Finite Group Databasebeta

← #10585263

Subgroups — #10585263

Order 512.

6028 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#63009C211yesmaximal, characteristic
2Q8×2−1+4C211yesmaximal, characteristic, complemented
3#62582C216yesmaximal, complemented
4#62542C213yesmaximal, complemented
5#62530C211yesmaximal, characteristic, complemented
6#62398C212yesmaximal, complemented
7#62366C213yesmaximal, complemented
8#62131C216yesmaximal, complemented
9#62108C213yesmaximal, complemented
10#62096C211yesmaximal, characteristic, complemented
11#61991C216yesmaximal, complemented
12#61966C213yesmaximal, complemented
13#61952C211yesmaximal, characteristic, complemented
14#61909C212yesmaximal, complemented
15#61889C213yesmaximal, complemented
16#61838C212yesmaximal, complemented
17#61830C213yesmaximal, complemented
18#61457C216yesmaximal, complemented
19#61438C213yesmaximal, complemented
20SD16×#41C211yesmaximal, characteristic, complemented
21#61319C212yesmaximal, complemented
22C2×#3369C213yesmaximal, complemented
23#60343C211yesmaximal, characteristic, complemented
24#3523C2212yes—
25#3521—26no—
26#3518—22no—
27#3514C2216yes—
28#3511C2213yes—
29#3507C2213yes—
30#3503—21no—
31#3503—23no—
32#3503—26no—
33#3503C2211yescharacteristic
34#3503C2211yescharacteristic
35#3503C2213yescomplemented
36#3503C2216yescomplemented
37#3502—23no—
38#3502—22no—
39#3502C2213yescomplemented
40#3502C2212yescomplemented
41#3495—23no—
42#3493—23no—
43#3489—21no—
44#3482C2216yes—
45#3480C2212yes—
46Q8×#41C2211yescharacteristic
47Q8×#41C2213yescomplemented
48Q8×#41C2216yescomplemented
49C2×Q82C2213yescomplemented
50C2×Q82C2212yescomplemented
51#3475C2213yes—
52C2×#556C2213yes—
53D4×#41C2211yescharacteristic
54C4×2−1+4—21no—
55C4×2−1+4C2211yescharacteristic
56#3428—21no—
57#3400C2216yescomplemented
58#3398C2216yes—
59#3398C2213yes—
60#3398C2216yescomplemented
61#3398C2216yescomplemented
62#3395C2212yescomplemented
63#3392C2211yescharacteristic
64#3387C2216yescomplemented
65#3387C2216yescomplemented
66#3387C2216yescomplemented
67#3385C2213yescomplemented
68#3385C2216yescomplemented
69Q8×SD16C2211yescharacteristic
70Q8×SD16C2212yes—
71#3375C2216yescomplemented
72#3375C2216yescomplemented
73#3375C2216yescomplemented
74#3374C2216yescomplemented
75#3372C2213yescomplemented
76#3369C2216yes—
77#3369C2216yes—
78#3369C2216yes—
79#3369C2213yes—
80#3369C2216yes—
81#3369C2216yescomplemented
82#3369C2216yescomplemented
83#3369C2216yescomplemented
84#3369C2216yescomplemented
85#3369C2216yescomplemented
86#3369C2216yescomplemented
87#3363C2212yescomplemented
88#3363C2212yescomplemented
89#3363C2212yescomplemented
90#3362C2211yescharacteristic
91#3362C2212yes—
92#3359C2211yescharacteristic
93#3357C2213yes—
94#3344C22112yescomplemented
95#3344C2216yescomplemented
96#3335C2216yes—
97#3335C2213yes—
98#3331C2216yescomplemented
99#3331C2213yescomplemented
100#3329C2211yescharacteristic
