented
65#3372C2216yescomplemented
66#3363C2212yescomplemented
67#3363C2211yescharacteristic, complemented
68#3359C2212yescomplemented
69#3359C2212yescomplemented
70#3359C2212yescomplemented
71#3358C2211yescharacteristic
72#3356C2213yescomplemented
73#3353C2216yescomplemented
74#3353C2216yescomplemented
75#3350C2216yescomplemented
76#3350C22112yescomplemented
77#3342C2216yescomplemented
78#3340C2216yescomplemented
79#3340C2213yescomplemented
80#3340C2216yescomplemented
81#3331C2213yescomplemented
82#3330C2216yescomplemented
83#3330C2216yescomplemented
84#3329C2216yescomplemented
85#3329C2216yescomplemented
86#3329C2216yescomplemented
87#3329C2216yescomplemented
88#3329C2216yescomplemented
89#3328C2216yescomplemented
90#3328C2216yescomplemented
91#3324C2213yes—
92#3324C2216yescomplemented
93#3320C22112yescomplemented
94#3320C22112yescomplemented
95#3320C22112yescomplemented
96#3311C2216yescomplemented
97#3307C2216yescomplemented
98#3307C22112yescomplemented
99#3304C2213yescomplemented
100#3303C2213yescomplemented
101#3303C2216yescomplemented
102#3303C2216yescomplemented
103#3302C2216yescomplemented
104#3299C2216yescomplemented
105#3298C2216yescomplemented
106#3298C2216yescomplemented
107#3298C2216yescomplemented
108#3298C2216yescomplemented
109#3284C2213yescomplemented
110D4×SD16C2216yes—
111D4×SD16C2216yescomplemented
112D4×SD16C2216yescomplemented
113#3278C2216yescomplemented
114#3272C2213yes—
115#3272C2216yescomplemented
116#3267C2216yescomplemented
117#3266C22112yescomplemented
118#3254C2213yes—
119#3254C2213yescomplemented
120#3248C2216yescomplemented
121#3246C2216yescomplemented
122#3237C2216yescomplemented
123#3231C2216yescomplemented
124#3230C2213yescomplemented
125#3229C2213yescomplemented
126#3218C2216yescomplemented
127#3206C2213yes—
128#3206C2213yescomplemented
129#3206C2216yescomplemented
130#3201C22112yescomplemented
131#3200C22112yescomplemented
132#3200C22112yescomplemented
133#3182C2216yescomplemented
134#3172C2216yescomplemented
135#3167C2213yes—
136#3167C2213yescomplemented
137#3139C2216yescomplemented
138C2×#487C2213yescomplemented
139#3115C2216yescomplemented
140#3110C2216yescomplemented
141#3107C2213yescomplemented
142#3107C2213yescomplemented
143#3106C2213yes—
144#3106C2213yescomplemented
145#3102C2216yescomplemented
146#3101C2216yescomplemented
147#3097C22112yescomplemented
148#3097C2216yescomplemented
149#3079C2213yescomplemented
150#3076C2216yescomplemented
151#3063C2216yescomplemented
152#3057C22112yescomplemented
153#3039C2213yescomplemented
154C2×#461C2216yescomplemented
155#3013C2216yescomplemented
156#3010C22112yescomplemented
157#2991C2211yescharacteristic, complemented
158#2990C2213yescomplemented
159#2988C2212yescomplemented
160#2981C2216yescomplemented
161#2979C2213yescomplemented
162#2971C2212yescomplemented
163#2965C2213yescomplemented
164C8×#41C2211yescharacteristic, complemented
165C4×AGL(1,ℤ/8)C2216yescomplemented
166C4×#135C2213yescomplemented
167#2935C2216yescomplemented
168#2931C2213yescomplemented
169#2898C2216yescomplemented
170C2×2−1+4—21no—
