Finite Group Databasebeta

← #10584875

Subgroups — #10584875

Order 512.

6114 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63037C211yesmaximal, characteristic, complemented
2#63016C211yesmaximal, characteristic, complemented
3#62486C216yesmaximal, complemented
4#62469C213yesmaximal, complemented
5#62469C211yesmaximal, characteristic, complemented
6#62372C213yesmaximal, complemented
7#62362C212yesmaximal, complemented
8#62205C216yesmaximal, complemented
9#62202C216yesmaximal, complemented
10#62150C211yesmaximal, characteristic, complemented
11#62147C211yesmaximal, characteristic, complemented
12#62131C213yesmaximal, complemented
13#62128C213yesmaximal, complemented
14#61871C213yesmaximal, complemented
15#61871C213yesmaximal, complemented
16#61843C212yesmaximal, complemented
17#61838C212yesmaximal, complemented
18#61483C216yesmaximal, complemented
19#61434C211yesmaximal, characteristic, complemented
20#61432C213yesmaximal, complemented
21#61374C213yesmaximal, complemented
22C2×Q8×SD16C212yesmaximal, complemented
23#60331C211yesmaximal, characteristic, complemented
24#3552—23no—
25#3552C2216yes—
26#3550—23no—
27#3550C2213yes—
28#3550C2213yescomplemented
29#3544—26no—
30#3544C2216yescomplemented
31#3538—26no—
32#3523—21no—
33#3523C2212yes—
34#3522—22no—
35#3522C2212yescomplemented
36#3522C2216yescomplemented
37#3520—23no—
38#3520C2216yes—
39#3503—21no—
40#3503C2213yes—
41#3503C2213yes—
42#3503C2211yescharacteristic, complemented
43#3503C2213yescomplemented
44#3499—23no—
45#3499C2211yescharacteristic
46#3499C2213yes—
47#3486—22no—
48#3483C2211yescharacteristic, complemented
49#3482—21no—
50#3482C2211yescharacteristic
51#3482C2213yes—
52#3482C2211yescharacteristic
53#3481C2213yes—
54C2×Q82C2212yescomplemented
55C2×D4×Q8—21no—
56C2×D4×Q8C2212yes—
57#3394C2213yes—
58#3394C2216yescomplemented
59#3392C2211yescharacteristic, complemented
60#3387C2216yescomplemented
61#3387C2216yescomplemented
62#3387C2216yescomplemented
63#3384C2216yes—
64#3384C2216yes—
65#3384C2216yescomplemented
66#3381C2213yes—
67#3381C2216yescomplemented
68Q8×SD16C2216yes—
69Q8×SD16C2212yes—
70Q8×SD16C2211yescharacteristic
71Q8×SD16C2216yes—
72Q8×SD16C2212yescomplemented
73Q8×SD16C2212yescomplemented
74Q8×SD16C2216yescomplemented
75Q8×SD16C2216yescomplemented
76Q8×SD16C2216yescomplemented
77Q8×SD16C2212yescomplemented
78Q8×SD16C2216yescomplemented
79#3373C2216yes—
80#3373C2216yes—
81#3373C2216yescomplemented
82#3369C2216yescomplemented
83#3369C2216yescomplemented
84#3369C2216yescomplemented
85#3365C2213yes—
86#3365C2216yescomplemented
87#3363C2211yescharacteristic, complemented
88#3363C2212yescomplemented
89#3360C2213yes—
90#3360C2216yescomplemented
91#3358C2211yescharacteristic
92#3358C2212yescomplemented
93#3356C2216yescomplemented
94#3354C2216yescomplemented
95#3345C22112yes—
96#3344C22112yescomplemented
97#3340C2213yescomplemented
98#3337C2216yes—
99#3335C2213yes—
100#3335C2216yes—
101#3335C2216yescomplemented
102#3335C22112yescomplemented
103#3335C2216yescomplemented
104#3335C22112yescomplemented
105#3332C2216yescomplemented
106#3331C2216yes—
107#3316C22112yescomplemented
108#3306C22112yes—
