Finite Group Databasebeta

← #10575771

Subgroups — #10575771

Order 512.

6173 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62813C211yesmaximal, characteristic, complemented
2#62800C211yesmaximal, characteristic
3#60892C216yesmaximal, complemented
4#60888C216yesmaximal, complemented
5#60886C216yesmaximal, complemented
6#60883C216yesmaximal, complemented
7#60875C2112yesmaximal, complemented
8#60864C213yesmaximal, complemented
9#60863C213yesmaximal, complemented
10#60854C213yesmaximal, complemented
11C2×#3235C213yesmaximal, complemented
12#60668C212yesmaximal, complemented
13#60626C212yesmaximal, complemented
14#60523C214yesmaximal, complemented
15#60495C212yesmaximal, complemented
16#60494C212yesmaximal, complemented
17#60128C211yesmaximal, characteristic, complemented
18#3522—21no—
19#3519—23no—
20#3517—21no—
21#3514—23no—
22#3511C2213yes—
23#3508C2213yes—
24#3504C2212yes—
25#3504C2216yescomplemented
26#3503C2211yescharacteristic
27#3503C2211yescharacteristic
28#3503C2211yescharacteristic
29#3503C2213yescomplemented
30#3503C2213yescomplemented
31#3502—21no—
32#3502—21no—
33#3501—23no—
34#3501—23no—
35#3498C2211yescharacteristic
36#3494C2216yes—
37#3488C2212yes—
38#3483—21no—
39#3481—23no—
40#3480—21no—
41Q8×#41—23no—
42Q8×#41—21no—
43Q8×#41—23no—
44Q8×#41—21no—
45D4×#41—23no—
46#3460C2216yes—
47#3458C2216yescomplemented
48#3444C2213yes—
49C2×#533C2213yescomplemented
50C2×#533C2213yescomplemented
51C2×#532C2213yes—
52C4×H(5,𝔽2)C2212yes—
53#3428C2212yes—
54C2×C4×#41C2211yescharacteristic
55#3244C22124yescomplemented
56#3243C22124yescomplemented
57#3241C22124yescomplemented
58#3241C22124yescomplemented
59#3240C22112yescomplemented
60#3239C2216yescomplemented
61#3238C2216yescomplemented
62#3237C2211yescharacteristic, complemented
63#3237C2213yescomplemented
64#3237C2216yescomplemented
65#3236C2216yescomplemented
66#3235C2213yescomplemented
67#3235C2216yescomplemented
68#3235C22112yescomplemented
69#3235C22112yescomplemented
70#3235C22112yescomplemented
71#3235C2213yescomplemented
72#3235C2216yescomplemented
73#3234C2216yescomplemented
74#3234C22112yescomplemented
75#3233C22112yescomplemented
76#3233C22112yescomplemented
77#3228C22112yescomplemented
78#3227C2216yescomplemented
79#3226C2216yescomplemented
80#3166C2216yescomplemented
81#3165C2216yescomplemented
82#3164C22112yescomplemented
83#3163C22112yescomplemented
84#3162C2216yescomplemented
85C2×#501C2216yescomplemented
86#3142C2216yescomplemented
87#3138C2216yescomplemented
88#3136C22112yescomplemented
89#3136C22112yescomplemented
90#3135C2216yescomplemented
91C2×#490C2216yescomplemented
92#3099C22112yescomplemented
93#3098C22112yescomplemented
94#3096C22112yescomplemented