101#3316C22112yescomplemented
102#3316C22112yescomplemented
103#3316C22112yescomplemented
104#3314C22112yes—
105#3314C2216yes—
106#3312C2216yescomplemented
107#3299C2216yescomplemented
108#3299C2216yescomplemented
109#3299C2216yescomplemented
110#3298C2213yes—
111#3295C2216yes—
112#3295C2213yes—
113D4×Q16C2216yescomplemented
114D4×SD16C2213yes—
115#3276C2213yescomplemented
116#3270C22112yescomplemented
117#3266C2216yes—
118#3255C2216yescomplemented
119#3252C2216yes—
120#3249C2213yescomplemented
121#3248C22112yescomplemented
122#3246C2213yes—
123#3239C22112yescomplemented
124#3238C2216yes—
125#3230C2213yescomplemented
126#3229C2216yescomplemented
127#3227C2213yes—
128#3216C2216yescomplemented
129#3215C22112yes—
130#3210C2216yescomplemented
131#3209C2213yescomplemented
132#3209C2213yescomplemented
133#3185C2216yescomplemented
134#3181C22112yescomplemented
135#3172C2216yes—
136#3170C2213yescomplemented
137#3167C2213yes—
138#3141C2216yescomplemented
139C2×#489C2216yes—
140C2×#487C2213yescomplemented
141#3117C22112yescomplemented
142#3116C2216yescomplemented
143#3113C2216yescomplemented
144#3113C22112yescomplemented
145#3108C2216yes—
146#3107C2216yescomplemented
147#3104C2213yescomplemented
148#3103C2213yes—
149#3101C2213yes—
150#3101C2213yes—
151#3079C2216yescomplemented
152C2×#475C2216yescomplemented
153C2×#476C2213yes—
154#3037C2216yescomplemented
155C2×#464C2216yes—
156C2×#462C2213yescomplemented
157#2990C2216yescomplemented
158#2989C2213yescomplemented
159#2988C2211yescharacteristic
160#2984C2212yescomplemented
161#2983C2213yescomplemented
162#2970C2216yescomplemented
163#2965C2213yescomplemented
164C8×#41C2211yescharacteristic
165Q8×M16C2212yescomplemented
166C2×#446C2213yescomplemented
167C4×#137C2216yescomplemented
168C2×#441C2216yescomplemented
169C2×C4×SD16C2213yes—
170C2×2−1+4D411yescharacteristic
171C22×#41—21no—
172C2×#137C2316yes—
173C22×Q16C2316yes—
174C22×SD16C2313yes—
175#559C2316yes—
176Q82—22no—
177Q82—26no—
178Q82—26no—
179Q82—26no—
180Q82—21no—
181Q82C2311yescharacteristic
182Q82C2312yes—
183Q82C2313yes—
184Q82C2316yes—
185Q82C2316yes—
186Q82C2316yes—
187Q82C2316yes—
188#557—21no—
189#557—26no—
190#557—23no—
191#557—21no—
192#557—26no—
193#557—23no—
194#557—22no—
195#557—26no—
196#557—26no—
197#557—26no—
198#557C2311yescharacteristic
199#557C2312yes—
200#557C2313yes—
201#557C2316yes—
202#557C2316yes—
203#556—26no—
204#556—26no—
205#556—26no—
206#556—26no—
207#556C2313yes—
208#556C2316yes—
209#556C2316yes—
210#556C2316yes—
211#555—23no—
212#555—26no—
213#555C2311yescharacteristic
214#554—23no—
215#554—23no—
216#554—26no—
217#554—212no—
218#554—26no—
219#554—23no—
220#554—23no—
221#554C2313yes—
222#554C2313yes—
223#554C2313yes—
224#554C2316yes—
225#554C23112yes—
226#554C2316yes—
227#553—23no—
228#553—26no—
229#553—26no—
230#552—23no—
231#552—26no—
232#552—212no—
233#552—26no—
234#552C2316yes—
235#551—26no—
236#551—212no—
237#550C2311yescharacteristic
