Finite Group Databasebeta

← #10585260

Subgroups — #10585260

Order 512.

6035 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63004C211yesmaximal, characteristic, complemented
2#63000C211yesmaximal, characteristic
3#62577C216yesmaximal, complemented
4#62540C213yesmaximal, complemented
5#62530C211yesmaximal, characteristic, complemented
6#62394C212yesmaximal, complemented
7#62366C213yesmaximal, complemented
8#62139C216yesmaximal, complemented
9#62114C213yesmaximal, complemented
10#62100C211yesmaximal, characteristic, complemented
11#61980C216yesmaximal, complemented
12#61960C213yesmaximal, complemented
13#61948C211yesmaximal, characteristic, complemented
14#61906C212yesmaximal, complemented
15#61893C213yesmaximal, complemented
16#61846C212yesmaximal, complemented
17#61826C213yesmaximal, complemented
18#61453C216yesmaximal, complemented
19#61438C213yesmaximal, complemented
20SD16×#41C211yesmaximal, characteristic, complemented
21#61322C212yesmaximal, complemented
22C2×#3372C213yesmaximal, complemented
23#60343C211yesmaximal, characteristic, complemented
24#3522C2212yes—
25#3520—26no—
26#3516—22no—
27#3515C2216yes—
28#3511C2213yes—
29#3507C2213yes—
30#3504—21no—
31#3504—23no—
32#3504—26no—
33#3503C2211yescharacteristic
34#3503C2211yescharacteristic
35#3503C2213yescomplemented
36#3503C2216yescomplemented
37#3502—23no—
38#3502—22no—
39#3502C2213yescomplemented
40#3502C2212yescomplemented
41#3495—23no—
42#3492—23no—
43#3489—21no—
44#3481C2216yes—
45Q8×#41C2212yes—
46Q8×#41C2211yescharacteristic
47Q8×#41C2216yescomplemented
48Q8×#41C2213yescomplemented
49C2×#557C2213yescomplemented
50C2×#557C2212yescomplemented
51#3475C2213yes—
52C2×#554C2213yes—
53D4×#41C2211yescharacteristic
54C4×2−1+4—21no—
55C4×2−1+4C2211yescharacteristic
56C2×#520—21no—
57#3400C2216yescomplemented
58#3400C2216yescomplemented
59#3400C2216yescomplemented
60#3398C2216yescomplemented
61#3398C2213yescomplemented
62#3392C2212yes—
63#3392C2211yescharacteristic
64#3387C2216yescomplemented
65#3385C2216yes—
66#3385C2213yes—
67#3385C2216yescomplemented
68#3385C2216yescomplemented
69Q8×Q16C2212yescomplemented
70Q8×SD16C2211yescharacteristic
71#3375C2216yescomplemented
72#3374C2216yescomplemented
73#3374C2216yescomplemented
74#3374C2216yescomplemented
75#3372C2216yes—
76#3372C2216yes—
77#3372C2216yes—
78#3372C2216yes—
79#3372C2213yes—
80#3372C2216yescomplemented
81#3372C2216yescomplemented
82#3372C2216yescomplemented
83#3372C2216yescomplemented
84#3372C2216yescomplemented
85#3372C2216yescomplemented
86#3369C2213yescomplemented
87#3363C2212yescomplemented
88#3363C2212yescomplemented
89#3363C2212yescomplemented
90#3362C2211yescharacteristic
91#3359C2211yescharacteristic
92#3359C2212yes—
93#3357C2213yescomplemented
94#3346C22112yescomplemented
95#3344C2216yescomplemented
96#3338C2216yescomplemented
97#3335C2213yes—
98#3331C2211yescharacteristic
99#3329C2216yescomplemented
100#3329C2213yescomplemented
101#3320C22112yescomplemented
102#3320C22112yescomplemented
103#3320C22112yescomplemented
104#3314C2216yes—
105#3312C22112yescomplemented
106#3312C2216yescomplemented
107#3299C2216yescomplemented
108#3299C2216yescomplemented
109#3299C2216yescomplemented