171C2×2−1+4C2316yes—
172C22×#41—22no—
173C2×#137C2316yes—
174C2×AGL(1,ℤ/8)C2316yes—
175C2×#135C2313yes—
176C22×SD16C23112yes—
177C2×#131C2316yes—
178#563—212no—
179#563—26no—
180H(3,𝔽4)—26no—
181#560—212no—
182#559—23no—
183#559—26no—
184#559—212no—
185#559C2311yescharacteristic
186Q82—23no—
187Q82—26no—
188Q82—21no—
189Q82—22no—
190Q82—23no—
191Q82D411yescharacteristic
192Q82C2311yescharacteristic
193#557C2312yes—
194#557C2311yescharacteristic
195#557C2313yes—
196#556—26no—
197#556—23no—
198#556—26no—
199#556C2316yes—
200#556C2313yes—
201#556C2316yes—
202#556C2313yes—
203#556C2316yes—
204#555—23no—
205#555—23no—
206#555D413yes—
207#555D416yes—
208#555C2313yes—
209#555C2316yes—
210#555C2316yes—
211#554—23no—
212#554—26no—
213#554—23no—
214#554—26no—
215#554C2313yes—
216#554C2313yes—
217#553—26no—
218#553—23no—
219#553C2316yes—
220#553C23112yes—
221#552—23no—
222#552—26no—
223#552—23no—
224#552—26no—
225#551—26no—
226#550—21no—
227#550—26no—
228#550—26no—
229#550D411yescharacteristic
230#550D412yes—
231#550D413yes—
232#550C2313yes—
233#550C2311yescharacteristic
234D4×Q8—21no—
235D4×Q8C2316yes—
236D4×Q8C2316yes—
237D4×Q8C2316yes—
238D4×Q8C2316yes—
239D4×Q8C23112yes—
240D4×Q8C2311yescharacteristic
241D4×Q8C2312yes—
242D4×Q8C2311yescharacteristic
243#548—22no—
244#548—22no—
245#548—21no—
246#548—23no—
247#548—26no—
248#548—22no—
249#548—26no—
250#547—26no—
251#547—26no—
252#547—26no—
253#547—26no—
254#547—212no—
255#547—23no—
256#547—23no—
257#547C2313yes—
258#547C2316yes—
259#547C2313yes—
260#547C2316yes—
261#547C2316yes—
262#547C2316yes—
263#546—23no—
264#546—26no—
265#546—26no—
266#546C2316yes—
267D42—23no—
268D42C2316yes—
269D42C2313yes—
270#544—23no—
271#544—26no—
272#544—23no—
273#544—26no—
274#542—26no—
275#542—26no—
276#542—26no—
277#542—26no—
278#542—26no—
279#542—26no—
280#542—212no—
281#542—26no—
282#542—26no—
283#538—212no—
284#538—212no—
285#537—23no—
286#537C2316yes—
287#536—212no—
288#536—26no—
289#536—23no—
290#536C2316yes—
291#536C23112yes—
292#535—26no—
293#535—26no—
294#535—26no—
295#535C23112yes—
296#533—23no—
297#533C2316yes—
298#533C2313yes—
299#533C2313yes—
300#533C2316yes—
301#533C2316yes—
302#532—23no—
303#532—23no—
304#532—26no—
305#532—23no—
306#532C2313yes—
307#532C2313yes—
308#532C2316yes—
309#532C2313yes—
310#532C2316yes—
311C2×C4⋊Q8—23no—
312C2×C4⋊Q8—26no—
313C2×C4⋊Q8C2313yes—
314C2×C4⋊Q8C2316yes—
315C2×C4⋊Q8C2313yes—
316#529—23no—
317#529—23no—
318#529—26no—
319#529—23no—
320#529—26no—
321#529C2316yes—
322#525—26no—
323#525—26no—
324#525—26no—
325#525—26no—
326#520—22no—
327#520—21no—
328#520—23no—
329#520—23no—
330#520C2316yes—
331#519—22no—
332C4×#41—21no—
333C4×#41C2316yes—
334C4×#41C2313yes—
335C4×#41C2313yes—
336C4×#41C2312yes—
337C4×#41C2311yescharacteristic
338C4×#41C2313yes—
339C2×C4×Q8—21no—
340C2×C4×Q8—22no—
341C2×C4×Q8—23no—
342C2×C4×D4—23no—
343C2×C4×D4C2316yes—
344#501C2316yes—
345#500C2316yes—
346#498C2313yes—
347#498C2313yes—
348#497C2316yes—
349#492C2313yes—
350#492C2316yes—
351#492C2313yes—
352#491C2316yes—
353#491C23112yes—
354#489C2312yes—
