Finite Group Databasebeta

← #10584770

Subgroups — #10584770

Order 512.

6110 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63001C211yesmaximal, characteristic, complemented
2#63000C211yesmaximal, characteristic, complemented
3#62475C216yesmaximal, complemented
4#62470C213yesmaximal, complemented
5#62469C211yesmaximal, characteristic, complemented
6#62362C212yesmaximal, complemented
7#62358C213yesmaximal, complemented
8#62104C216yesmaximal, complemented
9#62103C216yesmaximal, complemented
10#62102C213yesmaximal, complemented
11#62100C211yesmaximal, characteristic, complemented
12#62097C213yesmaximal, complemented
13#62095C211yesmaximal, characteristic, complemented
14#61824C212yesmaximal, complemented
15#61823C212yesmaximal, complemented
16#61822C213yesmaximal, complemented
17#61819C213yesmaximal, complemented
18#61432C216yesmaximal, complemented
19#61428C213yesmaximal, complemented
20SD16×#41C211yesmaximal, characteristic, complemented
21Q8×#135C212yesmaximal, complemented
22C2×#3381C213yesmaximal, complemented
23C8×2−1+4C211yesmaximal, characteristic, complemented
24#3523—22no—
25#3523C2212yescomplemented
26#3522C2212yes—
27#3520—26no—
28#3516—22no—
29#3515—26no—
30#3515C2216yes—
31#3515C2216yescomplemented
32#3511C2213yes—
33#3509—23no—
34#3509C2213yescomplemented
35#3507—23no—
36#3507C2213yes—
37#3507C2213yescomplemented
38#3503C2211yescharacteristic
39#3499—21no—
40#3499C2211yescharacteristic
41#3495—23no—
42#3492—23no—
43#3489—21no—
44#3482C2216yescomplemented
45#3481C2216yes—
46#3480C2213yescomplemented
47Q8×#41C2212yes—
48Q8×#41C2211yescharacteristic
49Q8×#41C2212yescomplemented
50C2×#557C2213yescomplemented
51#3475C2213yes—
52C2×#554C2213yes—
53D4×#41C2211yescharacteristic
54C4×2−1+4—21no—
55C4×2−1+4C2211yescharacteristic
56C2×#520—21no—
57#3394C2213yescomplemented
58#3394C2216yescomplemented
59#3392C2211yescharacteristic
60#3383C2216yescomplemented
61#3383C2216yescomplemented
62Q8×Q16C2212yescomplemented
63#3381C2216yes—
64#3381C2216yes—
65#3381C2213yes—
66#3381C2216yes—
67#3381C2216yescomplemented
68#3381C2216yescomplemented
69#3381C2216yescomplemented
70#3381C2216yescomplemented
71#3381C2216yescomplemented
72#3381C2216yescomplemented
73#3380C2216yes—
74#3380C2216yescomplemented
75Q8×SD16C2211yescharacteristic
76Q8×SD16C2212yescomplemented
77Q8×SD16C2212yescomplemented
78Q8×D8C2212yes—
79#3365C2216yescomplemented
80#3365C2216yescomplemented
81#3364C2213yescomplemented
82#3364C2216yescomplemented
83#3364C2216yescomplemented
84#3363C2212yescomplemented
85#3362C2211yescharacteristic
86#3361C2213yes—
87#3361C2216yescomplemented
88#3361C2216yescomplemented
89#3360C2216yes—
90#3360C2216yescomplemented
91#3359C2211yescharacteristic
92#3358C2212yes—
93#3340C2213yescomplemented
94#3340C2216yescomplemented
95#3339C22112yescomplemented
96#3338C2216yescomplemented
97#3337C22112yescomplemented
98#3337C22112yescomplemented
99#3337C2216yescomplemented
100#3336C22112yescomplemented
101#3335C2213yes—
102#3335C2216yescomplemented
103#3335C2216yescomplemented
104#3334C2216yes—
105#3305C2213yescomplemented
106#3302C2213yes—
107#3301C22112yescomplemented
108#3300C2216yescomplemented
109#3299C2216yescomplemented
110#3298C2213yes—