110#3298C2213yes—
111#3298C2216yes—
112#3295C2213yes—
113D4×SD16C2216yes—
114D4×SD16C2213yes—
115#3276C2213yes—
116#3266C22112yes—
117#3266C2216yes—
118#3254C2216yescomplemented
119#3252C2216yescomplemented
120#3249C2213yescomplemented
121#3248C22112yescomplemented
122#3246C2213yes—
123#3237C2216yescomplemented
124#3236C22112yescomplemented
125#3231C2216yescomplemented
126#3230C2213yescomplemented
127#3230C2213yescomplemented
128#3218C2216yescomplemented
129#3218C22112yescomplemented
130#3209C2213yescomplemented
131#3206C2213yes—
132#3206C2216yescomplemented
133#3182C2216yescomplemented
134#3181C22112yescomplemented
135#3172C2216yescomplemented
136#3170C2213yescomplemented
137#3167C2213yes—
138#3139C2216yescomplemented
139C2×#491C2216yescomplemented
140C2×#487C2213yescomplemented
141#3117C22112yescomplemented
142#3116C2216yes—
143#3112C2216yescomplemented
144#3110C22112yes—
145#3108C2216yescomplemented
146#3107C2216yes—
147#3104C2213yescomplemented
148#3103C2213yes—
149#3101C2213yes—
150#3101C2213yes—
151#3078C2216yescomplemented
152C2×#479C2216yescomplemented
153C2×#477C2213yescomplemented
154#3039C2216yes—
155C2×#461C2213yes—
156C2×#461C2216yes—
157#2990C2216yescomplemented
158#2989C2213yescomplemented
159#2988C2211yescharacteristic
160#2984C2212yescomplemented
161#2983C2213yescomplemented
162#2970C2216yescomplemented
163#2965C2213yescomplemented
164C8×#41C2211yescharacteristic
165Q8×M16C2212yescomplemented
166C2×#446C2213yescomplemented
167C4×#137C2216yes—
168C2×#440C2216yes—
169C2×C4×SD16C2213yes—
170C2×2−1+4D411yescharacteristic
171C22×#41—21no—
172C2×#137C2316yes—
173C22×SD16C2313yes—
174C22×SD16C2316yes—
175#559C2316yes—
176Q82—21no—
177Q82—26no—
178Q82—23no—
179Q82C2311yescharacteristic
180Q82C2312yes—
181Q82C2313yes—
182Q82C2316yes—
183#557—22no—
184#557—26no—
185#557—26no—
186#557—26no—
187#557—21no—
188#557—26no—
189#557—23no—
190#557—22no—
191#557—26no—
192#557—26no—
193#557—26no—
194#557—21no—
195#557C2311yescharacteristic
196#557C2312yes—
197#557C2313yes—
198#557C2316yes—
199#557C2316yes—
200#557C2316yes—
201#557C2316yes—
202#557C2316yes—
203#556—23no—
204#556—26no—
205#556C2313yes—
206#555C2313yes—
207#554—26no—
208#554—26no—
209#554—23no—
210#554—26no—
211#554—212no—
212#554—23no—
213#554—26no—
214#554—23no—
215#554—26no—
216#554—212no—
217#554—23no—
218#554—26no—
219#554—26no—
220#554C2313yes—
221#554C2316yes—
222#554C2316yes—
223#554C2316yes—
224#554C2311yescharacteristic
225#554C2313yes—
226#554C2316yes—
227#554C2316yes—
228#553—23no—
229#553—26no—
230#553C23112yes—
231#552—23no—
232#552—26no—
233#552—26no—
234#552—212no—
235#552C2316yes—
236#551—26no—
237#551—212no—
238#550C2311yescharacteristic
239D4×Q8—22no—
240D4×Q8—23no—
241D4×Q8C2313yes—
242D4×Q8C2313yes—
243D4×Q8C2316yes—
244D4×Q8C23112yes—
245D4×Q8C2316yes—
246D4×Q8C2311yescharacteristic
247#548—22no—
248#548—21no—
249#548—26no—
250#547—26no—
251#547—23no—
252#547—26no—
253#547C2311yescharacteristic
254#547C2313yes—
255#546—26no—
256#546—23no—
257#546C2316yes—
258D42C2313yes—
259#544—23no—
260#544—23no—
261#544—23no—
262#544—26no—
263#544—212no—
264#544—26no—
265#544—23no—
266#544—26no—
267#544—26no—