238D4×Q8—22no—
239D4×Q8—23no—
240D4×Q8—26no—
241D4×Q8—212no—
242D4×Q8—26no—
243D4×Q8—23no—
244D4×Q8C2311yescharacteristic
245D4×Q8C2313yes—
246D4×Q8C2316yes—
247D4×Q8C2316yes—
248D4×Q8C2311yescharacteristic
249#548—22no—
250#548—21no—
251#548C23112yes—
252#547—26no—
253#547C2313yes—
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—26no—
272#538—212no—
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#532C2316yes—
289#532C2313yes—
290C2×C4⋊Q8—23no—
291C2×C4⋊Q8—26no—
292C2×C4⋊Q8—26no—
293C2×C4⋊Q8C2313yes—
294C2×C4⋊Q8C2316yes—
295C2×C4⋊Q8C2316yes—
296C2×C4⋊Q8C2313yes—
297#529—26no—
298#529—212no—
299#529—26no—
300#529C2316yes—
301#529C23112yes—
302C2×#126—26no—
303C2×#124C2316yes—
304#525—23no—
305#525—23no—
306C2×C22⋊Q8—23no—
307#520—21no—
308#520—21no—
309#520—23no—
310#520—26no—
311#520—23no—
312#520—23no—
313#520D411yescharacteristic
314#520D413yes—
315#520D416yes—
316#519—23no—
317#519—22no—
318#519—22no—
319#519D413yes—
320#519D412yes—
321#518—26no—
322C4×#41—21no—
323C4×#41—23no—
324C4×#41—26no—
325C4×#41—22no—
326C4×#41—26no—
327C4×#41C2316yes—
328C4×#41C2311yescharacteristic
329C4×#41C2313yes—
330C4×#41C2316yes—
331C2×C4×Q8—23no—
332C2×C4×Q8—22no—
333C2×C4×Q8C2316yes—
334C2×C4×Q8C2313yes—
335C2×C4×Q8C2316yes—
336C2×C4×Q8C2316yes—
337C2×C4×Q8C2313yes—
338C2×C4×Q8C2312yes—
339C2×C4×D4C2313yes—
340C2×#117—23no—
341C2×#117—23no—
342#501C2316yes—
343#501C23112yes—
344#500C2313yes—
345#498C2313yes—
346#498C2316yes—
347#497C2316yes—
348#497C23112yes—
349#494C2316yes—
350#494C2313yes—
351#492C2313yes—
352#491C2316yes—
353#489C2316yes—
354#489C23112yes—
355#489C23112yes—
356#489C23112yes—
357#489C23112yes—
358#487C2311yescharacteristic
359#487C2313yes—
360#487C2316yes—
361#487C2313yes—
362#487C2316yes—
363#487C2316yes—
364#487C2316yes—
365#486C2313yes—
366#486C2316yes—
367#485C2312yes—
368#485C2316yes—
369#484C2316yes—
370#484C23112yes—
371#483C2316yes—
372#483C23112yes—
373#483C2316yes—
374#483C2316yes—
375#481C2316yes—
376#481C23112yes—
377#480C2316yes—
378#479C2316yes—
379#479C23112yes—
380#479C2316yes—
381#477C2311yescharacteristic
382#477C2316yes—
383#477C2316yes—
384#477C2313yes—
385#477C2316yes—
386#476C2313yes—
387#476C2316yes—
388#476C2313yes—
389#476C2316yes—
390#476C2313yes—
391#476C2313yes—
392#476C2316yes—
393#475C2316yes—
394#475C23112yes—
395#475C23112yes—
396#475C23112yes—
397#475C2313yes—
398#475C2316yes—
399#475C2313yes—
400#475C23112yes—
401#474C23112yes—
402#474C2316yes—
403#470C23112yes—
404#470C2316yes—
405#470C2316yes—
406#468C2312yes—
407#468C2316yes—
408#467C2316yes—
409#467C23112yes—
410#467C2316yes—
411#465C2316yes—
412#465C23112yes—
413#465C2316yes—
414#464C2316yes—
415#464C2316yes—
416#464C23112yes—
417#464C23112yes—
418#464C23112yes—
419#464C23112yes—
420#464C23112yes—
421#462C2313yes—
422#462C2316yes—
423#462C2313yes—
424#462C2316yes—
425#462C2316yes—
426#462C2316yes—
427#462C2316yes—
428#462C23112yes—