95#3096C22112yescomplemented
96#3094C22112yescomplemented
97#3093C22112yescomplemented
98#3091C22112yescomplemented
99C2×#482C22112yescomplemented
100#3084C22112yescomplemented
101#3083C22112yescomplemented
102#3081C22112yescomplemented
103#3081C22112yescomplemented
104#3079C2216yescomplemented
105#3079C2216yescomplemented
106#3077C2216yescomplemented
107#3077C2216yescomplemented
108#3076C2216yescomplemented
109#3076C2216yescomplemented
110C2×#476C2216yescomplemented
111C2×#474C2216yescomplemented
112#2925C2216yescomplemented
113#2924C2216yescomplemented
114#2923C2216yescomplemented
115#2920C2213yescomplemented
116C2×#432C2213yescomplemented
117#2913C2214yes—
118#2912C2214yes—
119#2906C2212yes—
120#2897C2214yes—
121#2897C2214yes—
122#2880C2212yes—
123#2875C2212yes—
124C2×H(5,𝔽2)C2312yes—
125C22×#41—23no—
126C22×#41C2311yescharacteristic
127C2×#131C2314yes—
128#559—23no—
129#559—23no—
130Q82—21no—
131Q82—21no—
132Q82—23no—
133Q82—23no—
134Q82—21no—
135#557—21no—
136#557—21no—
137#557—23no—
138#557—23no—
139#557—22no—
140#557—22no—
141#557—26no—
142#557—26no—
143#557—21no—
144#556—23no—
145#555—23no—
146#555—26no—
147#554—23no—
148#554—23no—
149#554—23no—
150#554—26no—
151#554—23no—
152#554—26no—
153#554—23no—
154#554—26no—
155#554—26no—
156#554—212no—
157#554—212no—
158#554—26no—
159#554—26no—
160#554—23no—
161#553—26no—
162#553—26no—
163#553—26no—
164#551—212no—
165#550—22no—
166#550—21no—
167#550—21no—
168#550—23no—
169#550—23no—
170D4×Q8—23no—
171D4×Q8—23no—
172D4×Q8—23no—
173D4×Q8—26no—
174D4×Q8—23no—
175D4×Q8—26no—
176D4×Q8—23no—
177#548—22no—
178#548—26no—
179#547—23no—
180#547—26no—
181#546—26no—
182#546—26no—
183#546—26no—
184#546—212no—
185D42—26no—
186D42—23no—
187D42—23no—
188#544—26no—
189#544—26no—
190#544C2316yes—
191#544C2316yes—
192#544C2316yes—
193#544C2316yes—
194#544C2316yes—
195#544C23112yes—
196#544C23112yes—
197#543—212no—
198#542—26no—
199#542C23112yes—
200#540—26no—
201#540C23112yes—
202#538—212no—
203#537C2316yes—
204#535C2316yes—
205#535C2316yes—
206#533—212no—
207#533—26no—
208#533—26no—
209#533—23no—
210#533—23no—
211#533—23no—
212#533—23no—
213#533—23no—
214#533—23no—
215#533—23no—
216#533—23no—
217#533C2311yescharacteristic
218#533C2313yes—
219#533C2313yes—
220#533C2313yes—
221#533C2316yes—
222#533C2313yes—
223#533C2313yes—
224#533C2311yescharacteristic
225#533C2316yes—
226#533C2316yes—
227#533C2316yes—
228#533C2316yes—
229#532—26no—
230#532—23no—
231#532—23no—
232#532—23no—
233#532—23no—
234#532C2313yes—
235#532C2313yes—
236#532C2316yes—
237#532C2316yes—
238#532C2316yes—
239#532C2313yes—
240C2×C4⋊Q8C2313yes—
241C2×C4⋊Q8C2313yes—
242C2×C4⋊Q8C2313yes—
243C2×C4⋊Q8C2313yes—
244C2×C4⋊Q8C2313yes—