268#542—26no—
269#542—26no—
270#541—26no—
271#539—212no—
272#539—26no—
273#537—23no—
274#536—23no—
275#533—26no—
276#533—23no—
277#533—23no—
278#533—26no—
279#533—212no—
280#533—26no—
281#533C2313yes—
282#533C2313yes—
283#533C2313yes—
284#533C2316yes—
285#533C23112yes—
286#533C2316yes—
287#533C2316yes—
288#532C2313yes—
289#532C2316yes—
290C2×C4⋊Q8C2313yes—
291C2×C4⋊Q8C2316yes—
292C2×C4⋊Q8C2316yes—
293C2×C4⋊Q8C2313yes—
294#529—26no—
295#529—26no—
296#529C2316yes—
297#529C23112yes—
298C2×#125—23no—
299C2×#125—26no—
300C2×#125—26no—
301C2×#125C2316yes—
302#525—23no—
303#525—212no—
304#525—23no—
305C2×C22⋊Q8—23no—
306C2×C22⋊Q8—26no—
307#520—21no—
308#520—21no—
309#520—23no—
310#520—26no—
311#520—22no—
312#520—26no—
313#520—23no—
314#520—23no—
315#520D411yescharacteristic
316#520D413yes—
317#520D416yes—
318#519—23no—
319#519—22no—
320#519D413yes—
321#519D412yes—
322C4×#41—21no—
323C4×#41—23no—
324C4×#41—26no—
325C4×#41C2316yes—
326C4×#41C2311yescharacteristic
327C4×#41C2313yes—
328C4×#41C2316yes—
329C2×C4×Q8—23no—
330C2×C4×Q8—22no—
331C2×C4×Q8—22no—
332C2×C4×Q8C2313yes—
333C2×C4×Q8C2316yes—
334C2×C4×Q8C2316yes—
335C2×C4×Q8C2313yes—
336C2×C4×Q8C2312yes—
337C2×C4×D4—26no—
338C2×C4×D4C2313yes—
339C2×C4×D4C2316yes—
340C2×#117—23no—
341C22×C4⋊C4—23no—
342#501C2316yes—
343#501C23112yes—
344#500C2316yes—
345#500C2313yes—
346#498C2313yes—
347#497C2316yes—
348#497C23112yes—
349#494C2313yes—
350#492C2313yes—
351#492C2316yes—
352#491C2316yes—
353#491C23112yes—
354#491C23112yes—
355#491C23112yes—
356#491C23112yes—
357#489C2316yes—
358#487C2313yes—
359#487C2316yes—
360#487C2311yescharacteristic
361#487C2313yes—
362#487C2316yes—
363#487C2316yes—
364#487C2316yes—
365#487C2316yes—
366#486C2313yes—
367#485C2316yes—
368#485C23112yes—
369#485C2316yes—
370#484C2316yes—
371#484C23112yes—
372#484C23112yes—
373#483C2312yes—
374#483C2316yes—
375#483C2316yes—
376#481C2316yes—
377#480C2316yes—
378#479C2316yes—
379#479C23112yes—
380#479C23112yes—
381#479C23112yes—
382#479C23112yes—
383#479C2316yes—
384#479C23112yes—
385#477C2316yes—
386#477C2313yes—
387#477C2313yes—
388#477C2316yes—
389#477C2316yes—
390#477C2316yes—
391#477C2316yes—
392#477C2316yes—
393#476C2311yescharacteristic
394#476C2313yes—
395#476C2313yes—
396#476C2313yes—
397#475C2313yes—
398#475C2316yes—
399#475C2316yes—
400#475C2313yes—
401#474C23112yes—
402#474C2316yes—
403#470C2312yes—
404#470C2316yes—
405#468C23112yes—
406#468C2316yes—
407#468C2316yes—
408#467C23112yes—
409#467C2316yes—
410#467C2316yes—
411#465C2316yes—
412#465C23112yes—
413#465C2316yes—
414#464C2316yes—
415#464C2316yes—
416#464C23112yes—
417#462C2311yescharacteristic
418#462C2313yes—
419#462C2316yes—
420#462C2316yes—
421#462C2316yes—
422#462C2316yes—
423#462C23112yes—
424#461C2313yes—
425#461C2316yes—
426#461C2313yes—
427#461C2313yes—
428#461C2313yes—
429#461C2316yes—
430#461C2316yes—
431#461C23112yes—
432#461C23112yes—
433#461C2316yes—
434#461C23112yes—
435#461C23112yes—
436#460C2313yes—
437#460C2313yes—
438#460C2316yes—
439#452C2312yes—
440#452C2316yes—
441#451C2316yes—
442#451C2316yes—
443#451C23112yes—
444#450C2316yes—
445#450C2316yes—
446#448C2316yes—
447#448C23112yes—
448#448C2316yes—