429#462C2316yes—
430#462C2316yes—
431#461C2311yescharacteristic
432#461C2313yes—
433#461C2313yes—
434#461C2313yes—
435#461C2316yes—
436#460C2313yes—
437#460C2313yes—
438#460C2316yes—
439#452C2316yes—
440#452C23112yes—
441#452C2316yes—
442#451C2316yes—
443#451C2316yes—
444#451C23112yes—
445#451C23112yes—
446#450C2316yes—
447#450C2316yes—
448#448C2312yes—
449#448C2316yes—
450#446C2313yes—
451#446C2316yes—
452#446C2316yes—
453#446C2316yes—
454#446C2316yes—
455#446C2313yes—
456#446C2316yes—
457C8×Q8C2311yescharacteristic
458C8×Q8C2312yes—
459C8×Q8C2311yescharacteristic
460#441C2316yes—
461#441C23112yes—
462#441C23112yes—
463#441C23112yes—
464#441C23112yes—
465#441C2316yes—
466#441C23112yes—
467#440C23112yes—
468#440C2316yes—
469#440C2316yes—
470C4×Q16C2316yes—
471C4×Q16C2316yes—
472C4×Q16C2316yes—
473C4×Q16C2316yes—
474C4×SD16C2311yescharacteristic
475C4×SD16C2316yes—
476C4×SD16C2313yes—
477C4×SD16C2316yes—
478C4×SD16C2313yes—
479C4×SD16C2313yes—
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#432C2316yes—
494#432C23112yes—
495#431C2313yes—
496#431C2313yes—
497#431C2316yes—
498#428C2316yes—
499C2×#106C2313yes—
500C2×#106C2316yes—
501#423C2316yes—
502C2×C4⋊C8C2316yes—
503C2×C4⋊C8C2313yes—
504#419C2312yes—
505#417C23112yes—
506#417C2316yes—
507C2×#103C2316yes—
508C2×#103C2316yes—
509C2×#103C2316yes—
510C2×#103C2313yes—
511C2×#102C2313yes—
512C2×#102C2316yes—
513C4×M16C2316yes—
514C2×#97C2316yes—
515C2×C4×C8C2313yes—
5162−1+4—28no—
517C2×#41—21no—
518C2×#41—23no—
519C2×#41—23no—
520C2×#41—48no—
521C2×#41C2×D413yes—
522C2×#41C2×D416yes—
523C2×#41C2×D411yescharacteristic
524C2×#41C2416yes—
525C22×Q8—21no—
526C22×Q8—26no—
527C22×Q8—23no—
528C22×Q8—26no—
529C22×Q8C2×D413yes—
530C22×Q8C2×D412yes—
531C22×Q8C2413yes—
532C22×Q8C2412yes—
533C22×Q8C2416yes—
534C22×D4—23no—
535C22×D4C2413yes—
536C23×C4—23no—
537#137—412no—
538C2×Q16—412no—
539C2×Q16C2416yes—
540C2×Q16C24112yes—
541C2×Q16C2416yes—
542C2×Q16C2416yes—
543C2×Q16C2416yes—
544C2×SD16—46no—
545C2×SD16C2411yescharacteristic
546C2×SD16C2413yes—
547C2×SD16C2413yes—
548C2×SD16C2413yes—
549C2×SD16C2416yes—
550C2×SD16C2412yes—
551C2×SD16C2416yes—
552C2×M16C2416yes—
553C2×M16C2412yes—
554C22×C8C2413yes—
555C22×C8C2416yes—
556C22×C8C2413yes—
557C4⋊Q8—26no—
558C4⋊Q8—23no—
559C4⋊Q8—26no—
560C4⋊Q8—23no—
561C4⋊Q8—26no—
562C4⋊Q8—212no—
563C4⋊Q8—26no—
564C4⋊Q8—26no—
565C4⋊Q8—26no—
566C4⋊Q8—26no—
567C4⋊Q8—212no—
568C4⋊Q8—212no—
569C4⋊Q8—212no—
570C4⋊Q8—21no—
571C4⋊Q8—23no—
572C4⋊Q8—26no—
573C4⋊Q8—26no—
574C4⋊Q8—23no—
575C4⋊Q8—26no—
576C4⋊Q8—26no—
577C4⋊Q8—212no—
578C4⋊Q8—23no—
579C4⋊Q8—23no—
580C4⋊Q8—23no—
581C4⋊Q8C2413yes—
582C4⋊Q8C2416yes—
583C4⋊Q8C2411yescharacteristic
584C4⋊Q8C2413yes—
585C4⋊Q8C2416yes—
586C4⋊Q8C2416yes—
587C4⋊Q8C24112yes—
588C4⋊Q8C2413yes—
589C4⋊Q8C2413yes—
590C4⋊Q8C2416yes—
591C4⋊Q8C2413yes—
592C4⋊Q8C2411yescharacteristic
593#127C2413yes—
594#126—26no—
595#126—212no—
596#126—212no—
597#126—212no—