355#487C2316yes—
356#487C2316yes—
357#487C2313yes—
358#487C2313yes—
359#487C2316yes—
360#487C2316yes—
361#487C2316yes—
362#486C2313yes—
363#486C2311yescharacteristic
364#485C23112yes—
365#485C23112yes—
366#485C2316yes—
367#485C23112yes—
368#485C23112yes—
369#485C2316yes—
370#485C2316yes—
371#484C23112yes—
372#484C23112yes—
373#483C2316yes—
374#483C23112yes—
375#483C2316yes—
376#482C2316yes—
377#482C2316yes—
378#482C23112yes—
379#482C2316yes—
380#479C23112yes—
381#479C2316yes—
382#478C2316yes—
383#477C2316yes—
384#477C2313yes—
385#477C2313yes—
386#477C2316yes—
387#476C2313yes—
388#476C2313yes—
389#476C2312yes—
390#476C2316yes—
391#475C2316yes—
392#475C2316yes—
393#475C2316yes—
394#475C2313yes—
395#475C2311yescharacteristic
396#474C2316yes—
397#474C2313yes—
398#474C2313yes—
399#474C2316yes—
400#470C2316yes—
401#470C2316yes—
402#468C2316yes—
403#468C2316yes—
404#468C23112yes—
405#468C23112yes—
406#468C23112yes—
407#468C23112yes—
408#467C23112yes—
409#465C2316yes—
410#465C23112yes—
411#465C23112yes—
412#465C2316yes—
413#465C23112yes—
414#465C2316yes—
415#465C2316yes—
416#464C2316yes—
417#463C2312yes—
418#462C2313yes—
419#462C2316yes—
420#462C2313yes—
421#461C2313yes—
422#461C2316yes—
423#461C2316yes—
424#461C2316yes—
425#461C2316yes—
426#461C2316yes—
427#461C2316yes—
428#461C2316yes—
429#461C2313yes—
430#461C23112yes—
431#460C2313yes—
432#460C2313yes—
433#460C2316yes—
434#459C2313yes—
435#459C2311yescharacteristic
436#452C2316yes—
437#452C2316yes—
438#452C2316yes—
439#451C23112yes—
440#450C2316yes—
441#450C2316yes—
442#450C23112yes—
443#449C2316yes—
444#449C23112yes—
445#449C2316yes—
446#449C2316yes—
447#448C23112yes—
448#448C23112yes—
449#448C23112yes—
450#448C23112yes—
451#448C23112yes—
452#446C2311yescharacteristic
453#446C2313yes—
454C8×Q8C2311yescharacteristic
455C8×Q8C2311yescharacteristic
456C8×Q8C2312yes—
457#442C2316yes—
458#442C2312yes—
459#440C2316yes—
460#440C23112yes—
461#440C2316yes—
462C4×Q16C2313yes—
463C4×Q16C2316yes—
464C4×Q16C2313yes—
465C4×SD16C2313yes—
466C4×SD16C2316yes—
467C4×SD16C2316yes—
468C4×SD16C2316yes—
469C4×SD16C2316yes—
470C4×SD16C2311yescharacteristic
471C4×SD16C2313yes—
472C4×SD16C2316yes—
473C4×SD16C2313yes—
474C4×D8C2313yes—
475C4×D8C2316yes—
476C4×D8C2313yes—
477#436C2316yes—
478#436C2316yes—
479#436C2313yes—
480#436C2313yes—
481#436C2316yes—
482#435C23112yes—
483#435C2316yes—
484#435C2316yes—
485C8×D4C2316yes—
486C8×D4C2316yes—
487C8×D4C2313yes—
488C8×D4C2316yes—
489C8×D4C2313yes—
490#432C2316yes—
491#431C2316yes—
492#431C2313yes—
493#431C2313yes—
494#428C2316yes—
495#428C2316yes—
496#427C23112yes—
497#427C2313yes—
498#423C2313yes—
499C2×C4⋊C8C2316yes—
500#419C23112yes—
501#419C23112yes—
502#419C2316yes—
503#418C2316yes—
504#417C2316yes—
505#417C2316yes—
506#416C23112yes—
507#416C2313yes—
508#416C2313yes—
509C2×#103C2316yes—
510C2×#103C23112yes—
511C2×#103C2316yes—
512#408C2316yes—
513#408C23112yes—
514C4×M16C2316yes—
515C2×C4×C8C2313yes—
5162−1+4—412no—
5172−1+4—86no—
5182−1+4—84no—
519C2×#41—21no—
520C2×#41—26no—
521C2×#41—26no—
522C2×#41—26no—