109#3304C2213yescomplemented
110#3303C2213yes—
111#3301C2216yes—
112#3299C2213yes—
113#3296C2216yes—
114#3294C2213yes—
115#3284C2213yes—
116#3282C2216yes—
117D4×SD16C2211yescharacteristic
118#3263C22112yescomplemented
119#3255C2213yescomplemented
120#3253C2213yes—
121#3248C2216yescomplemented
122#3247C2216yes—
123#3244C22112yescomplemented
124#3244C22112yescomplemented
125#3239C2216yescomplemented
126#3238C2216yes—
127#3229C2216yescomplemented
128#3229C2213yescomplemented
129#3229C2213yescomplemented
130#3227C2213yes—
131#3227C2216yescomplemented
132#3227C2213yescomplemented
133#3173C22112yescomplemented
134#3168C2216yes—
135#3167C2213yes—
136#3167C2216yescomplemented
137#3167C2213yescomplemented
138#3163C2216yescomplemented
139C2×#498C2213yescomplemented
140C2×#498C2216yescomplemented
141#3125C22112yes—
142#3125C22112yescomplemented
143#3113C2216yescomplemented
144#3109C2216yes—
145#3108C2216yes—
146#3107C2213yes—
147#3107C2213yescomplemented
148#3106C2213yes—
149#3106C2213yes—
150#3105C2216yes—
151#3084C2216yes—
152#3084C2216yescomplemented
153#3079C2213yes—
154#3079C2213yescomplemented
155C2×#475C2216yescomplemented
156C2×#476C2216yes—
157#2994C2216yescomplemented
158#2991C2211yescharacteristic, complemented
159#2990C2213yes—
160#2986C2213yescomplemented
161#2984C2212yescomplemented
162#2966C2216yescomplemented
163C8×#41C2213yes—
164C8×#41C2211yescharacteristic, complemented
165#2960C2213yescomplemented
166C2×C8×Q8C2212yescomplemented
167#2952C2216yes—
168C4×#135C2213yes—
169C2×C4×SD16C2216yes—
170C2×2−1+4—21no—
171C2×2−1+4—23no—
172C23×Q8—22no—
173C2×#135C2313yes—
174C22×SD16C2312yes—
175#563—212no—
176#563—212no—
177#563—26no—
178#563—26no—
179#559—26no—
180#559C2313yes—
181#559C2316yes—
182Q82—22no—
183Q82—26no—
184Q82C2311yescharacteristic
185Q82C2312yes—
186Q82C2316yes—
187Q82C2316yes—
188Q82C2316yes—
189#557—21no—
190#557—23no—
191#557D411yescharacteristic
192#557C2311yescharacteristic
193#557C2313yes—
194#557C2316yes—
195#556—23no—
196#556—23no—
197#556—23no—
198#556D413yes—
199#556C2313yes—
200#556C2316yes—
201#556C2313yes—
202#555—23no—
203#555C2313yes—
204#554—26no—
205#554—26no—
206#554—26no—
207#554C2313yes—
208#554C2316yes—
209#554C2316yes—
210#554C2313yes—
211#554C23112yes—
212#553—23no—
213#553C2316yes—
214#552—26no—
215#552—26no—
216#552—23no—
217#552—26no—
218#552—26no—
219#552D416yes—
220#552C2316yes—
221#551—212no—
222#551—26no—
223#550—21no—
224#550C2313yes—
225#550C2311yescharacteristic
226D4×Q8—22no—
227D4×Q8—23no—
228D4×Q8—23no—
229D4×Q8—26no—
230D4×Q8—26no—
231D4×Q8—26no—
232D4×Q8—21no—
233D4×Q8—22no—
234D4×Q8—26no—
235D4×Q8—23no—
236D4×Q8—23no—
237D4×Q8—26no—
238D4×Q8—23no—
239D4×Q8D411yescharacteristic
240D4×Q8C2311yescharacteristic
241D4×Q8C2311yescharacteristic
242D4×Q8C2312yes—
243D4×Q8C2316yes—
244D4×Q8C2316yes—
245D4×Q8C2316yes—
246#548—21no—
247#548—22no—
248#548—26no—
249#548—26no—
250#548D412yes—
251#548C2316yes—
252#547—23no—
253#547—212no—
254#547—26no—
255#547—23no—
256#547—23no—
257#547—26no—
258#547—26no—
259#547D413yes—
260#547C2313yes—
261#547C2316yes—
262#547C2313yes—
263#547C23112yes—
264#546—23no—
265#546C2316yes—