111#3297C2216yes—
112#3296C22112yes—
113#3295C2213yes—
114#3294C2216yes—
115#3284C2211yescharacteristic
116#3282C2216yes—
117D4×SD16C2213yes—
118#3250C22112yescomplemented
119#3249C2213yescomplemented
120#3248C2216yescomplemented
121#3247C2216yescomplemented
122#3245C2213yes—
123#3233C2216yescomplemented
124#3233C2216yescomplemented
125#3232C22112yescomplemented
126#3232C22112yescomplemented
127#3231C2216yescomplemented
128#3230C2213yescomplemented
129#3229C2213yescomplemented
130#3228C2216yescomplemented
131#3227C2213yescomplemented
132#3226C2213yes—
133#3168C22112yescomplemented
134#3168C2216yescomplemented
135#3167C2213yes—
136#3167C2213yescomplemented
137#3167C2216yescomplemented
138#3160C2216yescomplemented
139C2×#499C2216yescomplemented
140C2×#498C2213yescomplemented
141#3108C22112yescomplemented
142#3107C2216yes—
143#3106C2216yescomplemented
144#3105C22112yes—
145#3104C2213yescomplemented
146#3103C2213yes—
147#3102C2216yes—
148#3102C2216yescomplemented
149#3101C2213yes—
150#3100C2213yes—
151#3076C2216yes—
152#3076C2216yescomplemented
153C2×#479C2216yescomplemented
154C2×#477C2213yescomplemented
155C2×#478C2216yes—
156C2×#474C2213yes—
157#2988C2211yescharacteristic
158#2988C2213yescomplemented
159#2988C2216yescomplemented
160#2982C2213yescomplemented
161#2982C2212yescomplemented
162C8×#41C2211yescharacteristic
163C8×#41C2213yescomplemented
164C8×#41C2216yescomplemented
165C2×C8×Q8C2213yescomplemented
166C2×C8×Q8C2212yescomplemented
167C4×#135C2216yes—
168C2×C4×SD16C2213yes—
169C2×C4×SD16C2216yes—
170C2×2−1+4—21no—
171C2×2−1+4D411yescharacteristic
172C22×#41—21no—
173C2×#135C2312yes—
174C22×SD16C2313yes—
175#559—23no—
176#559C2313yes—
177#559C2316yes—
178Q82C2311yescharacteristic
179Q82C2312yes—
180#557—26no—
181#557—26no—
182#557—21no—
183#557—21no—
184#557—23no—
185#557C2311yescharacteristic
186#557C2313yes—
187#557C2316yes—
188#557C2316yes—
189#557C2316yes—
190#557C2316yes—
191#556—23no—
192#556—23no—
193#556—26no—
194#556—26no—
195#556—23no—
196#556—26no—
197#556C2316yes—
198#556C2313yes—
199#556C2313yes—
200#555C2313yes—
201#554—26no—
202#554—26no—
203#554—23no—
204#554—26no—
205#554—26no—
206#554C2316yes—
207#554C2316yes—
208#554C2313yes—
209#554C2316yes—
210#554C2316yes—
211#554C2313yes—
212#554C2316yes—
213#553—23no—
214#553—26no—
215#553—26no—
216#553C23112yes—
217#553C2316yes—
218#552—23no—
219#552—26no—
220#552—26no—
221#552—26no—
222#552—212no—
223#552—26no—
224#552—212no—
225#552—26no—
226#552—212no—
227#552—26no—
228#552C2316yes—
229#552C23112yes—
230#551—26no—
231#551—212no—
232#550C2311yescharacteristic
233#550C2311yescharacteristic
234D4×Q8—22no—
235D4×Q8—22no—
236D4×Q8—22no—
237D4×Q8—21no—
238D4×Q8—23no—
239D4×Q8C2313yes—
240D4×Q8C2312yes—
241D4×Q8C2311yescharacteristic
242#548—22no—
243#548—21no—
244#548—26no—
245#548C2316yes—
246#547—26no—
247#547—26no—
248#547—26no—
249#547—23no—
250#547—23no—
251#547—26no—
252#547C2311yescharacteristic
253#547C2313yes—
254#547C2316yes—
255#546—26no—
256#546—23no—
257#546C2316yes—
258D42C2313yes—
259#544—23no—
260#542—26no—
261#542—26no—
262#541—26no—
263#541—26no—
264#541—26no—
265#541—26no—
266#539—212no—
267#539—212no—
268#539—26no—
269#539—26no—
270#537—23no—