523C2×#41—212no—
524C2×#41—23no—
525C2×#41—23no—
526C2×#41—26no—
527C2×#41—88no—
528C2×#41C2×D412yes—
529C2×#41C2×D411yescharacteristic
530C2×#41C2×D413yes—
531C2×#41C2413yes—
532C2×#41C2416yes—
533C2×#41C2413yes—
534C2×#41C2416yes—
535C22×Q8—21no—
536C22×Q8—21no—
537C22×Q8—22no—
538C22×Q8—26no—
539C22×Q8—23no—
540C22×Q8C24112yes—
541C22×Q8C2416yes—
542C22×D4—23no—
543C22×D4—26no—
544C22×D4C2416yes—
545C23×C4—26no—
546#137—86no—
547AGL(1,ℤ/8)—412no—
548#135—46no—
549C2×Q16C2413yes—
550C2×Q16C2416yes—
551C2×SD16—812no—
552C2×SD16C2411yescharacteristic
553C2×SD16C2416yes—
554C2×SD16C2416yes—
555C2×SD16C2416yes—
556C2×SD16C24112yes—
557C2×SD16C2413yes—
558C2×SD16C2416yes—
559C2×SD16C2416yes—
560C2×D8C2413yes—
561C2×D8C2412yes—
562#131—86no—
563C2×M16C2416yes—
564C2×M16C2416yes—
565C2×M16C2416yes—
566C22×C8C2413yes—
567C22×C8C24112yes—
568C22×C8C2413yes—
569C4⋊Q8—26no—
570C4⋊Q8—212no—
571C4⋊Q8—26no—
572C4⋊Q8—26no—
573C4⋊Q8—26no—
574C4⋊Q8—26no—
575C4⋊Q8—212no—
576C4⋊Q8—23no—
577C4⋊Q8—23no—
578C4⋊Q8—26no—
579C4⋊Q8—23no—
580C4⋊Q8—23no—
581C4⋊Q8—23no—
582C4⋊Q8—26no—
583C4⋊Q8C2×D413yes—
584C4⋊Q8C2×D416yes—
585C4⋊Q8C2416yes—
586C4⋊Q8C2413yes—
587C4⋊Q8C2416yes—
588C4⋊Q8C2413yes—
589C4⋊Q8C2413yes—
590C4⋊Q8C2416yes—
591C4⋊Q8C2413yes—
592C4⋊Q8C2411yescharacteristic
593C4⋊Q8C2413yes—
594C4⋊Q8C2412yes—
595#127—23no—
596#127—212no—
597#127C2×D413yes—
598#127C2×D416yes—
599#127C2411yescharacteristic
600#127C2413yes—
601#126—26no—
602#126—212no—
603#126—26no—
604#126—26no—
605#126—26no—
606#126—212no—
607#126—26no—
608#126—212no—
609#126—26no—
610#125—23no—
611#125—23no—
612#125—23no—
613#125—26no—
614#125—26no—
615#125—23no—
616#125—23no—
617#125—26no—
618#125—26no—
619#125C2416yes—
620#124—21no—
621#124—212no—
622#124—23no—
623#124—26no—
624#124—23no—
625#124—26no—
626#124—26no—
627#124—26no—
628#124—212no—
629#124—26no—
630#124—212no—
631#124—212no—
632#124—26no—
633#124—23no—
634#124—23no—
635#124C2×D4112yes—
636#124C2×D416yes—
637#124C2412yes—
638#123—212no—
639#123—212no—
640#123—212no—
641#123—26no—
642#123—22no—
643#123—26no—
644#123—26no—
645#123—212no—
646#123—212no—
647#123—26no—
648#123—26no—
649#123—26no—
650#123—212no—
651#123—26no—
652#123—212no—
653C22⋊Q8—23no—
654C22⋊Q8—26no—
655C22⋊Q8—26no—
656C22⋊Q8—26no—
657C22⋊Q8—23no—
658C22⋊Q8—23no—
659C22⋊Q8—26no—
660C22⋊Q8—26no—
661C22⋊Q8—26no—
662C22⋊Q8—26no—
663C22⋊Q8—26no—
664C22⋊Q8—26no—
665C22⋊Q8—21no—
666C22⋊Q8—23no—
667C22⋊Q8—22no—
668C22⋊Q8—26no—
669C22⋊Q8—212no—
670C22⋊Q8—212no—
671C22⋊Q8—212no—
672C22⋊Q8—212no—
673C22⋊Q8—212no—
674C22⋊Q8—212no—
675C22⋊Q8C2416yes—
676C22⋊Q8C2416yes—
677C22⋊Q8C2416yes—
678C22⋊Q8C24112yes—
679C22⋊Q8C2416yes—
680C22⋊Q8C2416yes—
681#121—23no—
682#121—26no—
683#121—26no—
684#121—23no—
685#121—26no—
686#121—23no—
687#121—26no—
688#121—26no—
689#121—26no—
690#121—212no—
691#121—212no—
692#121—23no—
693#121—23no—
694#121—26no—
695#121—23no—
696#121—26no—
697#121—23no—
698#121—26no—
699#121—26no—
700#121C2×D416yes—
701#121C2×D416yes—
702#121C2×D416yes—
703#121C2×D416yes—
704#121C2×D4112yes—
705#121C2416yes—