449#448C23112yes—
450#446C2313yes—
451#446C2316yes—
452#446C2316yes—
453#446C2316yes—
454#446C2316yes—
455#446C2313yes—
456#446C2316yes—
457C8×Q8C2311yescharacteristic
458C8×Q8C2312yes—
459C8×Q8C2311yescharacteristic
460#441C2316yes—
461#441C2316yes—
462#441C23112yes—
463#440C23112yes—
464#440C2316yes—
465#440C23112yes—
466#440C23112yes—
467#440C23112yes—
468#440C2316yes—
469#440C23112yes—
470C4×Q16C2316yes—
471C4×Q16C2316yes—
472C4×Q16C2316yes—
473C4×Q16C2316yes—
474C4×SD16C2316yes—
475C4×SD16C2313yes—
476C4×SD16C2311yescharacteristic
477C4×SD16C2313yes—
478C4×SD16C2313yes—
479C4×SD16C2316yes—
480C4×SD16C2316yes—
481C4×SD16C2313yes—
482C4×SD16C2313yes—
483C4×SD16C2313yes—
484C4×SD16C2313yes—
485#436C2311yescharacteristic
486#436C2313yes—
487#435C2316yes—
488#435C23112yes—
489#435C2316yes—
490C8×D4C2313yes—
491C8×D4C2316yes—
492C8×D4C2313yes—
493#432C23112yes—
494#432C2316yes—
495#431C2313yes—
496#431C2313yes—
497#431C2316yes—
498#428C2316yes—
499C2×#107C2316yes—
500C2×#106C2313yes—
501#423C2316yes—
502C2×C4⋊C8C2313yes—
503C2×C4⋊C8C2316yes—
504#419C23112yes—
505#419C2316yes—
506#417C2312yes—
507C2×#103C2316yes—
508C2×#103C2316yes—
509C2×#103C2316yes—
510C2×#103C2316yes—
511C2×#103C2313yes—
512C2×#102C2313yes—
513C4×M16C2316yes—
514C2×#97C2316yes—
515C2×C4×C8C2313yes—
5162−1+4—28no—
517C2×#41—21no—
518C2×#41—23no—
519C2×#41—23no—
520C2×#41—26no—
521C2×#41—48no—
522C2×#41C2×D413yes—
523C2×#41C2×D416yes—
524C2×#41C2×D411yescharacteristic
525C2×#41C2412yes—
526C22×Q8—21no—
527C22×Q8—23no—
528C22×Q8C2×D413yes—
529C22×Q8C2×D412yes—
530C22×Q8C2413yes—
531C22×Q8C2416yes—
532C22×Q8C2416yes—
533C22×D4—23no—
534C22×D4C2413yes—
535C23×C4—23no—
536C23×C4—26no—
537#137—412no—
538C2×Q16C2416yes—
539C2×Q16C2416yes—
540C2×Q16C2412yes—
541C2×Q16C2416yes—
542C2×SD16—46no—
543C2×SD16—412no—
544C2×SD16C2411yescharacteristic
545C2×SD16C2416yes—
546C2×SD16C2413yes—
547C2×SD16C2413yes—
548C2×SD16C2413yes—
549C2×SD16C24112yes—
550C2×SD16C2416yes—
551C2×SD16C2416yes—
552C2×M16C2416yes—
553C2×M16C2412yes—
554C22×C8C2413yes—
555C22×C8C2416yes—
556C22×C8C2413yes—
557C4⋊Q8—26no—
558C4⋊Q8—26no—
559C4⋊Q8—23no—
560C4⋊Q8—23no—
561C4⋊Q8—26no—
562C4⋊Q8—26no—
563C4⋊Q8—212no—
564C4⋊Q8—23no—
565C4⋊Q8—26no—
566C4⋊Q8—23no—
567C4⋊Q8—26no—
568C4⋊Q8—212no—
569C4⋊Q8—23no—
570C4⋊Q8—23no—
571C4⋊Q8—26no—
572C4⋊Q8—212no—
573C4⋊Q8—26no—
574C4⋊Q8—23no—
575C4⋊Q8—23no—
576C4⋊Q8C2413yes—
577C4⋊Q8C2416yes—
578C4⋊Q8C24112yes—
579C4⋊Q8C2416yes—
580C4⋊Q8C2413yes—
581C4⋊Q8C2411yescharacteristic
582C4⋊Q8C2413yes—
583C4⋊Q8C2416yes—
584C4⋊Q8C2413yes—
585C4⋊Q8C2416yes—
586C4⋊Q8C2411yescharacteristic
587C4⋊Q8C2413yes—
588#127C2413yes—
589#126—26no—
590#126—212no—
591#126—26no—
592#126—212no—
593#126—26no—
594#125—23no—
595#125—26no—
596#125—23no—
597#125—26no—
598#125—212no—
599#125—26no—
600#125—26no—
601#125—26no—
602#125—26no—
603#125—212no—
604#125—212no—
605#125—212no—
606#125—26no—
607#125—26no—
608#125—21no—
609#125—23no—
610#125—26no—
611#125—212no—
612#125—212no—
613#125—23no—
614#125—26no—
615#125—212no—
616#125—26no—
617#125—23no—
618#125—23no—
619#125C2416yes—
620#125C24112yes—
621#124—26no—
622#124—26no—
623#124—23no—
624#124—26no—
625#124C2416yes—