266D42C2311yescharacteristic
267#544—26no—
268#544—26no—
269#544—26no—
270#544—26no—
271#544—23no—
272#544—23no—
273#544C2316yes—
274#544C2316yes—
275#542—212no—
276#542—26no—
277#542—26no—
278#542—26no—
279#542—26no—
280#542C23112yes—
281#542C23112yes—
282#541—26no—
283#541—26no—
284#539—212no—
285#539—212no—
286#536—26no—
287#536—212no—
288#536—26no—
289#536—26no—
290#536—23no—
291#536—26no—
292#536—23no—
293#533—23no—
294#533—23no—
295#533—23no—
296#533C2313yes—
297#533C2313yes—
298#533C2316yes—
299#533C2313yes—
300#532—26no—
301#532—23no—
302#532C2313yes—
303#532C2313yes—
304#532C2316yes—
305C2×C4⋊Q8—23no—
306C2×C4⋊Q8—23no—
307C2×C4⋊Q8—26no—
308C2×C4⋊Q8C2316yes—
309C2×C4⋊Q8C2313yes—
310C2×C4⋊Q8C2313yes—
311C2×C4⋊Q8C2316yes—
312#529—26no—
313#529—23no—
314#529—23no—
315#529—26no—
316#529C2316yes—
317#529C2316yes—
318#529C2316yes—
319#525—26no—
320#525—26no—
321C2×C22⋊Q8—26no—
322C2×C22⋊Q8—26no—
323#520—23no—
324#520—21no—
325#520—22no—
326#520C2316yes—
327#520C2316yes—
328#519—22no—
329C4×#41—21no—
330C4×#41—23no—
331C4×#41C2313yes—
332C4×#41C2313yes—
333C4×#41C2313yes—
334C4×#41C2311yescharacteristic
335C2×C4×Q8—22no—
336C2×C4×Q8—21no—
337C2×C4×Q8C2316yes—
338C2×C4×Q8C2312yes—
339C2×C4×D4—23no—
340C2×C4×D4C2316yes—
341#501C23112yes—
342#501C23112yes—
343#499C2316yes—
344#498C2313yes—
345#498C2316yes—
346#498C23112yes—
347#498C23112yes—
348#498C2316yes—
349#498C2316yes—
350#498C2313yes—
351#498C2316yes—
352#498C2316yes—
353#495C2316yes—
354#492C2313yes—
355#492C2311yescharacteristic
356#489C23112yes—
357#489C23112yes—
358#488C2316yes—
359#488C2316yes—
360#487C2316yes—
361#487C2313yes—
362#487C2313yes—
363#486C2316yes—
364#486C2313yes—
365#486C2313yes—
366#485C2316yes—
367#485C2316yes—
368#484C2316yes—
369#483C23112yes—
370#483C2316yes—
371#483C23112yes—
372#483C23112yes—
373#482C2316yes—
374#482C2316yes—
375#481C23112yes—
376#481C2316yes—
377#481C23112yes—
378#481C23112yes—
379#480C2316yes—
380#479C2316yes—
381#479C23112yes—
382#479C2316yes—
383#478C2316yes—
384#478C2316yes—
385#478C23112yes—
386#477C2316yes—
387#477C2313yes—
388#477C2313yes—
389#476C2316yes—
390#476C2316yes—
391#476C2313yes—
392#476C23112yes—
393#476C2316yes—
394#476C2316yes—
395#476C23112yes—
396#476C23112yes—
397#476C23112yes—
398#476C2316yes—
399#476C2313yes—
400#475C2313yes—
401#475C2316yes—
402#475C2316yes—
403#475C23112yes—
404#475C23112yes—
405#475C2316yes—
406#475C2316yes—
407#475C2313yes—
408#475C23112yes—
409#475C2316yes—
410#475C23112yes—
411#474C2313yes—
412#474C2316yes—
413#474C2313yes—
414#470C23112yes—
415#469C23112yes—
416#467C2316yes—
417#466C2316yes—
418#465C2316yes—
419#465C23112yes—
420#465C2316yes—
421#465C2316yes—
422#465C2316yes—
423#465C2316yes—
424#465C2312yes—
425#464C2316yes—
426#464C2316yes—
427#464C23112yes—
428#463C2316yes—
429#463C23112yes—
430#463C2316yes—
431#462C2316yes—
432#462C2313yes—
433#462C2313yes—
434#461C2311yescharacteristic
435#461C2313yes—
436#460C2311yescharacteristic
437#460C2313yes—
438#459C2316yes—
439#459C2313yes—
440#459C2313yes—
441#452C2316yes—
442#452C2316yes—
443#451C2316yes—
444#450C2312yes—
445#449C2316yes—
446#449C2316yes—
447#448C2312yes—