271#536—23no—
272#536—23no—
273#536—23no—
274#536—23no—
275#533—26no—
276#533—26no—
277#533—26no—
278#533—23no—
279#533C2313yes—
280#533C2313yes—
281#533C2316yes—
282#533C2316yes—
283#533C2316yes—
284#532—23no—
285#532C2313yes—
286#532C2313yes—
287#532C2316yes—
288C2×C4⋊Q8—23no—
289C2×C4⋊Q8C2313yes—
290C2×C4⋊Q8C2313yes—
291#529—26no—
292#529—212no—
293#529—26no—
294#529—26no—
295#529C2316yes—
296#529C2316yes—
297#529C23112yes—
298#529C23112yes—
299C2×#125—26no—
300C2×#125C2316yes—
301C2×#125C2316yes—
302#525—23no—
303#525—212no—
304#525—23no—
305C2×C22⋊Q8—23no—
306C2×C22⋊Q8—26no—
307#520—21no—
308#520—22no—
309#520—26no—
310#520—26no—
311#520—23no—
312#520—23no—
313#520—23no—
314#520D411yescharacteristic
315#520D413yes—
316#520D416yes—
317#519—22no—
318#519—23no—
319#519D413yes—
320#519D412yes—
321C4×#41—21no—
322C4×#41—26no—
323C4×#41—23no—
324C4×#41C2316yes—
325C4×#41C2316yes—
326C4×#41C2311yescharacteristic
327C4×#41C2313yes—
328C4×#41C2316yes—
329C2×C4×Q8—22no—
330C2×C4×Q8—22no—
331C2×C4×Q8—23no—
332C2×C4×Q8C2313yes—
333C2×C4×Q8C2316yes—
334C2×C4×Q8C2313yes—
335C2×C4×Q8C2312yes—
336C2×C4×D4—26no—
337C2×C4×D4C2316yes—
338C2×C4×D4C2313yes—
339C2×#117—23no—
340C22×C4⋊C4—23no—
341#500C2316yes—
342#500C2316yes—
343#499C23112yes—
344#499C23112yes—
345#499C2316yes—
346#499C23112yes—
347#499C23112yes—
348#498C2313yes—
349#498C2316yes—
350#498C2316yes—
351#498C2313yes—
352#498C2316yes—
353#495C2316yes—
354#492C2313yes—
355#492C2311yescharacteristic
356#488C23112yes—
357#488C2316yes—
358#488C23112yes—
359#488C2316yes—
360#487C2313yes—
361#487C2316yes—
362#487C2313yes—
363#486C2316yes—
364#486C2313yes—
365#486C2313yes—
366#485C2316yes—
367#485C23112yes—
368#485C2316yes—
369#484C23112yes—
370#484C2316yes—
371#483C2316yes—
372#483C23112yes—
373#482C2316yes—
374#482C2316yes—
375#482C23112yes—
376#481C2316yes—
377#481C23112yes—
378#480C2316yes—
379#480C23112yes—
380#479C2316yes—
381#479C23112yes—
382#479C23112yes—
383#479C23112yes—
384#479C23112yes—
385#479C2316yes—
386#479C23112yes—
387#478C2316yes—
388#478C23112yes—
389#478C23112yes—
390#478C23112yes—
391#478C23112yes—
392#478C2316yes—
393#478C23112yes—
394#477C2313yes—
395#477C2316yes—
396#477C2316yes—
397#477C2316yes—
398#477C2316yes—
399#477C2313yes—
400#476C2313yes—
401#476C2316yes—
402#476C2313yes—
403#476C2316yes—
404#475C2316yes—
405#475C2313yes—
406#475C2313yes—
407#475C2316yes—
408#474C2316yes—
409#474C2316yes—
410#474C2316yes—
411#474C2313yes—
412#474C2316yes—
413#474C2313yes—
414#467C2316yes—
415#467C23112yes—
416#466C23112yes—
417#466C2316yes—
418#465C2316yes—
419#465C2316yes—
420#465C2316yes—
421#465C2312yes—
422#465C2316yes—
423#465C2316yes—
424#465C23112yes—
425#464C2316yes—
426#464C2316yes—
427#464C23112yes—
428#463C2316yes—
429#463C2316yes—
430#463C23112yes—
431#462C2311yescharacteristic
432#462C2313yes—
433#462C2316yes—
434#461C2313yes—
435#461C2313yes—
436#460C2313yes—
437#460C2313yes—
438#459C2311yescharacteristic
439#459C2313yes—
440#459C2316yes—
441#452C2316yes—
442#452C2312yes—
443#451C2316yes—
444#450C2316yes—
445#449C2312yes—
446#449C2316yes—
447#448C2316yes—
448#447C2316yes—
449C8×Q8C2312yes—
450C8×Q8C2311yescharacteristic
451C8×Q8C2316yes—
452C8×Q8C2316yes—