626#123—26no—
627#123—212no—
628#123—26no—
629#123—212no—
630#123—26no—
631#123—26no—
632#123—212no—
633#123—22no—
634C22⋊Q8—23no—
635C22⋊Q8—26no—
636C22⋊Q8—26no—
637C22⋊Q8—26no—
638C22⋊Q8—23no—
639C22⋊Q8—26no—
640C22⋊Q8—26no—
641C22⋊Q8—23no—
642C22⋊Q8—23no—
643C22⋊Q8—23no—
644C22⋊Q8—212no—
645C22⋊Q8—26no—
646C22⋊Q8—26no—
647C22⋊Q8—26no—
648C22⋊Q8—212no—
649C22⋊Q8—212no—
650C22⋊Q8—212no—
651C22⋊Q8—23no—
652C22⋊Q8—23no—
653C22⋊Q8—212no—
654C22⋊Q8—26no—
655C22⋊Q8—26no—
656C22⋊Q8—26no—
657C22⋊Q8—22no—
658C22⋊Q8—26no—
659C22⋊Q8—212no—
660C22⋊Q8—26no—
661C22⋊Q8—212no—
662C22⋊Q8—26no—
663C22⋊Q8—212no—
664C22⋊Q8—26no—
665C22⋊Q8C2412yes—
666C22⋊Q8C2416yes—
667C22⋊Q8C2416yes—
668C22⋊Q8C2416yes—
669C22⋊Q8C2412yes—
670C22⋊Q8C2416yes—
671#121—21no—
672#121—23no—
673#121—212no—
674#121—26no—
675#121—23no—
676#121—23no—
677#121—23no—
678#121—26no—
679#121C2416yes—
680#121C2416yes—
681#120—26no—
682#120—26no—
683C4×Q8—23no—
684C4×Q8—26no—
685C4×Q8—21no—
686C4×Q8—26no—
687C4×Q8—26no—
688C4×Q8—26no—
689C4×Q8—22no—
690C4×Q8—22no—
691C4×Q8—23no—
692C4×Q8—26no—
693C4×Q8—21no—
694C4×Q8—26no—
695C4×Q8—26no—
696C4×Q8—26no—
697C4×Q8—212no—
698C4×Q8—26no—
699C4×Q8—23no—
700C4×Q8—23no—
701C4×Q8—23no—
702C4×Q8—26no—
703C4×Q8—26no—
704C4×Q8—212no—
705C4×Q8—26no—
706C4×Q8—23no—
707C4×Q8—23no—
708C4×Q8C2×D412yes—
709C4×Q8C2×D416yes—
710C4×Q8C2×D416yes—
711C4×Q8C2×D416yes—
712C4×Q8C2×D416yes—
713C4×Q8C2×D411yescharacteristic
714C4×Q8C2×D413yes—
715C4×Q8C2411yescharacteristic
716C4×Q8C2413yes—
717C4×Q8C2416yes—
718C4×Q8C2413yes—
719C4×Q8C2413yes—
720C4×Q8C2416yes—
721C4×Q8C24112yes—
722C4×Q8C2416yes—
723C4×Q8C2416yes—
724C4×Q8C2416yes—
725C4×Q8C2411yescharacteristic
726C4×Q8C2413yes—
727C4×Q8C2416yes—
728C4×D4—26no—
729C4×D4—26no—
730C4×D4—21no—
731C4×D4—23no—
732C4×D4—26no—
733C4×D4—212no—
734C4×D4—23no—
735C4×D4—23no—
736C4×D4—26no—
737C4×D4—212no—
738C4×D4—26no—
739C4×D4—26no—
740C4×D4—26no—
741C4×D4—26no—
742C4×D4—212no—
743C4×D4—26no—
744C4×D4—23no—
745C4×D4—212no—
746C4×D4—23no—
747C4×D4—23no—
748C4×D4C2×D416yes—
749C4×D4C2×D4112yes—
750C4×D4C2×D413yes—
751C4×D4C2×D413yes—
752C4×D4C2×D416yes—
753C4×D4C2411yescharacteristic
754C4×D4C2416yes—
755C4×D4C2413yes—
756C4×D4C2413yes—
757C4×D4C24112yes—
758C4×D4C2413yes—
759C4×D4C2413yes—
760C4×D4C2416yes—
761C4×D4C2411yescharacteristic
762#117—23no—
763#117—212no—
764#117—26no—
765#117—26no—
766#117—23no—
767#117—23no—
768#117—23no—
769#117—23no—
770#117—26no—
771#117—26no—
772#117—26no—
773#117—212no—
774#117C2×D413yes—
775#117C2×D413yes—
776#117C2×D416yes—
777#117C2×D4112yes—
778#117C2×D416yes—
779#117C2416yes—
780C2×C4⋊C4—26no—
781C2×C4⋊C4—23no—
782C2×C4⋊C4—26no—
783C2×C4⋊C4—26no—
784C2×C4⋊C4—23no—
785C2×C4⋊C4—23no—
786C2×C4⋊C4—26no—
787C2×C4⋊C4—26no—
788C2×C4⋊C4—26no—
789C2×C4⋊C4—23no—
790C2×C4⋊C4—26no—
791C2×C4⋊C4—26no—
792C2×C4⋊C4—23no—
793C2×C4⋊C4—26no—
794C2×C4⋊C4—26no—
795C2×C4⋊C4—26no—
796C2×C4⋊C4—21no—
797C2×C4⋊C4C2×D413yes—
798C2×C4⋊C4C2×D416yes—
799C2×C4⋊C4C2×D416yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2416yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2412yes—
804C2×C22⋊C4—23no—
805C2×C22⋊C4—26no—
806C2×C22⋊C4—26no—
807C2×C42—26no—
808C2×C42—26no—