448#447C2316yes—
449#446C2316yes—
450#446C2316yes—
451#446C2316yes—
452C8×Q8C2311yescharacteristic
453C8×Q8C2312yes—
454C8×Q8C2313yes—
455C8×Q8C2316yes—
456C8×Q8C2311yescharacteristic
457C8×Q8C2316yes—
458C8×Q8C2313yes—
459#442C23112yes—
460#442C23112yes—
461#441C23112yes—
462#441C23112yes—
463C4×Q16C2316yes—
464C4×Q16C2313yes—
465C4×Q16C2313yes—
466C4×SD16C2316yes—
467C4×SD16C2316yes—
468C4×SD16C2316yes—
469C4×SD16C2313yes—
470C4×SD16C23112yes—
471C4×SD16C2316yes—
472C4×SD16C2316yes—
473C4×SD16C23112yes—
474C4×SD16C2316yes—
475C4×SD16C2313yes—
476C4×SD16C2316yes—
477C4×SD16C2316yes—
478C4×SD16C2313yes—
479C4×SD16C2316yes—
480C4×SD16C2311yescharacteristic
481C4×D8C2316yes—
482C4×D8C2313yes—
483C4×D8C2313yes—
484#436C2316yes—
485#435C23112yes—
486C8×D4C2311yescharacteristic
487C8×D4C2313yes—
488C8×D4C2316yes—
489C8×D4C2313yes—
490C8×D4C2316yes—
491C8×D4C2313yes—
492#433C23112yes—
493#432C2316yes—
494#431C2316yes—
495#431C2313yes—
496#431C2313yes—
497#428C2316yes—
498#428C2316yes—
499#427C2313yes—
500C2×#106C23112yes—
501C2×#106C2316yes—
502C2×#106C2316yes—
503C2×#106C2316yes—
504#424C2316yes—
505#423C2313yes—
506C2×C4⋊C8C2316yes—
507#417C2316yes—
508#417C2316yes—
509#416C2313yes—
510#416C2313yes—
511C2×#103C2316yes—
512C2×#102C2316yes—
513#405C2316yes—
514C2×C4×C8C2313yes—
515C2×C4×C8C2316yes—
5162−1+4—84no—
5172−1+4—812no—
518C2×#41—21no—
519C2×#41—23no—
520C2×#41—26no—
521C2×#41—212no—
522C2×#41—23no—
523C2×#41—23no—
524C2×#41—26no—
525C2×#41C2×D413yes—
526C2×#41C2×D411yescharacteristic
527C2×#41C2413yes—
528C2×#41C2413yes—
529C22×Q8—21no—
530C22×Q8—22no—
531C22×Q8—26no—
532C22×Q8—26no—
533C22×Q8—26no—
534C22×Q8—26no—
535C22×Q8—26no—
536C22×Q8—23no—
537C22×Q8—23no—
538C22×Q8—88no—
539C22×Q8C2×D412yes—
540C22×Q8C2412yes—
541C22×D4—21no—
542C22×D4C2412yes—
543C23×C4—26no—
544#135—212no—
545C2×Q16C2413yes—
546C2×Q16C2416yes—
547C2×SD16—28no—
548C2×SD16C2412yes—
549C2×SD16C2412yes—
550C2×SD16C2412yes—
551C2×SD16C2413yes—
552C2×SD16C2412yes—
553C2×SD16C2416yes—
554C2×SD16C2411yescharacteristic
555C2×D8C2413yes—
556C2×D8C2416yes—
557C2×M16C2416yes—
558C22×C8C2412yes—
559C22×C8C2413yes—
560C22×C8C2416yes—
561C22×C8C2413yes—
562C4⋊Q8—23no—
563C4⋊Q8—26no—
564C4⋊Q8—26no—
565C4⋊Q8—23no—
566C4⋊Q8—26no—
567C4⋊Q8—212no—
568C4⋊Q8—26no—
569C4⋊Q8—212no—
570C4⋊Q8—26no—
571C4⋊Q8—26no—
572C4⋊Q8—26no—
573C4⋊Q8—21no—
574C4⋊Q8—212no—
575C4⋊Q8—23no—
576C4⋊Q8—23no—
577C4⋊Q8—23no—
578C4⋊Q8—23no—
579C4⋊Q8—26no—
580C4⋊Q8—26no—
581C4⋊Q8—26no—
582C4⋊Q8—26no—
583C4⋊Q8C2×D413yes—
584C4⋊Q8C2×D413yes—
585C4⋊Q8C2413yes—
586C4⋊Q8C2411yescharacteristic
587C4⋊Q8C2416yes—
588C4⋊Q8C2413yes—
589C4⋊Q8C2413yes—
590C4⋊Q8C2416yes—
591C4⋊Q8C2413yes—
592C4⋊Q8C2413yes—
593C4⋊Q8C24112yes—
594C4⋊Q8C24112yes—
595#127—23no—
596#127C2411yescharacteristic
597#127C2413yes—
598#126—26no—
599#126—26no—
600#126—212no—
601#126—212no—
602#126—212no—
603#126—26no—
604#126—26no—
605#126—26no—
606#126—26no—
607#126C2×D4112yes—
608#125—23no—
609#125—26no—
610#125—26no—
611#125—23no—
612#125—26no—
613#125—26no—
614#125—26no—
615#125—212no—
616#125—212no—
617#125—26no—
618#125—23no—
619#125—23no—
620#125C2×D416yes—
621#125C2×D416yes—