706#121C2416yes—
707#121C2416yes—
708#121C24112yes—
709#120—212no—
710#120—26no—
711#120—212no—
712#120—26no—
713#120—212no—
714C4×Q8—23no—
715C4×Q8—21no—
716C4×Q8—22no—
717C4×Q8—21no—
718C4×Q8—26no—
719C4×Q8—23no—
720C4×Q8—23no—
721C4×Q8—26no—
722C4×Q8—26no—
723C4×Q8—26no—
724C4×Q8—23no—
725C4×Q8—23no—
726C4×Q8—26no—
727C4×Q8—26no—
728C4×Q8—26no—
729C4×Q8—26no—
730C4×Q8C2×D411yescharacteristic
731C4×Q8C2×D412yes—
732C4×Q8C2×D413yes—
733C4×Q8C2411yescharacteristic
734C4×Q8C2413yes—
735C4×Q8C2416yes—
736C4×Q8C2413yes—
737C4×Q8C2413yes—
738C4×Q8C2416yes—
739C4×Q8C2411yescharacteristic
740C4×Q8C2411yescharacteristic
741C4×D4—23no—
742C4×D4—26no—
743C4×D4—26no—
744C4×D4—26no—
745C4×D4—26no—
746C4×D4—212no—
747C4×D4—26no—
748C4×D4—212no—
749C4×D4—26no—
750C4×D4—23no—
751C4×D4—23no—
752C4×D4—23no—
753C4×D4—26no—
754C4×D4—26no—
755C4×D4—23no—
756C4×D4—21no—
757C4×D4—23no—
758C4×D4—26no—
759C4×D4—212no—
760C4×D4—23no—
761C4×D4—26no—
762C4×D4—26no—
763C4×D4—23no—
764C4×D4—26no—
765C4×D4C2×D413yes—
766C4×D4C2×D416yes—
767C4×D4C2×D413yes—
768C4×D4C2×D416yes—
769C4×D4C2412yes—
770C4×D4C2413yes—
771C4×D4C2416yes—
772C4×D4C2416yes—
773C4×D4C2413yes—
774C4×D4C2411yescharacteristic
775C4×D4C2412yes—
776C4×D4C2413yes—
777C4×D4C2416yes—
778C4×D4C2413yes—
779C4×D4C2416yes—
780C4×D4C2413yes—
781#117—23no—
782#117—23no—
783#117—26no—
784#117—26no—
785#117—23no—
786#117—26no—
787#117—26no—
788#117—23no—
789#117—26no—
790#117—23no—
791#117—26no—
792#117C2×D413yes—
793#117C2×D416yes—
794#117C2×D413yes—
795#117C2×D416yes—
796#117C2413yes—
797#117C2413yes—
798#117C2416yes—
799#117C24112yes—
800C2×C4⋊C4—23no—
801C2×C4⋊C4—23no—
802C2×C4⋊C4—23no—
803C2×C4⋊C4—26no—
804C2×C4⋊C4—26no—
805C2×C4⋊C4—23no—
806C2×C4⋊C4—23no—
807C2×C4⋊C4—23no—
808C2×C4⋊C4—26no—
809C2×C4⋊C4—26no—
810C2×C4⋊C4C2416yes—
811C2×C4⋊C4C2416yes—
812C2×C22⋊C4—26no—
813C2×C22⋊C4—26no—
814C2×C42—23no—
815C2×C42—23no—
816C2×C42—26no—
817C2×C42C2416yes—
818C2×C42C2413yes—
819#107C2416yes—
820#107C2413yes—
821#107C24112yes—
822#107C2413yes—
823#107C2416yes—
824#106C2411yescharacteristic
825#106C2416yes—
826#106C2416yes—
827#106C2413yes—
828#106C2412yes—
829#106C2416yes—
830#106C2416yes—
831C4⋊C8C2413yes—
832C4⋊C8C2416yes—
833C4⋊C8C2416yes—
834C4⋊C8C2413yes—
835C4⋊C8C2412yes—
836C4⋊C8C2411yescharacteristic
837C4⋊C8C2413yes—
838#103C2413yes—
839#103C24112yes—
840#103C2416yes—
841#103C2416yes—
842#103C2416yes—
843#103C24112yes—
844#103C24112yes—
845#103C2411yescharacteristic
846#103C2413yes—
847#103C24112yes—
848#103C2413yes—
849#103C2416yes—
850#103C2416yes—
851#103C2416yes—
852#103C2412yes—
853#102C2413yes—
854#102C2411yescharacteristic
855#102C2416yes—
856#102C2413yes—
857#102C2413yes—
858#102C2412yes—
859#102C2416yes—
860#102C2416yes—
861#102C2412yes—
862#102C2412yes—
863#102C2416yes—
864C22⋊C8C2416yes—
865C22⋊C8C2416yes—
866C22⋊C8C2416yes—
867C22⋊C8C2416yes—
868C22⋊C8C24112yes—
869#97C2412yes—
870#97C2416yes—
871C4×C8C2411yescharacteristic
872C4×C8C2413yes—
873C4×C8C2413yes—
874C4×C8C2413yes—
875C4×C8C2416yes—
876C24—26no—
877#41—28no—
878#41—24no—