453C8×Q8C2313yes—
454C8×Q8C2316yes—
455C8×Q8C2316yes—
456C8×Q8C2311yescharacteristic
457C8×Q8C2313yes—
458C8×Q8C2316yes—
459C4×Q16C23112yes—
460C4×Q16C2316yes—
461C4×Q16C2316yes—
462C4×Q16C2316yes—
463C4×SD16C2313yes—
464C4×SD16C2316yes—
465C4×SD16C2316yes—
466C4×SD16C23112yes—
467C4×SD16C23112yes—
468C4×SD16C2316yes—
469C4×SD16C2316yes—
470C4×SD16C2313yes—
471C4×SD16C2313yes—
472C4×SD16C2313yes—
473C4×SD16C2313yes—
474C4×SD16C2313yes—
475C4×SD16C23112yes—
476C4×SD16C23112yes—
477C4×SD16C2313yes—
478C4×SD16C2311yescharacteristic
479C4×SD16C2316yes—
480C4×D8C2316yes—
481C4×D8C23112yes—
482C4×D8C2316yes—
483C4×D8C2316yes—
484C8×D4C2316yes—
485C8×D4C2313yes—
486C8×D4C2313yes—
487C8×D4C23112yes—
488C8×D4C2316yes—
489C8×D4C2316yes—
490C8×D4C2311yescharacteristic
491C8×D4C2313yes—
492#431C2313yes—
493#431C2313yes—
494#431C2316yes—
495#431C23112yes—
496#431C2316yes—
497#427C23112yes—
498#427C2316yes—
499C2×#107C2316yes—
500C2×#107C2316yes—
501C2×#106C2316yes—
502C2×#106C2313yes—
503C2×#106C2316yes—
504C2×C4⋊C8C2316yes—
505C2×C4⋊C8C2313yes—
506C2×C4⋊C8C2316yes—
507#416C2316yes—
508#416C2316yes—
509C2×#103C2316yes—
510C2×#103C2313yes—
511C2×#102C2313yes—
512C2×#102C2316yes—
513C2×C4×C8C2313yes—
514C2×C4×C8C2316yes—
515C2×C4×C8C2316yes—
5162−1+4—28no—
5172−1+4—48no—
518C2×#41—21no—
519C2×#41—26no—
520C2×#41—23no—
521C2×#41—23no—
522C2×#41—23no—
523C2×#41—26no—
524C2×#41—48no—
525C2×#41C2×D413yes—
526C2×#41C2×D416yes—
527C2×#41C2×D411yescharacteristic
528C2×#41C2412yes—
529C2×#41C2412yes—
530C22×Q8—21no—
531C22×Q8—22no—
532C22×Q8—23no—
533C22×Q8—23no—
534C22×Q8C2×D413yes—
535C22×Q8C2×D412yes—
536C22×Q8C2413yes—
537C22×D4—23no—
538C22×D4C2413yes—
539C23×C4—23no—
540C23×C4—26no—
541#135—28no—
542C2×Q16C2412yes—
543C2×Q16C2416yes—
544C2×SD16—212no—
545C2×SD16C2413yes—
546C2×SD16C2413yes—
547C2×SD16C2413yes—
548C2×SD16C2412yes—
549C2×SD16C2416yes—
550C2×SD16C2412yes—
551C2×SD16C2411yescharacteristic
552C2×D8C2412yes—
553C2×D8C2416yes—
554C22×C8C2413yes—
555C22×C8C2412yes—
556C22×C8C2413yes—
557C22×C8C2416yes—
558C22×C8C2416yes—
559C4⋊Q8—23no—
560C4⋊Q8—26no—
561C4⋊Q8—26no—
562C4⋊Q8—26no—
563C4⋊Q8—26no—
564C4⋊Q8—23no—
565C4⋊Q8—23no—
566C4⋊Q8—26no—
567C4⋊Q8—23no—
568C4⋊Q8—23no—
569C4⋊Q8—23no—
570C4⋊Q8—23no—
571C4⋊Q8C2411yescharacteristic
572C4⋊Q8C2413yes—
573C4⋊Q8C2413yes—
574C4⋊Q8C2413yes—
575C4⋊Q8C2416yes—
576C4⋊Q8C2416yes—
577C4⋊Q8C2413yes—
578C4⋊Q8C2413yes—
579#127—21no—
580#127C2413yes—
581#127C2411yescharacteristic
582#126—26no—
583#126—212no—
584#126—26no—
585#126—212no—
586#126—26no—
587#126—212no—
588#126—26no—
589#126—212no—
590#126—212no—
591#126—26no—
592#126—26no—
593#125—26no—
594#125—212no—
595#125—212no—
596#125—212no—
597#125—26no—
598#125—26no—
599#125—212no—
600#125—212no—
601#125—23no—
602#125—23no—
603#125—212no—
604#125—212no—
605#125—26no—
606#125—23no—
607#125—23no—
608#125C2416yes—
609#125C2416yes—
610#125C24112yes—
611#125C24112yes—
612#124—26no—
613#124—23no—
614#124—23no—
615#124—26no—
616#124—26no—
617#124—23no—
618#124—23no—
619#124—26no—
620#124C2416yes—
621#124C2416yes—
622#123—26no—
623#123—212no—
624#123—212no—
625#123—212no—
626#123—26no—
627#123—26no—
628#123—212no—
629#123—26no—
630#123—26no—
631#123—26no—