598#126—26no—
599#126—212no—
600#126—26no—
601#125—26no—
602#125—212no—
603#125—26no—
604#125—23no—
605#125—26no—
606#125—23no—
607#125—26no—
608#125—212no—
609#125—23no—
610#125—23no—
611#125—26no—
612#125—26no—
613#125—212no—
614#125—26no—
615#125—23no—
616#125—26no—
617#125—26no—
618#125—212no—
619#125—23no—
620#125—23no—
621#125C2416yes—
622#124—26no—
623#124—22no—
624#124—212no—
625#124—212no—
626#124—23no—
627#124C2416yes—
628#124C24112yes—
629#123—26no—
630#123—212no—
631#123—26no—
632#123—212no—
633#123—26no—
634#123—26no—
635#123—26no—
636C22⋊Q8—23no—
637C22⋊Q8—26no—
638C22⋊Q8—26no—
639C22⋊Q8—26no—
640C22⋊Q8—23no—
641C22⋊Q8—26no—
642C22⋊Q8—23no—
643C22⋊Q8—212no—
644C22⋊Q8—23no—
645C22⋊Q8—23no—
646C22⋊Q8—26no—
647C22⋊Q8—26no—
648C22⋊Q8—23no—
649C22⋊Q8—23no—
650C22⋊Q8—26no—
651C22⋊Q8—212no—
652C22⋊Q8—212no—
653C22⋊Q8—26no—
654C22⋊Q8—26no—
655C22⋊Q8—26no—
656C22⋊Q8—22no—
657C22⋊Q8—26no—
658C22⋊Q8—212no—
659C22⋊Q8—26no—
660C22⋊Q8—212no—
661C22⋊Q8—26no—
662C22⋊Q8—212no—
663C22⋊Q8—26no—
664C22⋊Q8C2416yes—
665C22⋊Q8C2416yes—
666C22⋊Q8C2416yes—
667C22⋊Q8C2416yes—
668C22⋊Q8C2412yes—
669C22⋊Q8C2416yes—
670#121—21no—
671#121—23no—
672#121—212no—
673#121—26no—
674#121—26no—
675#121—23no—
676#121—23no—
677#121—23no—
678#121—26no—
679#121C2412yes—
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—23no—
691C4×Q8—26no—
692C4×Q8—21no—
693C4×Q8—22no—
694C4×Q8—26no—
695C4×Q8—212no—
696C4×Q8—26no—
697C4×Q8—26no—
698C4×Q8—212no—
699C4×Q8—23no—
700C4×Q8—23no—
701C4×Q8—26no—
702C4×Q8—23no—
703C4×Q8—26no—
704C4×Q8—26no—
705C4×Q8—212no—
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×Q8C2416yes—
719C4×Q8C24112yes—
720C4×Q8C2413yes—
721C4×Q8C2413yes—
722C4×Q8C2416yes—
723C4×Q8C2416yes—
724C4×Q8C24112yes—
725C4×Q8C2416yes—
726C4×Q8C2411yescharacteristic
727C4×Q8C2413yes—
728C4×Q8C2416yes—
729C4×D4—26no—
730C4×D4—21no—
731C4×D4—23no—
732C4×D4—26no—
733C4×D4—26no—
734C4×D4—212no—
735C4×D4—23no—
736C4×D4—23no—
737C4×D4—26no—
738C4×D4—212no—
739C4×D4—26no—
740C4×D4—26no—
741C4×D4—26no—
742C4×D4—26no—
743C4×D4—212no—
744C4×D4—23no—
745C4×D4—23no—
746C4×D4—26no—
747C4×D4—23no—
748C4×D4—26no—
749C4×D4C2×D416yes—
750C4×D4C2×D4112yes—
751C4×D4C2×D413yes—
752C4×D4C2×D416yes—
753C4×D4C2×D413yes—
754C4×D4C2411yescharacteristic
755C4×D4C2413yes—
756C4×D4C2413yes—
757C4×D4C2413yes—
758C4×D4C2416yes—
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—26no—
769#117—21no—
770#117—23no—
771#117—26no—
772#117—26no—
773#117—26no—
774#117—26no—
775#117—26no—
776#117—26no—
777#117—212no—
778#117C2×D413yes—
779#117C2×D413yes—
780#117C2×D416yes—
781#117C2×D4112yes—
782#117C2×D416yes—
783#117C2412yes—
784C2×C4⋊C4—23no—
785C2×C4⋊C4—26no—
786C2×C4⋊C4—26no—
787C2×C4⋊C4—23no—
788C2×C4⋊C4—26no—
789C2×C4⋊C4—26no—
790C2×C4⋊C4—23no—
791C2×C4⋊C4—26no—
792C2×C4⋊C4—23no—
793C2×C4⋊C4—23no—
794C2×C4⋊C4—23no—
795C2×C4⋊C4C2×D413yes—
796C2×C4⋊C4C2×D416yes—