622#125C2416yes—
623#125C2416yes—
624#124—23no—
625#124—26no—
626#124—23no—
627#124—26no—
628#124—212no—
629#124—26no—
630#124—212no—
631#124—26no—
632#124—23no—
633#124—23no—
634#124C2×D416yes—
635#124C2416yes—
636#124C2416yes—
637#123—26no—
638#123—26no—
639#123—26no—
640#123—26no—
641#123—26no—
642#123—212no—
643#123—212no—
644#123—26no—
645#123—212no—
646#123—26no—
647#123—26no—
648#123—212no—
649#123—212no—
650#123—212no—
651#123C2×D4112yes—
652C22⋊Q8—26no—
653C22⋊Q8—23no—
654C22⋊Q8—23no—
655C22⋊Q8—26no—
656C22⋊Q8—26no—
657C22⋊Q8—23no—
658C22⋊Q8—23no—
659C22⋊Q8—23no—
660C22⋊Q8—26no—
661C22⋊Q8—26no—
662C22⋊Q8—26no—
663C22⋊Q8—26no—
664C22⋊Q8—212no—
665C22⋊Q8—212no—
666C22⋊Q8—212no—
667C22⋊Q8—26no—
668C22⋊Q8—26no—
669C22⋊Q8—23no—
670C22⋊Q8—26no—
671C22⋊Q8—212no—
672C22⋊Q8—212no—
673C22⋊Q8—212no—
674C22⋊Q8—212no—
675C22⋊Q8—212no—
676C22⋊Q8—26no—
677C22⋊Q8—22no—
678C22⋊Q8—212no—
679C22⋊Q8—212no—
680C22⋊Q8—212no—
681C22⋊Q8—212no—
682C22⋊Q8C2×D416yes—
683C22⋊Q8C2×D416yes—
684C22⋊Q8C2×D416yes—
685C22⋊Q8C2412yes—
686C22⋊Q8C2416yes—
687C22⋊Q8C2416yes—
688C22⋊Q8C2416yes—
689#121—23no—
690#121—26no—
691#121—26no—
692#121—23no—
693#121—26no—
694#121—23no—
695#121—23no—
696#121—21no—
697#121—23no—
698#121—26no—
699#121—26no—
700#121C2×D416yes—
701#121C2412yes—
702#121C2416yes—
703#121C2416yes—
704#121C2416yes—
705#120—26no—
706#120—22no—
707C4×Q8—21no—
708C4×Q8—21no—
709C4×Q8—22no—
710C4×Q8—26no—
711C4×Q8—26no—
712C4×Q8—26no—
713C4×Q8—23no—
714C4×Q8—23no—
715C4×Q8—26no—
716C4×Q8—23no—
717C4×Q8—26no—
718C4×Q8—26no—
719C4×Q8—23no—
720C4×Q8—26no—
721C4×Q8C2×D411yescharacteristic
722C4×Q8C2×D412yes—
723C4×Q8C2×D416yes—
724C4×Q8C2×D413yes—
725C4×Q8C2413yes—
726C4×Q8C2416yes—
727C4×Q8C2416yes—
728C4×Q8C2416yes—
729C4×Q8C2411yescharacteristic
730C4×Q8C2413yes—
731C4×Q8C2413yes—
732C4×Q8C24112yes—
733C4×Q8C2411yescharacteristic
734C4×Q8C2416yes—
735C4×Q8C2413yes—
736C4×D4—23no—
737C4×D4—21no—
738C4×D4—212no—
739C4×D4—26no—
740C4×D4—26no—
741C4×D4—26no—
742C4×D4—23no—
743C4×D4—23no—
744C4×D4—23no—
745C4×D4—23no—
746C4×D4—23no—
747C4×D4—23no—
748C4×D4—26no—
749C4×D4—26no—
750C4×D4—26no—
751C4×D4—212no—
752C4×D4—212no—
753C4×D4—23no—
754C4×D4—26no—
755C4×D4—26no—
756C4×D4—23no—
757C4×D4—26no—
758C4×D4C2×D413yes—
759C4×D4C2×D416yes—
760C4×D4C2×D413yes—
761C4×D4C2413yes—
762C4×D4C2416yes—
763C4×D4C2416yes—
764C4×D4C2416yes—
765C4×D4C2411yescharacteristic
766C4×D4C2413yes—
767C4×D4C2413yes—
768C4×D4C24112yes—
769C4×D4C2411yescharacteristic
770C4×D4C2416yes—
771C4×D4C2413yes—
772#117—23no—
773#117—23no—
774#117—26no—
775#117—23no—
776#117—23no—
777#117—26no—
778#117—26no—
779#117—26no—
780#117—26no—
781#117—23no—
782#117—23no—
783#117—26no—
784#117—26no—
785#117C2×D416yes—
786#117C2×D413yes—
787#117C2×D413yes—
788#117C2413yes—
789#117C2413yes—
790#117C2416yes—
791C2×C4⋊C4—26no—
792C2×C4⋊C4—26no—
793C2×C4⋊C4—26no—
794C2×C4⋊C4—23no—
795C2×C4⋊C4—23no—
796C2×C4⋊C4—23no—
797C2×C4⋊C4—23no—
798C2×C4⋊C4—26no—
799C2×C4⋊C4—26no—
800C2×C4⋊C4—26no—
801C2×C4⋊C4C2×D416yes—
802C2×C4⋊C4C2416yes—
803C2×C4⋊C4C2416yes—
804C2×C4⋊C4C2416yes—
805C2×C4⋊C4C2416yes—
806C2×C22⋊C4—26no—
807C2×C22⋊C4—26no—