632#123—212no—
633#123—22no—
634#123—212no—
635#123—26no—
636C22⋊Q8—23no—
637C22⋊Q8—26no—
638C22⋊Q8—26no—
639C22⋊Q8—26no—
640C22⋊Q8—23no—
641C22⋊Q8—26no—
642C22⋊Q8—26no—
643C22⋊Q8—26no—
644C22⋊Q8—26no—
645C22⋊Q8—26no—
646C22⋊Q8—26no—
647C22⋊Q8—23no—
648C22⋊Q8—23no—
649C22⋊Q8—26no—
650C22⋊Q8—26no—
651C22⋊Q8—212no—
652C22⋊Q8—212no—
653C22⋊Q8—212no—
654C22⋊Q8—23no—
655C22⋊Q8—23no—
656C22⋊Q8—26no—
657C22⋊Q8—26no—
658C22⋊Q8—26no—
659C22⋊Q8—212no—
660C22⋊Q8—212no—
661C22⋊Q8—26no—
662C22⋊Q8—26no—
663C22⋊Q8C2412yes—
664C22⋊Q8C2416yes—
665C22⋊Q8C2416yes—
666C22⋊Q8C2416yes—
667#121—21no—
668#121—23no—
669#121—212no—
670#121—26no—
671#121—26no—
672#121—26no—
673#121—23no—
674#121—23no—
675#121—23no—
676#121—23no—
677#121—26no—
678#121—22no—
679#121C2412yes—
680#121C2416yes—
681#121C2416yes—
682#121C2416yes—
683#120—26no—
684#120—26no—
685C4×Q8—21no—
686C4×Q8—22no—
687C4×Q8—21no—
688C4×Q8—26no—
689C4×Q8—23no—
690C4×Q8—26no—
691C4×Q8—26no—
692C4×Q8—26no—
693C4×Q8—23no—
694C4×Q8—26no—
695C4×Q8—26no—
696C4×Q8—23no—
697C4×Q8—212no—
698C4×Q8—23no—
699C4×Q8—26no—
700C4×Q8—23no—
701C4×Q8—26no—
702C4×Q8—26no—
703C4×Q8—23no—
704C4×Q8C2×D412yes—
705C4×Q8C2×D416yes—
706C4×Q8C2×D416yes—
707C4×Q8C2×D416yes—
708C4×Q8C2×D416yes—
709C4×Q8C2×D411yescharacteristic
710C4×Q8C2×D413yes—
711C4×Q8C2411yescharacteristic
712C4×Q8C2416yes—
713C4×Q8C2413yes—
714C4×Q8C2413yes—
715C4×Q8C24112yes—
716C4×Q8C2413yes—
717C4×Q8C2416yes—
718C4×Q8C2416yes—
719C4×Q8C2411yescharacteristic
720C4×Q8C2413yes—
721C4×Q8C2416yes—
722C4×D4—26no—
723C4×D4—23no—
724C4×D4—23no—
725C4×D4—212no—
726C4×D4—212no—
727C4×D4—26no—
728C4×D4—26no—
729C4×D4—26no—
730C4×D4—26no—
731C4×D4—26no—
732C4×D4—26no—
733C4×D4—26no—
734C4×D4—21no—
735C4×D4—23no—
736C4×D4—212no—
737C4×D4—26no—
738C4×D4—26no—
739C4×D4—26no—
740C4×D4—23no—
741C4×D4—212no—
742C4×D4—23no—
743C4×D4—23no—
744C4×D4—23no—
745C4×D4C2×D416yes—
746C4×D4C2×D4112yes—
747C4×D4C2×D413yes—
748C4×D4C2×D413yes—
749C4×D4C2×D416yes—
750C4×D4C2411yescharacteristic
751C4×D4C2416yes—
752C4×D4C2413yes—
753C4×D4C2413yes—
754C4×D4C24112yes—
755C4×D4C2413yes—
756C4×D4C2416yes—
757C4×D4C2416yes—
758C4×D4C2413yes—
759C4×D4C2416yes—
760C4×D4C2411yescharacteristic
761#117—23no—
762#117—23no—
763#117—26no—
764#117—23no—
765#117—23no—
766#117—26no—
767#117—26no—
768#117—212no—
769#117—26no—
770#117—26no—
771#117—26no—
772#117—26no—
773#117—212no—
774#117—212no—
775#117C2×D413yes—
776#117C2×D413yes—
777#117C2×D416yes—
778#117C2×D4112yes—
779#117C2×D416yes—
780#117C2416yes—
781#117C2416yes—
782C2×C4⋊C4—26no—
783C2×C4⋊C4—23no—
784C2×C4⋊C4—26no—
785C2×C4⋊C4—23no—
786C2×C4⋊C4—26no—
787C2×C4⋊C4—26no—
788C2×C4⋊C4—23no—
789C2×C4⋊C4—26no—
790C2×C4⋊C4—23no—
791C2×C4⋊C4—26no—
792C2×C4⋊C4—26no—
793C2×C4⋊C4—26no—
794C2×C4⋊C4—21no—
795C2×C4⋊C4—26no—
796C2×C4⋊C4C2×D413yes—
797C2×C4⋊C4C2×D416yes—
798C2×C4⋊C4C2×D416yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2416yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2416yes—
803C2×C22⋊C4—23no—
804C2×C22⋊C4—26no—
805C2×C22⋊C4—26no—
806C2×C42—26no—
807C2×C42—23no—
808C2×C42—26no—
809C2×C42—26no—
810C2×C42C2416yes—
811C2×C42C2413yes—
812C2×C42C2416yes—
813#107C2416yes—
814#107C2416yes—
815#107C24112yes—
816#107C24112yes—