797C2×C4⋊C4C2×D416yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2416yes—
801C2×C4⋊C4C2416yes—
802C2×C22⋊C4—26no—
803C2×C22⋊C4—23no—
804C2×C22⋊C4—26no—
805C2×C22⋊C4—26no—
806C2×C42—26no—
807C2×C42—26no—
808C2×C42—26no—
809C2×C42—23no—
810C2×C42—26no—
811C2×C42C2413yes—
812C2×C42C2416yes—
813C2×C42C2416yes—
814#107C2416yes—
815#107C2416yes—
816#107C2412yes—
817#107C2416yes—
818#106C2411yescharacteristic
819#106C2416yes—
820#106C2413yes—
821#106C2413yes—
822#106C2413yes—
823#106C24112yes—
824#106C2416yes—
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#103C24112yes—
839#103C24112yes—
840#103C2413yes—
841#103C2413yes—
842#103C2413yes—
843#103C24112yes—
844#103C2416yes—
845#103C2412yes—
846#103C2412yes—
847#103C2412yes—
848#103C2416yes—
849#103C2416yes—
850#103C2412yes—
851#103C2416yes—
852#102C2411yescharacteristic
853#102C2416yes—
854#102C2413yes—
855#102C24112yes—
856#102C2413yes—
857#102C2413yes—
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—46no—
876#41—46no—
877#41—44no—
878#41—412no—
879#41—412no—
880#41#13718yescomplemented
881C2×Q8—28no—
882C2×Q8—212no—
883C2×Q8—22no—
884C2×Q8—23no—
885C2×Q8—23no—
886C2×Q8—21no—
887C2×Q8—26no—
888C2×Q8—26no—
889C2×Q8—212no—
890C2×Q8—23no—
891C2×Q8—26no—
892C2×Q8—23no—
893C2×Q8—26no—
894C2×Q8—24no—
895C2×Q8—43no—
896C2×Q8—42no—
897C2×Q8—46no—
898C2×Q8—46no—
899C2×Q8—44no—
900C2×Q8—166no—
901C2×Q8—166no—
902C2×Q8—163no—
903C2×Q8C22×D413yes—
904C2×Q8C22×D416yes—
905C2×Q8C22×D411yescharacteristic
906C2×Q8C2516yes—
907C2×Q8C2512yes—
908C2×Q8C2513yes—
909C2×Q8C2511yescharacteristic
910C2×D4—26no—
911C2×D4—22no—
912C2×D4—26no—
913C2×D4—23no—
914C2×D4—23no—
915C2×D4—23no—
916C2×D4—43no—
917C2×D4—43no—
918C2×D4—412no—
919C2×D4C22×D416yes—
920C2×D4C22×D411yescharacteristic
921C2×D4C22×D413yes—
922C2×D4C2511yescharacteristic
923C2×D4C2513yes—
924C22×C4—22no—
925C22×C4—23no—
926C22×C4—23no—
927C22×C4—26no—
928C22×C4—26no—
929C22×C4—26no—
930C22×C4—23no—
931C22×C4—23no—
932C22×C4—23no—
933C22×C4—21no—
934C22×C4—23no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—412no—
938C22×C4C22×D416yes—
939C22×C4C22×D416yes—
940C22×C4C22×D416yes—
941C22×C4C22×D413yes—
942C22×C4C22×D416yes—
943C22×C4C22×D413yes—
944C22×C4C2513yes—
945C22×C4C2512yes—
946Q16—212no—
947Q16—412no—
948Q16—46no—
949Q16—46no—
950Q16—46no—
951SD16—22no—
952SD16—26no—
953SD16—43no—
954SD16—43no—
955SD16—46no—
956SD16—42no—
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—21no—
970C4⋊C4—23no—
971C4⋊C4—26no—
972C4⋊C4—21no—
973C4⋊C4—23no—
974C4⋊C4—26no—
975C4⋊C4—212no—
976C4⋊C4—23no—
977C4⋊C4—26no—
978C4⋊C4—23no—
979C4⋊C4—26no—
980C4⋊C4—23no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—212no—
986C4⋊C4—212no—
987C4⋊C4—26no—
988C4⋊C4—23no—
989C4⋊C4—23no—
990C4⋊C4—26no—
991C4⋊C4—23no—
992C4⋊C4—26no—
993C4⋊C4—23no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—23no—
997C4⋊C4—21no—
998C4⋊C4—23no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—21no—