809C2×C42—23no—
810C2×C42—26no—
811C2×C42C2416yes—
812C2×C42C2413yes—
813C2×C42C2416yes—
814#107C2416yes—
815#107C24112yes—
816#107C2416yes—
817#107C2416yes—
818#107C2416yes—
819#106C2411yescharacteristic
820#106C2413yes—
821#106C2413yes—
822#106C2413yes—
823#106C2416yes—
824#106C2412yes—
825#106C2416yes—
826C4⋊C8C2416yes—
827C4⋊C8C2413yes—
828C4⋊C8C2416yes—
829C4⋊C8C24112yes—
830C4⋊C8C2413yes—
831C4⋊C8C2411yescharacteristic
832C4⋊C8C2413yes—
833C4⋊C8C2416yes—
834#103C2411yescharacteristic
835#103C2416yes—
836#103C2416yes—
837#103C2416yes—
838#103C2416yes—
839#103C2413yes—
840#103C24112yes—
841#103C24112yes—
842#103C24112yes—
843#103C2413yes—
844#103C2413yes—
845#103C24112yes—
846#103C2412yes—
847#103C2412yes—
848#103C2416yes—
849#103C2416yes—
850#103C2416yes—
851#103C2412yes—
852#103C2416yes—
853#102C2411yescharacteristic
854#102C2413yes—
855#102C2413yes—
856#102C2413yes—
857#102C2412yes—
858#102C2416yes—
859#102C2416yes—
860C22⋊C8C2412yes—
861C22⋊C8C2416yes—
862C22⋊C8C2416yes—
863C22⋊C8C2416yes—
864#97C2416yes—
865#97C24112yes—
866#97C2416yes—
867C4×C8C2411yescharacteristic
868C4×C8C2413yes—
869C4×C8C2413yes—
870C4×C8C2413yes—
871C4×C8C2416yes—
872C24—23no—
873#41—224no—
874#41—212no—
875#41—24no—
876#41—42no—
877#41—44no—
878#41—412no—
879#41—412no—
880#41—166no—
881#41#13718yescomplemented
882C2×Q8—28no—
883C2×Q8—212no—
884C2×Q8—23no—
885C2×Q8—26no—
886C2×Q8—21no—
887C2×Q8—23no—
888C2×Q8—26no—
889C2×Q8—26no—
890C2×Q8—23no—
891C2×Q8—23no—
892C2×Q8—26no—
893C2×Q8—43no—
894C2×Q8—46no—
895C2×Q8—46no—
896C2×Q8—43no—
897C2×Q8—46no—
898C2×Q8—46no—
899C2×Q8—44no—
900C2×Q8—163no—
901C2×Q8C22×D413yes—
902C2×Q8C22×D416yes—
903C2×Q8C22×D411yescharacteristic
904C2×Q8C2511yescharacteristic
905C2×Q8C2516yes—
906C2×Q8C2513yes—
907C2×Q8C2512yes—
908C2×D4—26no—
909C2×D4—22no—
910C2×D4—26no—
911C2×D4—26no—
912C2×D4—23no—
913C2×D4—23no—
914C2×D4—23no—
915C2×D4—43no—
916C2×D4—412no—
917C2×D4C22×D416yes—
918C2×D4C22×D411yescharacteristic
919C2×D4C22×D413yes—
920C2×D4C2513yes—
921C2×D4C2511yescharacteristic
922C22×C4—23no—
923C22×C4—22no—
924C22×C4—23no—
925C22×C4—26no—
926C22×C4—26no—
927C22×C4—23no—
928C22×C4—26no—
929C22×C4—22no—
930C22×C4—23no—
931C22×C4—21no—
932C22×C4—23no—
933C22×C4—23no—
934C22×C4—26no—
935C22×C4—212no—
936C22×C4—412no—
937C22×C4—166no—
938C22×C4C22×D416yes—
939C22×C4C22×D416yes—
940C22×C4C22×D413yes—
941C22×C4C22×D416yes—
942C22×C4C22×D416yes—
943C22×C4C22×D413yes—
944C22×C4C2513yes—
945C22×C4C2512yes—
946Q16—46no—
947Q16—42no—
948Q16—46no—
949Q16—46no—
950SD16—22no—
951SD16—212no—
952SD16—26no—
953SD16—43no—
954SD16—412no—
955SD16—43no—
956SD16—46no—
957SD16—46no—
958M16—42no—
959M16—46no—
960C2×C8—43no—
961C2×C8—43no—
962C2×C8—46no—
963C2×C8C2511yescharacteristic
964C2×C8C2511yescharacteristic
965C2×C8C2512yes—
966C2×C8C2513yes—
967C2×C8C2513yes—
968C2×C8C2516yes—
969C4⋊C4—23no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—212no—
973C4⋊C4—26no—
974C4⋊C4—21no—
975C4⋊C4—23no—
976C4⋊C4—26no—
977C4⋊C4—212no—
978C4⋊C4—23no—
979C4⋊C4—26no—
980C4⋊C4—23no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—212no—
984C4⋊C4—23no—
985C4⋊C4—26no—
986C4⋊C4—23no—
987C4⋊C4—21no—
988C4⋊C4—22no—