808C2×C42—26no—
809C2×C42—23no—
810C2×C42—23no—
811C2×C42C2416yes—
812C2×C42C2413yes—
813#107C2413yes—
814#107C2413yes—
815#107C2416yes—
816#107C2416yes—
817#106C2416yes—
818#106C2413yes—
819#106C2416yes—
820#106C24112yes—
821#106C2416yes—
822#106C24112yes—
823#106C24112yes—
824#106C2416yes—
825#106C2416yes—
826#106C24112yes—
827#106C2411yescharacteristic
828C4⋊C8C2413yes—
829C4⋊C8C2416yes—
830C4⋊C8C24112yes—
831C4⋊C8C2413yes—
832C4⋊C8C2416yes—
833C4⋊C8C2411yescharacteristic
834C4⋊C8C2413yes—
835C4⋊C8C2416yes—
836#103C2413yes—
837#103C2416yes—
838#103C2416yes—
839#103C2416yes—
840#103C2411yescharacteristic
841#103C2413yes—
842#103C2413yes—
843#103C24112yes—
844#103C2416yes—
845#103C2416yes—
846#103C2416yes—
847#103C2412yes—
848#102C2413yes—
849#102C2416yes—
850#102C2416yes—
851#102C2416yes—
852#102C2411yescharacteristic
853#102C2413yes—
854#102C2413yes—
855#102C24112yes—
856#102C2412yes—
857#102C2416yes—
858#102C2416yes—
859#102C2416yes—
860C22⋊C8C2412yes—
861C22⋊C8C2416yes—
862C22⋊C8C2416yes—
863C22⋊C8C2416yes—
864#97C24112yes—
865C4×C8C2411yescharacteristic
866C4×C8C2413yes—
867C4×C8C2416yes—
868C4×C8C2413yes—
869C4×C8C2413yes—
870C4×C8C2416yes—
871C4×C8C2416yes—
872C24—22no—
873#41—24no—
874#41—212no—
875#41—26no—
876#41—26no—
877#41—43no—
878#41—43no—
879#41—44no—
880#41—412no—
881#41—86no—
882#41—86no—
883#41—812no—
884#41—824no—
885#41—812no—
886C2×Q8—28no—
887C2×Q8—22no—
888C2×Q8—23no—
889C2×Q8—26no—
890C2×Q8—23no—
891C2×Q8—212no—
892C2×Q8—212no—
893C2×Q8—23no—
894C2×Q8—26no—
895C2×Q8—23no—
896C2×Q8—24no—
897C2×Q8—42no—
898C2×Q8—44no—
899C2×Q8—48no—
900C2×Q8—812no—
901C2×Q8—812no—
902C2×Q8—86no—
903C2×Q8—86no—
904C2×Q8—812no—
905C2×Q8—812no—
906C2×Q8—812no—
907C2×Q8C22×D416yes—
908C2×Q8C22×D413yes—
909C2×Q8C22×D411yescharacteristic
910C2×Q8C2512yes—
911C2×Q8C2513yes—
912C2×Q8C2511yescharacteristic
913C2×D4—24no—
914C2×D4—23no—
915C2×D4—22no—
916C2×D4—23no—
917C2×D4—26no—
918C2×D4—26no—
919C2×D4—26no—
920C2×D4—22no—
921C2×D4—21no—
922C2×D4—23no—
923C2×D4—21no—
924C2×D4—23no—
925C2×D4—42no—
926C2×D4—44no—
927C2×D4C22×D416yes—
928C2×D4C22×D413yes—
929C2×D4C22×D411yescharacteristic
930C2×D4C2512yes—
931C2×D4C2513yes—
932C2×D4C2511yescharacteristic
933C22×C4—22no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—21no—
939C22×C4—23no—
940C22×C4—23no—
941C22×C4—23no—
942C22×C4—23no—
943C22×C4—23no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—212no—
947C22×C4—26no—
948C22×C4—812no—
949C22×C4C22×D416yes—
950C22×C4C22×D416yes—
951C22×C4C22×D413yes—
952C22×C4C22×D413yes—
953C22×C4C2512yes—
954C22×C4C2513yes—
955Q16—26no—
956Q16—46no—
957SD16—24no—
958SD16—24no—
959SD16—24no—
960SD16—26no—
961SD16—42no—
962SD16—46no—
963SD162−1+414yescomplemented
964D8—26no—
965D8—46no—
966M16—46no—
967C2×C8—24no—
968C2×C8—26no—
969C2×C8—43no—
970C2×C8—46no—
971C2×C8C2512yes—
972C2×C8C2511yescharacteristic
973C2×C8C2513yes—
974C2×C8C2513yes—
975C2×C8C2516yes—
976C2×C8C2511yescharacteristic
977C4⋊C4—26no—
978C4⋊C4—23no—
979C4⋊C4—26no—
980C4⋊C4—23no—
981C4⋊C4—23no—
982C4⋊C4—23no—
983C4⋊C4—26no—
984C4⋊C4—23no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—23no—
989C4⋊C4—26no—