817#107C2416yes—
818#107C2416yes—
819#106C2411yescharacteristic
820#106C2416yes—
821#106C2416yes—
822#106C2413yes—
823#106C24112yes—
824#106C2413yes—
825#106C24112yes—
826#106C2413yes—
827#106C2416yes—
828C4⋊C8C2413yes—
829C4⋊C8C2416yes—
830C4⋊C8C2413yes—
831C4⋊C8C2416yes—
832C4⋊C8C24112yes—
833C4⋊C8C2411yescharacteristic
834C4⋊C8C2413yes—
835C4⋊C8C2416yes—
836#103C2411yescharacteristic
837#103C2416yes—
838#103C2413yes—
839#103C2413yes—
840#103C24112yes—
841#103C2413yes—
842#103C2416yes—
843#103C2416yes—
844#103C2416yes—
845#103C2416yes—
846#103C2416yes—
847#103C2412yes—
848#102C2411yescharacteristic
849#102C2416yes—
850#102C2413yes—
851#102C24112yes—
852#102C2413yes—
853#102C2413yes—
854#102C2416yes—
855#102C2416yes—
856#102C2412yes—
857#102C2416yes—
858#102C2416yes—
859#102C2416yes—
860C22⋊C8C2416yes—
861C22⋊C8C2416yes—
862C22⋊C8C2416yes—
863C22⋊C8C2412yes—
864C4×C8C2411yescharacteristic
865C4×C8C2413yes—
866C4×C8C2416yes—
867C4×C8C2416yes—
868C4×C8C24112yes—
869C4×C8C2416yes—
870C4×C8C2413yes—
871C4×C8C2413yes—
872C24—23no—
873#41—224no—
874#41—212no—
875#41—24no—
876#41—24no—
877#41—42no—
878#41—42no—
879#41—44no—
880#41—412no—
881#41—424no—
882#41—412no—
883#41—412no—
884#41—166no—
885#41#13518yescomplemented
886C2×Q8—28no—
887C2×Q8—212no—
888C2×Q8—23no—
889C2×Q8—23no—
890C2×Q8—26no—
891C2×Q8—23no—
892C2×Q8—23no—
893C2×Q8—23no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—43no—
897C2×Q8—44no—
898C2×Q8—48no—
899C2×Q8—412no—
900C2×Q8—163no—
901C2×Q8C22×D416yes—
902C2×Q8C22×D413yes—
903C2×Q8C22×D411yescharacteristic
904C2×Q8C2512yes—
905C2×Q8C2513yes—
906C2×Q8C2511yescharacteristic
907C2×D4—26no—
908C2×D4—22no—
909C2×D4—22no—
910C2×D4—26no—
911C2×D4—26no—
912C2×D4—22no—
913C2×D4—26no—
914C2×D4—23no—
915C2×D4—23no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—23no—
919C2×D4—43no—
920C2×D4—412no—
921C2×D4C22×D416yes—
922C2×D4C22×D411yescharacteristic
923C2×D4C22×D413yes—
924C2×D4C2512yes—
925C2×D4C2513yes—
926C2×D4C2511yescharacteristic
927C22×C4—23no—
928C22×C4—26no—
929C22×C4—23no—
930C22×C4—23no—
931C22×C4—26no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—23no—
935C22×C4—26no—
936C22×C4—21no—
937C22×C4—23no—
938C22×C4—23no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—212no—
942C22×C4—412no—
943C22×C4—166no—
944C22×C4C22×D416yes—
945C22×C4C22×D416yes—
946C22×C4C22×D416yes—
947C22×C4C22×D413yes—
948C22×C4C22×D416yes—
949C22×C4C22×D413yes—
950C22×C4C2513yes—
951C22×C4C2512yes—
952Q16—24no—
953Q16—46no—
954SD16—26no—
955SD16—26no—
956SD16—26no—
957SD16—24no—
958SD16—42no—
959SD16—46no—
960SD162−1+414yescomplemented
961D8—24no—
962D8—46no—
963C2×C8—26no—
964C2×C8—24no—
965C2×C8—46no—
966C2×C8—46no—
967C2×C8—43no—
968C2×C8C2513yes—
969C2×C8C2512yes—
970C2×C8C2513yes—
971C2×C8C2511yescharacteristic
972C2×C8C2516yes—
973C2×C8C2511yescharacteristic
974C4⋊C4—23no—
975C4⋊C4—26no—
976C4⋊C4—26no—
977C4⋊C4—212no—
978C4⋊C4—21no—
979C4⋊C4—23no—
980C4⋊C4—212no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—23no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—21no—
987C4⋊C4—22no—
988C4⋊C4—23no—
989C4⋊C4—212no—
990C4⋊C4—26no—
991C4⋊C4—212no—
992C4⋊C4—23no—
993C4⋊C4—23no—
994C4⋊C4—212no—
995C4⋊C4—23no—