989C4⋊C4—212no—
990C4⋊C4—212no—
991C4⋊C4—26no—
992C4⋊C4—23no—
993C4⋊C4—23no—
994C4⋊C4—26no—
995C4⋊C4—23no—
996C4⋊C4—26no—
997C4⋊C4—22no—
998C4⋊C4—23no—
999C4⋊C4—26no—
1000C4⋊C4—23no—
1001C4⋊C4—21no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—23no—
1006C4⋊C4—22no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—21no—
1011C4⋊C4C22×D413yes—
1012C4⋊C4C22×D416yes—
1013C4⋊C4C22×D411yescharacteristic
1014C4⋊C4C22×D413yes—
1015C4⋊C4C22×D416yes—
1016C4⋊C4C22×D4112yes—
1017C4⋊C4C22×D413yes—
1018C4⋊C4C22×D416yes—
1019C4⋊C4C2511yescharacteristic
1020C4⋊C4C2513yes—
1021C4⋊C4C2512yes—
1022C4⋊C4C2511yescharacteristic
1023C4⋊C4C2513yes—
1024C4⋊C4C2516yes—
1025C22⋊C4—26no—
1026C22⋊C4—22no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—26no—
1030C22⋊C4—26no—
1031C22⋊C4—22no—
1032C22⋊C4—21no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—23no—
1037C22⋊C4—23no—
1038C22⋊C4—212no—
1039C22⋊C4—23no—
1040C22⋊C4—26no—
1041C22⋊C4—26no—
1042C22⋊C4C22×D416yes—
1043C22⋊C4C22×D416yes—
1044C22⋊C4C22×D416yes—
1045C22⋊C4C22×D412yes—
1046C42—26no—
1047C42—23no—
1048C42—21no—
1049C42—26no—
1050C42—26no—
1051C42—26no—
1052C42—212no—
1053C42—26no—
1054C42—26no—
1055C42—23no—
1056C42—23no—
1057C42C22×D416yes—
1058C42C22×D4112yes—
1059C42C22×D416yes—
1060C42C22×D413yes—
1061C42C22×D413yes—
1062C42C2511yescharacteristic
1063C42C2513yes—
1064C42C2516yes—
1065C23—21no—
1066C23—23no—
1067C23—46no—
1068C23—46no—
1069C23—83no—
1070C23C23×D412yes—
1071C23C23×D413yes—
1072Q8—212no—
1073Q8—26no—
1074Q8—21no—
1075Q8—26no—
1076Q8—23no—
1077Q8—22no—
1078Q8—23no—
1079Q8—26no—
1080Q8—22no—
1081Q8—21no—
1082Q8—46no—
1083Q8—86no—
1084Q8—83no—
1085Q8—81no—
1086Q8—86no—
1087Q8—83no—
1088Q8—86no—
1089Q8—83no—
1090Q8—86no—
1091Q8C2×#13714yes—
1092D4—212no—
1093D4—23no—
1094D4—21no—
1095D4—23no—
1096D4—22no—
1097D4—46no—
1098D4—44no—
1099D4—412no—
1100D4—46no—
1101D4—83no—
1102D4—86no—
1103D4C2×#137112yes—
1104D4#58512yes—
1105C2×C4—212no—
1106C2×C4—23no—
1107C2×C4—22no—
1108C2×C4—23no—
1109C2×C4—22no—
1110C2×C4—212no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—23no—
1114C2×C4—22no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—26no—
1118C2×C4—23no—
1119C2×C4—26no—
1120C2×C4—21no—
1121C2×C4—46no—
1122C2×C4—43no—
1123C2×C4—46no—
1124C2×C4—44no—
1125C2×C4—46no—
1126C2×C4—42no—
1127C2×C4—46no—
1128C2×C4—46no—
1129C2×C4—46no—
1130C2×C4—86no—
1131C2×C4—812no—
1132C2×C4—83no—
1133C2×C4—82no—
1134C2×C4—86no—
1135C2×C4—83no—
1136C2×C4—86no—
1137C2×C4—86no—
1138C2×C4C2×#137112yes—
1139C2×C4C23×D416yes—
1140C2×C4C23×D412yes—
1141C2×C4C23×D416yes—
1142C2×C4C23×D413yes—
1143C2×C4C23×D411yescharacteristic
1144C2×C4C23×D413yes—
1145C2×C4C23×D413yes—
1146C2×C4C23×D411yescharacteristic
1147C2×C4C2611yescharacteristic
1148C8—21no—
1149C8—26no—
1150C8—23no—
1151C8—21no—
1152C8—23no—
1153C8—22no—
1154C22—23no—
1155C22—23no—
1156C22—22no—
1157C22—22no—
1158C22—22no—
1159C22—22no—
1160C22—41no—
1161C22—41no—
1162C22—43no—
1163C22—43no—
1164C22—43no—
1165C22—812no—
1166C22C22×#13716yes—
1167C22C24×D411yescharacteristic
1168C4—22no—
1169C4—23no—
1170C4—26no—
1171C4—26no—
1172C4—23no—
1173C4—21no—
1174C4—42no—
1175C4—41no—
1176C4—46no—