879#41—26no—
880#41—212no—
881#41—46no—
882#41—46no—
883#41—46no—
884#41—46no—
885#41—43no—
886#41—43no—
887#41—43no—
888#41—44no—
889#41—86no—
890#41—86no—
891#41—812no—
892#41—812no—
893#41—812no—
894#41—812no—
895#41—824no—
896C2×Q8—22no—
897C2×Q8—21no—
898C2×Q8—23no—
899C2×Q8—26no—
900C2×Q8—23no—
901C2×Q8—23no—
902C2×Q8—212no—
903C2×Q8—26no—
904C2×Q8—412no—
905C2×Q8—46no—
906C2×Q8—46no—
907C2×Q8—412no—
908C2×Q8—44no—
909C2×Q8—44no—
910C2×Q8—48no—
911C2×Q8—86no—
912C2×Q8—812no—
913C2×Q8C22×D411yescharacteristic
914C2×Q8C22×D416yes—
915C2×Q8C22×D411yescharacteristic
916C2×Q8C2516yes—
917C2×Q8C2513yes—
918C2×Q8C2511yescharacteristic
919C2×D4—26no—
920C2×D4—23no—
921C2×D4—26no—
922C2×D4—23no—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—212no—
926C2×D4—21no—
927C2×D4—23no—
928C2×D4—23no—
929C2×D4—26no—
930C2×D4—21no—
931C2×D4—46no—
932C2×D4—46no—
933C2×D4—86no—
934C2×D4—812no—
935C2×D4C22×D413yes—
936C2×D4C22×D416yes—
937C2×D4C22×D413yes—
938C2×D4C22×D416yes—
939C2×D4C22×D416yes—
940C2×D4C22×D4112yes—
941C2×D4C2512yes—
942C2×D4C2513yes—
943C2×D4C2511yescharacteristic
944C22×C4—26no—
945C22×C4—212no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—22no—
949C22×C4—21no—
950C22×C4—23no—
951C22×C4—26no—
952C22×C4—23no—
953C22×C4—23no—
954C22×C4—23no—
955C22×C4—26no—
956C22×C4—23no—
957C22×C4—26no—
958C22×C4—22no—
959C22×C4—812no—
960C22×C4C22×D413yes—
961C22×C4C22×D413yes—
962C22×C4C22×D416yes—
963C22×C4C22×D416yes—
964C22×C4C2513yes—
965C22×C4C2516yes—
966Q16—43no—
967Q16—46no—
968SD16—22no—
969SD16—46no—
970SD16—46no—
971SD16—46no—
972SD16—412no—
973SD16—43no—
974SD16—46no—
975SD16—46no—
976D8—26no—
977D8—24no—
978M16—46no—
979M16—46no—
980M16—46no—
981C2×C8—43no—
982C2×C8—412no—
983C2×C8—43no—
984C2×C8C2511yescharacteristic
985C2×C8C2511yescharacteristic
986C2×C8C2512yes—
987C2×C8C2513yes—
988C2×C8C2513yes—
989C2×C8C2516yes—
990C4⋊C4—23no—
991C4⋊C4—26no—
992C4⋊C4—23no—
993C4⋊C4—26no—
994C4⋊C4—23no—
995C4⋊C4—26no—
996C4⋊C4—23no—
997C4⋊C4—23no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—212no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—21no—
1009C4⋊C4—23no—
1010C4⋊C4—23no—
1011C4⋊C4—21no—
1012C4⋊C4—22no—
1013C4⋊C4—23no—
1014C4⋊C4—23no—
1015C4⋊C4—26no—
1016C4⋊C4—23no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4C22×D411yescharacteristic
1021C4⋊C4C22×D413yes—
1022C4⋊C4C22×D413yes—
1023C4⋊C4C22×D416yes—
1024C4⋊C4C22×D416yes—
1025C4⋊C4C22×D413yes—
1026C4⋊C4C22×D412yes—
1027C4⋊C4C2511yescharacteristic
1028C4⋊C4C2512yes—
1029C4⋊C4C2513yes—
1030C4⋊C4C2511yescharacteristic
1031C4⋊C4C2516yes—
1032C4⋊C4C2513yes—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—212no—
1037C22⋊C4—26no—
1038C22⋊C4—26no—
1039C22⋊C4—23no—
1040C22⋊C4—212no—
1041C22⋊C4—26no—
1042C22⋊C4—23no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—23no—
1046C22⋊C4—26no—
1047C22⋊C4—26no—
1048C22⋊C4—26no—
1049C22⋊C4—23no—
1050C22⋊C4—21no—
1051C22⋊C4—22no—
1052C22⋊C4—26no—
1053C22⋊C4—22no—
1054C22⋊C4—212no—
1055C22⋊C4—26no—
1056C22⋊C4—23no—
1057C22⋊C4C22×D416yes—
1058C22⋊C4C22×D416yes—