996C4⋊C4—26no—
997C4⋊C4—23no—
998C4⋊C4—26no—
999C4⋊C4—23no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—23no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—23no—
1007C4⋊C4—21no—
1008C4⋊C4C22×D413yes—
1009C4⋊C4C22×D416yes—
1010C4⋊C4C22×D411yescharacteristic
1011C4⋊C4C22×D413yes—
1012C4⋊C4C22×D416yes—
1013C4⋊C4C22×D4112yes—
1014C4⋊C4C22×D413yes—
1015C4⋊C4C22×D416yes—
1016C4⋊C4C2516yes—
1017C4⋊C4C2511yescharacteristic
1018C4⋊C4C2513yes—
1019C4⋊C4C2516yes—
1020C4⋊C4C2511yescharacteristic
1021C4⋊C4C2513yes—
1022C22⋊C4—26no—
1023C22⋊C4—26no—
1024C22⋊C4—26no—
1025C22⋊C4—26no—
1026C22⋊C4—26no—
1027C22⋊C4—22no—
1028C22⋊C4—21no—
1029C22⋊C4—26no—
1030C22⋊C4—26no—
1031C22⋊C4—26no—
1032C22⋊C4—23no—
1033C22⋊C4—23no—
1034C22⋊C4—212no—
1035C22⋊C4—23no—
1036C22⋊C4—22no—
1037C22⋊C4—26no—
1038C22⋊C4—26no—
1039C22⋊C4—26no—
1040C22⋊C4—26no—
1041C22⋊C4—26no—
1042C22⋊C4—26no—
1043C22⋊C4—26no—
1044C22⋊C4C22×D416yes—
1045C22⋊C4C22×D416yes—
1046C22⋊C4C22×D416yes—
1047C22⋊C4C22×D412yes—
1048C42—23no—
1049C42—26no—
1050C42—21no—
1051C42—26no—
1052C42—212no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—23no—
1057C42—23no—
1058C42C22×D416yes—
1059C42C22×D4112yes—
1060C42C22×D416yes—
1061C42C22×D413yes—
1062C42C22×D413yes—
1063C42C2516yes—
1064C42C2513yes—
1065C42C2511yescharacteristic
1066C23—21no—
1067C23—22no—
1068C23—23no—
1069C23—46no—
1070C23—46no—
1071C23—83no—
1072C23C23×D412yes—
1073C23C23×D413yes—
1074Q8—21no—
1075Q8—212no—
1076Q8—26no—
1077Q8—23no—
1078Q8—22no—
1079Q8—23no—
1080Q8—22no—
1081Q8—46no—
1082Q8—412no—
1083Q8—46no—
1084Q8—46no—
1085Q8—83no—
1086Q8—83no—
1087Q8—86no—
1088Q8C2×#13514yes—
1089Q8C2×2−1+412yes—
1090D4—212no—
1091D4—22no—
1092D4—23no—
1093D4—21no—
1094D4—22no—
1095D4—23no—
1096D4—22no—
1097D4—46no—
1098D4—44no—
1099D4—44no—
1100D4—412no—
1101D4—412no—
1102D4—46no—
1103D4—42no—
1104D4—81no—
1105D4—83no—
1106D4—82no—
1107D4—86no—
1108D4C2×#135112yes—
1109D4C2×2−1+412yes—
1110C2×C4—21no—
1111C2×C4—212no—
1112C2×C4—23no—
1113C2×C4—22no—
1114C2×C4—23no—
1115C2×C4—22no—
1116C2×C4—212no—
1117C2×C4—22no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—26no—
1122C2×C4—21no—
1123C2×C4—26no—
1124C2×C4—21no—
1125C2×C4—46no—
1126C2×C4—43no—
1127C2×C4—46no—
1128C2×C4—44no—
1129C2×C4—46no—
1130C2×C4—44no—
1131C2×C4—46no—
1132C2×C4—412no—
1133C2×C4—42no—
1134C2×C4—46no—
1135C2×C4—46no—
1136C2×C4—46no—
1137C2×C4—412no—
1138C2×C4—86no—
1139C2×C4—86no—
1140C2×C4—812no—
1141C2×C4—83no—
1142C2×C4—86no—
1143C2×C4C2×#135112yes—
1144C2×C4C23×D412yes—
1145C2×C4C23×D416yes—
1146C2×C4C23×D413yes—
1147C2×C4C23×D416yes—
1148C2×C4C23×D413yes—
1149C2×C4C23×D411yescharacteristic
1150C2×C4C23×D413yes—
1151C2×C4C23×D411yescharacteristic
1152C2×C4C2611yescharacteristic
1153C8—22no—
1154C8—23no—
1155C8—26no—
1156C8—23no—
1157C8—21no—
1158C8C2×2−1+412yes—
1159C22—23no—
1160C22—23no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—41no—
1166C22—41no—
1167C22—42no—
1168C22—43no—
1169C22—42no—
1170C22—43no—
1171C22—43no—
1172C22—42no—
1173C22—812no—
1174C22C22×#13516yes—
1175C22C24×D411yescharacteristic
1176C4—22no—
1177C4—23no—
1178C4—22no—
1179C4—26no—
1180C4—26no—
1181C4—21no—
1182C4—23no—
1183C4—42no—
1184C4—43no—
1185C4—41no—