1177C4—43no—
1178C4—41no—
1179C4—43no—
1180C4—41no—
1181C4—46no—
1182C4—43no—
1183C4—42no—
1184C4C22×#13716yes—
1185C4C22×#13712yes—
1186C4C2×#58511yescharacteristic
1187C42−1+611yescharacteristic
1188C2—26no—
1189C2—42no—
1190C2—42no—
1191C2—83no—
1192C2#6300211yescharacteristic
1193C2C23×#13711yescharacteristic
1194C2#6309211yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#63000C2
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. #63004C2semidirect
3. #62577C2semidirect
4. #62540C2semidirect
5. #62530C2semidirect
6. #62394C2semidirect
7. #62366C2semidirect
8. #62139C2semidirect
9. #62114C2semidirect
10. #62100C2semidirect
11. #61980C2semidirect
12. #61960C2semidirect
13. #61948C2semidirect
14. #61906C2semidirect
15. #61893C2semidirect
16. #61846C2semidirect
17. #61826C2semidirect
18. #61453C2semidirect
19. #61438C2semidirect
20. SD16×#41C2semidirect
21. #61322C2semidirect
22. C2×#3372C2semidirect
23. #60343C2semidirect
35. #3503C22semidirect
36. #3503C22semidirect
39. #3502C22semidirect
40. #3502C22semidirect
47. Q8×#41C22semidirect
48. Q8×#41C22semidirect
49. C2×#557C22semidirect
50. C2×#557C22semidirect
57. #3400C22semidirect
58. #3400C22semidirect
59. #3400C22semidirect
60. #3398C22semidirect
61. #3398C22semidirect
64. #3387C22semidirect
67. #3385C22semidirect
68. #3385C22semidirect
69. Q8×Q16C22semidirect
71. #3375C22semidirect
72. #3374C22semidirect
73. #3374C22semidirect
74. #3374C22semidirect
80. #3372C22semidirect
81. #3372C22semidirect
82. #3372C22semidirect
83. #3372C22semidirect
84. #3372C22semidirect
85. #3372C22semidirect
86. #3369C22semidirect
87. #3363C22semidirect
88. #3363C22semidirect
89. #3363C22semidirect
93. #3357C22semidirect
94. #3346C22semidirect
95. #3344C22semidirect
96. #3338C22semidirect
99. #3329C22semidirect
100. #3329C22semidirect
101. #3320C22semidirect
102. #3320C22semidirect
103. #3320C22semidirect
105. #3312C22semidirect
106. #3312C22semidirect
107. #3299C22semidirect
108. #3299C22semidirect
109. #3299C22semidirect
118. #3254C22semidirect
119. #3252C22semidirect
120. #3249C22semidirect
121. #3248C22semidirect
123. #3237C22semidirect
124. #3236C22semidirect
125. #3231C22semidirect
126. #3230C22semidirect
127. #3230C22semidirect
128. #3218C22semidirect
129. #3218C22semidirect
130. #3209C22semidirect
132. #3206C22semidirect
133. #3182C22semidirect
134. #3181C22semidirect
135. #3172C22semidirect
136. #3170C22semidirect
138. #3139C22semidirect
139. C2×#491C22semidirect
140. C2×#487C22semidirect
141. #3117C22semidirect
143. #3112C22semidirect
145. #3108C22semidirect
147. #3104C22semidirect
151. #3078C22semidirect
152. C2×#479C22semidirect
153. C2×#477C22semidirect
157. #2990C22semidirect
158. #2989C22semidirect
160. #2984C22semidirect
161. #2983C22semidirect
162. #2970C22semidirect
163. #2965C22semidirect
165. Q8×M16C22semidirect
166. C2×#446C22semidirect
881. #41#137semidirect

Maximal subgroups

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

subgroupindex
#630042
#630002
#625772
#625402
#625302
#623942
#623662
#621392
#621142
#621002
#619802
#619602
#619482
#619062
#618932
#618462
#618262
#614532
#614382
SD16×#412
#613222
C2×#33722
#603432