245C2×#127C2313yes—
246#529—26no—
247#529—23no—
248#529—23no—
249#529—23no—
250#529—23no—
251#529C2316yes—
252#529C2316yes—
253C2×#125C2316yes—
254C2×#125C2316yes—
255C2×#124—23no—
256#525—23no—
257#525—23no—
258#525—212no—
259#525C2316yes—
260C2×C22⋊Q8—23no—
261C2×C22⋊Q8—23no—
262C2×C22⋊Q8—23no—
263C2×C22⋊Q8—23no—
264C2×#121—23no—
265C2×#121C2316yes—
266#520—22no—
267#520C2316yes—
268#520C2316yes—
269#520C2316yes—
270#520C2312yes—
271#520C2312yes—
272#520C2312yes—
273#519—22no—
274#518—26no—
275#518—26no—
276#518C2316yes—
277C4×#41—26no—
278C4×#41—22no—
279C4×#41—22no—
280C4×#41—23no—
281C4×#41—23no—
282C4×#41D413yes—
283C4×#41D411yescharacteristic
284C4×#41D413yes—
285C4×#41D411yescharacteristic
286C4×#41C2316yes—
287C4×#41C2311yescharacteristic
288C4×#41C2311yescharacteristic
289C4×#41C2313yes—
290C4×#41C2313yes—
291C2×C4×Q8—23no—
292C2×C4×Q8—23no—
293C2×C4×Q8—23no—
294C2×C4×Q8—23no—
295C2×C4×Q8D411yescharacteristic
296C2×C4×Q8D411yescharacteristic
297C2×C4×D4—26no—
298C2×C4×D4—23no—
299C2×C4×D4D413yes—
300C2×C4×D4D413yes—
301C2×C4×D4C2316yes—
302C2×#117C2316yes—
303C2×#117C2316yes—
304C2×#117C2313yes—
305C22×C42C2313yes—
306#501C2316yes—
307#501C23124yes—
308#501C23112yes—
309#501C2312yes—
310#501C23112yes—
311#501C23112yes—
312#501C2316yes—
313#501C2316yes—
314#500C23112yes—
315#499C23124yes—
316#498C23112yes—
317#491C2312yes—
318#491C2316yes—
319#490C2316yes—
320#490C23124yes—
321#490C23112yes—
322#490C2316yes—
323#489C23112yes—
324#489C23112yes—
325#488C23124yes—
326#486C23112yes—
327#486C23112yes—
328#485C2314yes—
329#485C23112yes—
330#485C23124yes—
331#484C23112yes—
332#483C23112yes—
333#482C23112yes—
334#482C23124yes—
335#482C23124yes—
336#482C23124yes—
337#482C23112yes—
338#482C23124yes—
339#481C23112yes—
340#481C23124yes—
341#480C23112yes—
342#480C23124yes—
343#479C23112yes—
344#479C23112yes—
345#478C23112yes—
346#478C23112yes—
347#478C23124yes—
348#478C23124yes—
349#477C2312yes—
350#477C2316yes—
351#477C23112yes—
352#476C2316yes—
353#476C2316yes—
354#476C23112yes—
355#476C23112yes—
356#476C23124yes—
357#475C2312yes—
358#475C2316yes—
359#475C23112yes—
360#474C2316yes—
361#474C2316yes—
362#474C23112yes—
363#474C23112yes—
364#474C23124yes—
365#433C23124yes—
366#432C2311yescharacteristic
367#432C2313yes—
368#432C2316yes—
369#432C2316yes—
370#432C2316yes—
371#432C2316yes—
372#431C2316yes—
373#431C2316yes—
374#428C23112yes—
375#428C23112yes—
376#428C23112yes—
377#428C23112yes—
378#427C23112yes—
379#427C23112yes—
380C2×#107C23112yes—
381C2×#106C23112yes—
382#424C23112yes—
383#423C2316yes—
384C2×C4⋊C8C2316yes—
385#418C23112yes—
386#418C23112yes—
387#417C23112yes—
388#417C23112yes—
389#416C23112yes—
390#416C23112yes—
391C2×#102C23112yes—