1059C22⋊C4C22×D416yes—
1060C22⋊C4C22×D4112yes—
1061C22⋊C4C22×D416yes—
1062C42—21no—
1063C42—23no—
1064C42—23no—
1065C42—26no—
1066C42—23no—
1067C42—23no—
1068C42—26no—
1069C42—26no—
1070C42—23no—
1071C42—212no—
1072C42C22×D413yes—
1073C42C22×D416yes—
1074C42C22×D413yes—
1075C42C22×D416yes—
1076C42C2513yes—
1077C42C2511yescharacteristic
1078C42C2512yes—
1079C23—21no—
1080C23—22no—
1081C23—23no—
1082C23—86no—
1083C23—86no—
1084C23—86no—
1085C23C23×D416yes—
1086C23C23×D413yes—
1087Q8—22no—
1088Q8—21no—
1089Q8—26no—
1090Q8—23no—
1091Q8—23no—
1092Q8—26no—
1093Q8—21no—
1094Q8—46no—
1095Q8—44no—
1096Q8—42no—
1097Q8—46no—
1098Q8—412no—
1099Q8—86no—
1100Q8—812no—
1101Q8—83no—
1102Q8—83no—
1103Q8#57714yes—
1104D4—26no—
1105D4—22no—
1106D4—23no—
1107D4—21no—
1108D4—22no—
1109D4—23no—
1110D4—212no—
1111D4—26no—
1112D4—46no—
1113D4—46no—
1114D4—412no—
1115D4—46no—
1116D4—412no—
1117D4—42no—
1118D4—46no—
1119D4—86no—
1120D4—83no—
1121D4—81no—
1122D4—86no—
1123D4—812no—
1124D4—83no—
1125D4—86no—
1126D4—86no—
1127D4#58512yes—
1128C2×C4—26no—
1129C2×C4—23no—
1130C2×C4—26no—
1131C2×C4—26no—
1132C2×C4—23no—
1133C2×C4—212no—
1134C2×C4—26no—
1135C2×C4—23no—
1136C2×C4—22no—
1137C2×C4—21no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—26no—
1142C2×C4—26no—
1143C2×C4—23no—
1144C2×C4—46no—
1145C2×C4—46no—
1146C2×C4—412no—
1147C2×C4—44no—
1148C2×C4—46no—
1149C2×C4—42no—
1150C2×C4—46no—
1151C2×C4—412no—
1152C2×C4—46no—
1153C2×C4—82no—
1154C2×C4—86no—
1155C2×C4—83no—
1156C2×C4—86no—
1157C2×C4—86no—
1158C2×C4—812no—
1159C2×C4—86no—
1160C2×C4C23×D412yes—
1161C2×C4C23×D416yes—
1162C2×C4C23×D413yes—
1163C2×C4C23×D413yes—
1164C2×C4C23×D411yescharacteristic
1165C2×C4C23×D412yes—
1166C2×C4C23×D411yescharacteristic
1167C2×C4C23×D413yes—
1168C2×C4C2611yescharacteristic
1169C8—21no—
1170C8—23no—
1171C8—22no—
1172C8—23no—
1173C8—21no—
1174C8—26no—
1175C22—23no—
1176C22—26no—
1177C22—22no—
1178C22—23no—
1179C22—26no—
1180C22—23no—
1181C22—26no—
1182C22—41no—
1183C22—41no—
1184C22—43no—
1185C22—42no—
1186C22—42no—
1187C22—43no—
1188C22—43no—
1189C22—42no—
1190C22—1612no—
1191C22C24×D411yescharacteristic
1192C4—23no—
1193C4—26no—
1194C4—22no—
1195C4—21no—
1196C4—23no—
1197C4—22no—
1198C4—46no—
1199C4—43no—
1200C4—41no—
1201C4—41no—
1202C4—46no—
1203C4—43no—
1204C4—43no—
1205C4—42no—
1206C4—41no—
1207C4C2×#57716yes—
1208C4#358612yes—
1209C4C2×#58511yescharacteristic
1210C4H(7,𝔽2)11yescharacteristic
1211C2—43no—
1212C2—46no—
1213C2—42no—
1214C2—83no—
1215C2—82no—
1216C2#6298711yescharacteristic
1217C2C22×#57711yescharacteristic
1218C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3483 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63037C2semidirect
2. #63022C2semidirect
3. #62589C2semidirect
4. #62540C2semidirect
5. #62526C2semidirect
6. #62345C2semidirect
7. #62326C2semidirect
8. #62148C2semidirect
9. #62134C2semidirect
10. #62105C2semidirect
11. #62002C2semidirect
12. #61980C2semidirect
13. #61948C2semidirect
14. #61803C2semidirect
15. #61789C2semidirect
16. #61692C2semidirect
17. #61664C2semidirect