990C4⋊C4—212no—
991C4⋊C4—212no—
992C4⋊C4—26no—
993C4⋊C4—212no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—22no—
1002C4⋊C4—23no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—23no—
1006C4⋊C4—23no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4C22×D416yes—
1010C4⋊C4C22×D413yes—
1011C4⋊C4C22×D413yes—
1012C4⋊C4C22×D416yes—
1013C4⋊C4C22×D416yes—
1014C4⋊C4C22×D413yes—
1015C4⋊C4C22×D4112yes—
1016C4⋊C4C22×D411yescharacteristic
1017C4⋊C4C22×D416yes—
1018C4⋊C4C22×D416yes—
1019C4⋊C4C2516yes—
1020C4⋊C4C2516yes—
1021C4⋊C4C2513yes—
1022C4⋊C4C2513yes—
1023C4⋊C4C2511yescharacteristic
1024C4⋊C4C2511yescharacteristic
1025C22⋊C4—26no—
1026C22⋊C4—22no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—23no—
1030C22⋊C4—23no—
1031C22⋊C4—23no—
1032C22⋊C4—26no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—26no—
1037C22⋊C4—21no—
1038C22⋊C4—22no—
1039C22⋊C4—26no—
1040C22⋊C4—26no—
1041C22⋊C4—26no—
1042C22⋊C4—26no—
1043C22⋊C4—26no—
1044C22⋊C4—23no—
1045C22⋊C4—23no—
1046C22⋊C4—212no—
1047C22⋊C4C22×D416yes—
1048C22⋊C4C22×D412yes—
1049C22⋊C4C22×D416yes—
1050C22⋊C4C22×D416yes—
1051C22⋊C4C22×D4112yes—
1052C42—21no—
1053C42—23no—
1054C42—23no—
1055C42—26no—
1056C42—26no—
1057C42—23no—
1058C42—23no—
1059C42—26no—
1060C42—23no—
1061C42—212no—
1062C42C22×D413yes—
1063C42C22×D413yes—
1064C42C22×D416yes—
1065C42C22×D416yes—
1066C42C2511yescharacteristic
1067C42C2513yes—
1068C42C2516yes—
1069C23—21no—
1070C23—22no—
1071C23—23no—
1072C23—44no—
1073C23—44no—
1074C23—82no—
1075C23C23×D413yes—
1076C23C23×D412yes—
1077Q8—21no—
1078Q8—212no—
1079Q8—26no—
1080Q8—22no—
1081Q8—23no—
1082Q8—23no—
1083Q8—22no—
1084Q8—44no—
1085Q8—46no—
1086Q8—412no—
1087Q8—46no—
1088Q8—812no—
1089Q8—83no—
1090Q8—86no—
1091Q8—83no—
1092Q8—812no—
1093Q8#57714yes—
1094Q8C2×2−1+412yes—
1095D4—212no—
1096D4—23no—
1097D4—22no—
1098D4—21no—
1099D4—22no—
1100D4—23no—
1101D4—26no—
1102D4—44no—
1103D4—46no—
1104D4—46no—
1105D4—44no—
1106D4—412no—
1107D4—42no—
1108D4—46no—
1109D4—81no—
1110D4—83no—
1111D4—86no—
1112D4—86no—
1113D4#57714yes—
1114D4C2×2−1+412yes—
1115C2×C4—21no—
1116C2×C4—212no—
1117C2×C4—22no—
1118C2×C4—23no—
1119C2×C4—22no—
1120C2×C4—23no—
1121C2×C4—212no—
1122C2×C4—26no—
1123C2×C4—26no—
1124C2×C4—22no—
1125C2×C4—23no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—26no—
1131C2×C4—26no—
1132C2×C4—46no—
1133C2×C4—44no—
1134C2×C4—46no—
1135C2×C4—412no—
1136C2×C4—46no—
1137C2×C4—412no—
1138C2×C4—42no—
1139C2×C4—46no—
1140C2×C4—46no—
1141C2×C4—86no—
1142C2×C4—86no—
1143C2×C4—812no—
1144C2×C4—86no—
1145C2×C4—86no—
1146C2×C4—86no—
1147C2×C4C23×D413yes—
1148C2×C4C23×D416yes—
1149C2×C4C23×D416yes—
1150C2×C4C23×D412yes—
1151C2×C4C23×D411yescharacteristic
1152C2×C4C23×D413yes—
1153C2×C4C23×D413yes—
1154C2×C4C23×D411yescharacteristic
1155C2×C4C2611yescharacteristic
1156C8—23no—
1157C8—22no—
1158C8—21no—
1159C8—23no—
1160C8—26no—
1161C8C2×2−1+412yes—
1162C22—22no—
1163C22—22no—
1164C22—23no—
1165C22—22no—
1166C22—23no—
1167C22—23no—
1168C22—41no—
1169C22—41no—
1170C22—43no—
1171C22—42no—
1172C22—42no—
1173C22—43no—
1174C22—43no—
1175C22—42no—
1176C22—88no—
1177C22C2×#57714yes—
1178C22C24×D411yescharacteristic