1186C4—43no—
1187C4—46no—
1188C4—46no—
1189C4—41no—
1190C4—43no—
1191C4C22×#13516yes—
1192C4C22×#13512yes—
1193C4C22×2−1+411yescharacteristic
1194C42−1+611yescharacteristic
1195C2—26no—
1196C2—42no—
1197C2—42no—
1198C2—82no—
1199C2—83no—
1200C2D4×2−1+411yescharacteristic
1201C2C23×#13511yescharacteristic
1202C2#6309211yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×2−1+4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63001C2semidirect
2. #63000C2semidirect
3. #62475C2semidirect
4. #62470C2semidirect
5. #62469C2semidirect
6. #62362C2semidirect
7. #62358C2semidirect
8. #62104C2semidirect
9. #62103C2semidirect
10. #62102C2semidirect
11. #62100C2semidirect
12. #62097C2semidirect
13. #62095C2semidirect
14. #61824C2semidirect
15. #61823C2semidirect
16. #61822C2semidirect
17. #61819C2semidirect
18. #61432C2semidirect
19. #61428C2semidirect
20. SD16×#41C2semidirect
21. Q8×#135C2semidirect
22. C2×#3381C2semidirect
23. C8×2−1+4C2semidirect
25. #3523C22semidirect
31. #3515C22semidirect
34. #3509C22semidirect
37. #3507C22semidirect
44. #3482C22semidirect
46. #3480C22semidirect
49. Q8×#41C22semidirect
50. C2×#557C22semidirect
57. #3394C22semidirect
58. #3394C22semidirect
60. #3383C22semidirect
61. #3383C22semidirect
62. Q8×Q16C22semidirect
67. #3381C22semidirect
68. #3381C22semidirect
69. #3381C22semidirect
70. #3381C22semidirect
71. #3381C22semidirect
72. #3381C22semidirect
74. #3380C22semidirect
76. Q8×SD16C22semidirect
77. Q8×SD16C22semidirect
79. #3365C22semidirect
80. #3365C22semidirect
81. #3364C22semidirect
82. #3364C22semidirect
83. #3364C22semidirect
84. #3363C22semidirect
87. #3361C22semidirect
88. #3361C22semidirect
90. #3360C22semidirect
93. #3340C22semidirect
94. #3340C22semidirect
95. #3339C22semidirect
96. #3338C22semidirect
97. #3337C22semidirect
98. #3337C22semidirect
99. #3337C22semidirect
100. #3336C22semidirect
102. #3335C22semidirect
103. #3335C22semidirect
105. #3305C22semidirect
107. #3301C22semidirect
108. #3300C22semidirect
109. #3299C22semidirect
118. #3250C22semidirect
119. #3249C22semidirect
120. #3248C22semidirect
121. #3247C22semidirect
123. #3233C22semidirect
124. #3233C22semidirect
125. #3232C22semidirect
126. #3232C22semidirect
127. #3231C22semidirect
128. #3230C22semidirect
129. #3229C22semidirect
130. #3228C22semidirect
131. #3227C22semidirect
133. #3168C22semidirect
134. #3168C22semidirect
136. #3167C22semidirect
137. #3167C22semidirect
138. #3160C22semidirect
139. C2×#499C22semidirect
140. C2×#498C22semidirect
141. #3108C22semidirect
143. #3106C22semidirect
145. #3104C22semidirect
148. #3102C22semidirect
152. #3076C22semidirect
153. C2×#479C22semidirect
154. C2×#477C22semidirect
158. #2988C22semidirect
159. #2988C22semidirect
160. #2982C22semidirect
161. #2982C22semidirect
163. C8×#41C22semidirect
164. C8×#41C22semidirect
165. C2×C8×Q8C22semidirect
166. C2×C8×Q8C22semidirect
885. #41#135semidirect
960. SD162−1+4semidirect

Maximal subgroups

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

subgroupindex
#630012
#630002
#624752
#624702
#624692
#623622
#623582
#621042
#621032
#621022
#621002
#620972
#620952
#618242
#618232
#618222
#618192
#614322
#614282
SD16×#412
Q8×#1352
C2×#33812
C8×2−1+42