1004C4⋊C4—23no—
1005C4⋊C4—22no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4C22×D411yescharacteristic
1010C4⋊C4C22×D413yes—
1011C4⋊C4C22×D416yes—
1012C4⋊C4C22×D413yes—
1013C4⋊C4C22×D416yes—
1014C4⋊C4C22×D4112yes—
1015C4⋊C4C22×D413yes—
1016C4⋊C4C22×D416yes—
1017C4⋊C4C2511yescharacteristic
1018C4⋊C4C2516yes—
1019C4⋊C4C2513yes—
1020C4⋊C4C2511yescharacteristic
1021C4⋊C4C2513yes—
1022C4⋊C4C2512yes—
1023C22⋊C4—26no—
1024C22⋊C4—22no—
1025C22⋊C4—26no—
1026C22⋊C4—26no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—22no—
1030C22⋊C4—26no—
1031C22⋊C4—22no—
1032C22⋊C4—21no—
1033C22⋊C4—26no—
1034C22⋊C4—212no—
1035C22⋊C4—23no—
1036C22⋊C4—212no—
1037C22⋊C4—23no—
1038C22⋊C4—23no—
1039C22⋊C4—26no—
1040C22⋊C4—26no—
1041C22⋊C4C22×D416yes—
1042C22⋊C4C22×D416yes—
1043C22⋊C4C22×D416yes—
1044C22⋊C4C22×D412yes—
1045C42—22no—
1046C42—26no—
1047C42—26no—
1048C42—23no—
1049C42—21no—
1050C42—212no—
1051C42—26no—
1052C42—212no—
1053C42—26no—
1054C42—26no—
1055C42—23no—
1056C42—23no—
1057C42C22×D416yes—
1058C42C22×D416yes—
1059C42C22×D4112yes—
1060C42C22×D413yes—
1061C42C22×D413yes—
1062C42C2511yescharacteristic
1063C42C2513yes—
1064C42C2516yes—
1065C23—21no—
1066C23—23no—
1067C23—46no—
1068C23—83no—
1069C23—83no—
1070C23C23×D412yes—
1071C23C23×D413yes—
1072Q8—21no—
1073Q8—212no—
1074Q8—26no—
1075Q8—22no—
1076Q8—23no—
1077Q8—26no—
1078Q8—23no—
1079Q8—22no—
1080Q8—26no—
1081Q8—44no—
1082Q8—46no—
1083Q8—46no—
1084Q8—81no—
1085Q8—86no—
1086Q8—86no—
1087Q8—812no—
1088Q8—86no—
1089Q8—83no—
1090Q8—83no—
1091Q8C2×#13714yes—
1092Q8#58512yes—
1093D4—212no—
1094D4—21no—
1095D4—23no—
1096D4—21no—
1097D4—23no—
1098D4—22no—
1099D4—412no—
1100D4—46no—
1101D4—83no—
1102D4—83no—
1103D4—82no—
1104D4—86no—
1105D4C2×#137112yes—
1106C2×C4—21no—
1107C2×C4—212no—
1108C2×C4—23no—
1109C2×C4—22no—
1110C2×C4—23no—
1111C2×C4—22no—
1112C2×C4—212no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—23no—
1116C2×C4—22no—
1117C2×C4—26no—
1118C2×C4—23no—
1119C2×C4—26no—
1120C2×C4—23no—
1121C2×C4—21no—
1122C2×C4—46no—
1123C2×C4—46no—
1124C2×C4—43no—
1125C2×C4—46no—
1126C2×C4—44no—
1127C2×C4—46no—
1128C2×C4—42no—
1129C2×C4—46no—
1130C2×C4—46no—
1131C2×C4—46no—
1132C2×C4—86no—
1133C2×C4—86no—
1134C2×C4—86no—
1135C2×C4—83no—
1136C2×C4—86no—
1137C2×C4—86no—
1138C2×C4C2×#137112yes—
1139C2×C4C23×D416yes—
1140C2×C4C23×D416yes—
1141C2×C4C23×D412yes—
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—43no—
1160C22—41no—
1161C22—41no—
1162C22—43no—
1163C22—43no—
1164C22—41no—
1165C22—166no—
1166C22C22×#13716yes—
1167C22C24×D411yescharacteristic
1168C4—22no—
1169C4—23no—
1170C4—22no—
1171C4—26no—
1172C4—26no—
1173C4—23no—
1174C4—21no—
1175C4—42no—
1176C4—43no—
1177C4—46no—
1178C4—41no—
1179C4—43no—
1180C4—42no—
1181C4—41no—
1182C4—46no—
1183C4—43no—
1184C4C22×#13716yes—
1185C4C22×#13712yes—
1186C4C2×#58511yescharacteristic
1187C42−1+611yescharacteristic
1188C2—26no—
1189C2—42no—
1190C2—83no—
1191C2—81no—