392C2×#102C23112yes—
393#408C23112yes—
394#407C2316yes—
395C2×C22⋊C8C2316yes—
396#405C23112yes—
397C4×M16C2316yes—
398C2×#97C2316yes—
399H(5,𝔽2)—216no—
400C2×#41—28no—
401C2×#41—22no—
402C2×#41—23no—
403C2×#41—23no—
404C2×#41—26no—
405C2×#41—26no—
406C2×#41—26no—
407C2×#41—812no—
408C2×#41C2×D413yes—
409C2×#41C2×D411yescharacteristic
410C2×#41C2416yes—
411C2×#41C2413yes—
412C2×#41C2411yescharacteristic
413C22×Q8—23no—
414C22×Q8—23no—
415C22×Q8—23no—
416C22×Q8—23no—
417C22×Q8—23no—
418C22×Q8C2×D411yescharacteristic
419C22×D4—26no—
420C22×D4—26no—
421C22×D4—23no—
422C22×D4—23no—
423C22×D4C2×D413yes—
424C22×D4C2416yes—
425C23×C4—26no—
426C23×C4C2×D413yes—
427C23×C4C2×D413yes—
428C23×C4C2413yes—
429#131—216no—
430C2×M16C24112yes—
431C22×C8C24112yes—
432C4⋊Q8—26no—
433C4⋊Q8—26no—
434C4⋊Q8—26no—
435C4⋊Q8—26no—
436C4⋊Q8—26no—
437C4⋊Q8—212no—
438C4⋊Q8—212no—
439C4⋊Q8—23no—
440C4⋊Q8—23no—
441C4⋊Q8—23no—
442C4⋊Q8—23no—
443C4⋊Q8—23no—
444C4⋊Q8—23no—
445C4⋊Q8—23no—
446C4⋊Q8—23no—
447C4⋊Q8—23no—
448C4⋊Q8—23no—
449C4⋊Q8C2411yescharacteristic
450C4⋊Q8C2413yes—
451C4⋊Q8C2411yescharacteristic
452C4⋊Q8C2413yes—
453C4⋊Q8C2411yescharacteristic
454C4⋊Q8C2413yes—
455C4⋊Q8C2416yes—
456C4⋊Q8C2416yes—
457C4⋊Q8C2416yes—
458C4⋊Q8C2416yes—
459C4⋊Q8C2416yes—
460C4⋊Q8C2411yescharacteristic
461#127—26no—
462#127—23no—
463#127—23no—
464#127C2413yes—
465#127C2416yes—
466#126—212no—
467#126—26no—
468#126—26no—
469#125—26no—
470#125—26no—
471#125—26no—
472#125—26no—
473#125—26no—
474#125—212no—
475#125—212no—
476#125—26no—
477#125—26no—
478#125—26no—
479#125—26no—
480#125—21no—
481#125—23no—
482#125C2416yes—
483#125C2412yes—
484#125C2416yes—
485#125C2416yes—
486#125C24112yes—
487#125C2416yes—
488#124—26no—
489#124—212no—
490#124—23no—
491#124—26no—
492#124—26no—
493#124—26no—
494#124—23no—
495#124C2416yes—
496#123—26no—
497#123—26no—
498#123—26no—
499#123—212no—
500#123—212no—
501#123—212no—
502C22⋊Q8—26no—
503C22⋊Q8—23no—
504C22⋊Q8—21no—
505C22⋊Q8—23no—
506C22⋊Q8—21no—
507C22⋊Q8—26no—
508C22⋊Q8—26no—
509C22⋊Q8—26no—
510C22⋊Q8—26no—
511C22⋊Q8—23no—
512C22⋊Q8—23no—
513C22⋊Q8—26no—
514C22⋊Q8—23no—
515C22⋊Q8—23no—
516C22⋊Q8—26no—
517C22⋊Q8—26no—
518C22⋊Q8—26no—
519C22⋊Q8—26no—
520C22⋊Q8—26no—
521C22⋊Q8—21no—
522C22⋊Q8—23no—
523C22⋊Q8—23no—
524C22⋊Q8—23no—
525C22⋊Q8—212no—
526C22⋊Q8—212no—
527C22⋊Q8—212no—
528C22⋊Q8—212no—
529C22⋊Q8—212no—
530C22⋊Q8—212no—
531C22⋊Q8—212no—
532C22⋊Q8—212no—
533C22⋊Q8—212no—
534C22⋊Q8—212no—
535C22⋊Q8C2412yes—
536C22⋊Q8C2416yes—
537#121—212no—
538#121—26no—
539#121—23no—
540#121—26no—
541#121—26no—
542#121—26no—
543#121—26no—
544#121—26no—
545#121—23no—
546#121—23no—
547#121—23no—
548#121—26no—
549#121—26no—
550#121—212no—