18. #61466C2semidirect
19. #61448C2semidirect
20. #61434C2semidirect
21. #61217C2semidirect
22. #61209C2semidirect
23. #60328C2semidirect
24. #3550C22semidirect
25. #3550C22semidirect
41. #3503C22semidirect
42. #3503C22semidirect
43. #3503C22semidirect
45. #3499C22semidirect
46. #3499C22semidirect
50. #3482C22semidirect
51. #3482C22semidirect
52. #3482C22semidirect
60. #3384C22semidirect
61. Q8×SD16C22semidirect
62. Q8×D8C22semidirect
64. #3372C22semidirect
65. #3372C22semidirect
66. #3363C22semidirect
67. #3363C22semidirect
68. #3359C22semidirect
69. #3359C22semidirect
70. #3359C22semidirect
72. #3356C22semidirect
73. #3353C22semidirect
74. #3353C22semidirect
75. #3350C22semidirect
76. #3350C22semidirect
77. #3342C22semidirect
78. #3340C22semidirect
79. #3340C22semidirect
80. #3340C22semidirect
81. #3331C22semidirect
82. #3330C22semidirect
83. #3330C22semidirect
84. #3329C22semidirect
85. #3329C22semidirect
86. #3329C22semidirect
87. #3329C22semidirect
88. #3329C22semidirect
89. #3328C22semidirect
90. #3328C22semidirect
92. #3324C22semidirect
93. #3320C22semidirect
94. #3320C22semidirect
95. #3320C22semidirect
96. #3311C22semidirect
97. #3307C22semidirect
98. #3307C22semidirect
99. #3304C22semidirect
100. #3303C22semidirect
101. #3303C22semidirect
102. #3303C22semidirect
103. #3302C22semidirect
104. #3299C22semidirect
105. #3298C22semidirect
106. #3298C22semidirect
107. #3298C22semidirect
108. #3298C22semidirect
109. #3284C22semidirect
111. D4×SD16C22semidirect
112. D4×SD16C22semidirect
113. #3278C22semidirect
115. #3272C22semidirect
116. #3267C22semidirect
117. #3266C22semidirect
119. #3254C22semidirect
120. #3248C22semidirect
121. #3246C22semidirect
122. #3237C22semidirect
123. #3231C22semidirect
124. #3230C22semidirect
125. #3229C22semidirect
126. #3218C22semidirect
128. #3206C22semidirect
129. #3206C22semidirect
130. #3201C22semidirect
131. #3200C22semidirect
132. #3200C22semidirect
133. #3182C22semidirect
134. #3172C22semidirect
136. #3167C22semidirect
137. #3139C22semidirect
138. C2×#487C22semidirect
139. #3115C22semidirect
140. #3110C22semidirect
141. #3107C22semidirect
142. #3107C22semidirect
144. #3106C22semidirect
145. #3102C22semidirect
146. #3101C22semidirect
147. #3097C22semidirect
148. #3097C22semidirect
149. #3079C22semidirect
150. #3076C22semidirect
151. #3063C22semidirect
152. #3057C22semidirect
153. #3039C22semidirect
154. C2×#461C22semidirect
155. #3013C22semidirect
156. #3010C22semidirect
157. #2991C22semidirect
158. #2990C22semidirect
159. #2988C22semidirect
160. #2981C22semidirect
161. #2979C22semidirect
162. #2971C22semidirect
163. #2965C22semidirect
164. C8×#41C22semidirect
165. C4×AGL(1,ℤ/8)C22semidirect
166. C4×#135C22semidirect
167. #2935C22semidirect
168. #2931C22semidirect
169. #2898C22semidirect

Maximal subgroups

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

subgroupindex
#630372
#630222
#625892
#625402
#625262
#623452
#623262
#621482
#621342
#621052
#620022
#619802
#619482
#618032
#617892
#616922
#616642
#614662
#614482
#614342
#612172
#612092
#603282