1192C2#6300211yescharacteristic
1193C2C23×#13711yescharacteristic
1194C2#6309211yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#63009C2
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
2. Q8×2−1+4C2semidirect
3. #62582C2semidirect
4. #62542C2semidirect
5. #62530C2semidirect
6. #62398C2semidirect
7. #62366C2semidirect
8. #62131C2semidirect
9. #62108C2semidirect
10. #62096C2semidirect
11. #61991C2semidirect
12. #61966C2semidirect
13. #61952C2semidirect
14. #61909C2semidirect
15. #61889C2semidirect
16. #61838C2semidirect
17. #61830C2semidirect
18. #61457C2semidirect
19. #61438C2semidirect
20. SD16×#41C2semidirect
21. #61319C2semidirect
22. C2×#3369C2semidirect
23. #60343C2semidirect
35. #3503C22semidirect
36. #3503C22semidirect
39. #3502C22semidirect
40. #3502C22semidirect
47. Q8×#41C22semidirect
48. Q8×#41C22semidirect
49. C2×Q82C22semidirect
50. C2×Q82C22semidirect
57. #3400C22semidirect
60. #3398C22semidirect
61. #3398C22semidirect
62. #3395C22semidirect
64. #3387C22semidirect
65. #3387C22semidirect
66. #3387C22semidirect
67. #3385C22semidirect
68. #3385C22semidirect
71. #3375C22semidirect
72. #3375C22semidirect
73. #3375C22semidirect
74. #3374C22semidirect
75. #3372C22semidirect
81. #3369C22semidirect
82. #3369C22semidirect
83. #3369C22semidirect
84. #3369C22semidirect
85. #3369C22semidirect
86. #3369C22semidirect
87. #3363C22semidirect
88. #3363C22semidirect
89. #3363C22semidirect
94. #3344C22semidirect
95. #3344C22semidirect
98. #3331C22semidirect
99. #3331C22semidirect
101. #3316C22semidirect
102. #3316C22semidirect
103. #3316C22semidirect
106. #3312C22semidirect
107. #3299C22semidirect
108. #3299C22semidirect
109. #3299C22semidirect
113. D4×Q16C22semidirect
115. #3276C22semidirect
116. #3270C22semidirect
118. #3255C22semidirect
120. #3249C22semidirect
121. #3248C22semidirect
123. #3239C22semidirect
125. #3230C22semidirect
126. #3229C22semidirect
128. #3216C22semidirect
130. #3210C22semidirect
131. #3209C22semidirect
132. #3209C22semidirect
133. #3185C22semidirect
134. #3181C22semidirect
136. #3170C22semidirect
138. #3141C22semidirect
140. C2×#487C22semidirect
141. #3117C22semidirect
142. #3116C22semidirect
143. #3113C22semidirect
144. #3113C22semidirect
146. #3107C22semidirect
147. #3104C22semidirect
151. #3079C22semidirect
152. C2×#475C22semidirect
154. #3037C22semidirect
156. C2×#462C22semidirect
157. #2990C22semidirect
158. #2989C22semidirect
160. #2984C22semidirect
161. #2983C22semidirect
162. #2970C22semidirect
163. #2965C22semidirect
165. Q8×M16C22semidirect
166. C2×#446C22semidirect
167. C4×#137C22semidirect
168. C2×#441C22semidirect
880. #41#137semidirect

Maximal subgroups

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

subgroupindex
#630092
Q8×2−1+42
#625822
#625422
#625302
#623982
#623662
#621312
#621082
#620962
#619912
#619662
#619522
#619092
#618892
#618382
#618302
#614572
#614382
SD16×#412
#613192
C2×#33692
#603432