1179C4—23no—
1180C4—22no—
1181C4—22no—
1182C4—23no—
1183C4—21no—
1184C4—26no—
1185C4—26no—
1186C4—43no—
1187C4—42no—
1188C4—41no—
1189C4—43no—
1190C4—46no—
1191C4—46no—
1192C4—43no—
1193C4—41no—
1194C4C2×#57716yes—
1195C4C2×#57712yes—
1196C4C22×2−1+411yescharacteristic
1197C42−1+611yescharacteristic
1198C2—24no—
1199C2—43no—
1200C2—42no—
1201C2—83no—
1202C2—82no—
1203C2D4×2−1+411yescharacteristic
1204C2C22×#57711yescharacteristic
1205C2C22×#57711yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3482 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63037C2semidirect
2. #63016C2semidirect
3. #62486C2semidirect
4. #62469C2semidirect
5. #62469C2semidirect
6. #62372C2semidirect
7. #62362C2semidirect
8. #62205C2semidirect
9. #62202C2semidirect
10. #62150C2semidirect
11. #62147C2semidirect
12. #62131C2semidirect
13. #62128C2semidirect
14. #61871C2semidirect
15. #61871C2semidirect
16. #61843C2semidirect
17. #61838C2semidirect
18. #61483C2semidirect
19. #61434C2semidirect
20. #61432C2semidirect
21. #61374C2semidirect
22. C2×Q8×SD16C2semidirect
23. #60331C2semidirect
28. #3550C22semidirect
30. #3544C22semidirect
35. #3522C22semidirect
36. #3522C22semidirect
42. #3503C22semidirect
43. #3503C22semidirect
48. #3483C22semidirect
54. C2×Q82C22semidirect
58. #3394C22semidirect
59. #3392C22semidirect
60. #3387C22semidirect
61. #3387C22semidirect
62. #3387C22semidirect
65. #3384C22semidirect
67. #3381C22semidirect
72. Q8×SD16C22semidirect
73. Q8×SD16C22semidirect
74. Q8×SD16C22semidirect
75. Q8×SD16C22semidirect
76. Q8×SD16C22semidirect
77. Q8×SD16C22semidirect
78. Q8×SD16C22semidirect
81. #3373C22semidirect
82. #3369C22semidirect
83. #3369C22semidirect
84. #3369C22semidirect
86. #3365C22semidirect
87. #3363C22semidirect
88. #3363C22semidirect
90. #3360C22semidirect
92. #3358C22semidirect
93. #3356C22semidirect
94. #3354C22semidirect
96. #3344C22semidirect
97. #3340C22semidirect
101. #3335C22semidirect
102. #3335C22semidirect
103. #3335C22semidirect
104. #3335C22semidirect
105. #3332C22semidirect
107. #3316C22semidirect
109. #3304C22semidirect
118. #3263C22semidirect
119. #3255C22semidirect
121. #3248C22semidirect
123. #3244C22semidirect
124. #3244C22semidirect
125. #3239C22semidirect
127. #3229C22semidirect
128. #3229C22semidirect
129. #3229C22semidirect
131. #3227C22semidirect
132. #3227C22semidirect
133. #3173C22semidirect
136. #3167C22semidirect
137. #3167C22semidirect
138. #3163C22semidirect
139. C2×#498C22semidirect
140. C2×#498C22semidirect
142. #3125C22semidirect
143. #3113C22semidirect
147. #3107C22semidirect
152. #3084C22semidirect
154. #3079C22semidirect
155. C2×#475C22semidirect
157. #2994C22semidirect
158. #2991C22semidirect
160. #2986C22semidirect
161. #2984C22semidirect
162. #2966C22semidirect
164. C8×#41C22semidirect
165. #2960C22semidirect
166. C2×C8×Q8C22semidirect
963. SD162−1+4semidirect

Maximal subgroups

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

subgroupindex
#630372
#630162
#624862
#624692
#623722
#623622
#622052
#622022
#621502
#621472
#621312
#621282
#618712
#618432
#618382
#614832
#614342
#614322
#613742
C2×Q8×SD162
#603312