551#121—212no—
552#121C2416yes—
553#121C24112yes—
554#121C2416yes—
555#120—26no—
556#120—212no—
557#120—212no—
558C4×Q8—26no—
559C4×Q8—26no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—23no—
564C4×Q8—21no—
565C4×Q8—23no—
566C4×Q8—21no—
567C4×Q8—26no—
568C4×Q8—26no—
569C4×Q8—26no—
570C4×Q8—26no—
571C4×Q8—23no—
572C4×Q8—23no—
573C4×Q8—23no—
574C4×Q8—23no—
575C4×Q8—26no—
576C4×Q8—26no—
577C4×Q8—26no—
578C4×Q8—26no—
579C4×Q8—26no—
580C4×Q8—26no—
581C4×Q8—21no—
582C4×Q8—23no—
583C4×Q8—23no—
584C4×Q8—23no—
585C4×Q8C2×D411yescharacteristic
586C4×Q8C2×D411yescharacteristic
587C4×Q8C2×D413yes—
588C4×Q8C2×D413yes—
589C4×Q8C2×D411yescharacteristic
590C4×Q8C2×D411yescharacteristic
591C4×Q8C2×D413yes—
592C4×Q8C2×D413yes—
593C4×Q8C2412yes—
594C4×Q8C2416yes—
595C4×D4—26no—
596C4×D4—212no—
597C4×D4—212no—
598C4×D4—26no—
599C4×D4—26no—
600C4×D4—26no—
601C4×D4—26no—
602C4×D4—26no—
603C4×D4—26no—
604C4×D4—26no—
605C4×D4—26no—
606C4×D4—26no—
607C4×D4—26no—
608C4×D4—26no—
609C4×D4—26no—
610C4×D4—212no—
611C4×D4—23no—
612C4×D4—26no—
613C4×D4—26no—
614C4×D4—26no—
615C4×D4—26no—
616C4×D4—26no—
617C4×D4—23no—
618C4×D4—23no—
619C4×D4—23no—
620C4×D4C2×D413yes—
621C4×D4C2×D413yes—
622C4×D4C2×D416yes—
623C4×D4C2×D413yes—
624C4×D4C2×D416yes—
625C4×D4C2×D413yes—
626C4×D4C2×D413yes—
627C4×D4C2×D413yes—
628C4×D4C2×D416yes—
629C4×D4C2×D416yes—
630C4×D4C2×D413yes—
631C4×D4C2×D413yes—
632C4×D4C2416yes—
633C4×D4C24112yes—
634C4×D4C2416yes—
635#117—26no—
636#117—26no—
637#117—26no—
638#117—26no—
639#117—21no—
640#117—23no—
641#117—26no—
642#117—26no—
643#117—26no—
644#117—26no—
645#117C2×D416yes—
646#117C2×D413yes—
647#117C2×D413yes—
648#117C2416yes—
649#117C2412yes—
650#117C2416yes—
651#117C2416yes—
652#117C24112yes—
653#117C2416yes—
654#117C2413yes—
655#117C2413yes—
656#117C2416yes—
657C2×C4⋊C4—23no—
658C2×C4⋊C4—26no—
659C2×C4⋊C4—26no—
660C2×C4⋊C4—26no—
661C2×C4⋊C4—26no—
662C2×C4⋊C4—23no—
663C2×C4⋊C4—23no—
664C2×C4⋊C4—23no—
665C2×C4⋊C4—23no—
666C2×C4⋊C4—26no—
667C2×C4⋊C4C2×D413yes—
668C2×C4⋊C4C2×D413yes—
669C2×C4⋊C4C2416yes—
670C2×C4⋊C4C2416yes—
671C2×C4⋊C4C2416yes—
672C2×C4⋊C4C2416yes—
673C2×C4⋊C4C2416yes—
674C2×C22⋊C4—26no—
675C2×C22⋊C4—26no—
676C2×C22⋊C4—26no—
677C2×C22⋊C4—26no—
678C2×C22⋊C4—212no—
679C2×C22⋊C4C2×D416yes—
680C2×C42—26no—
681C2×C42—26no—
682C2×C42—26no—
683C2×C42C2×D413yes—
684C2×C42C2×D413yes—
685C2×C42C2×D413yes—
686C2×C42C2×D413yes—
687C2×C42C2×D413yes—
688C2×C42C2×D413yes—
689C2×C42C2413yes—
690C2×C42C2413yes—
691C2×C42C2413yes—
692C2×C42C2413yes—
693C2×C42C2413yes—
694C2×C42C2411yescharacteristic
695#107C24112yes—
696#107C24124yes—
697#107C2414yes—
698#107C24112yes—
699#107C24112yes—
700#106C24112yes—
701#106C24124yes—
702#106C2414yes—
703#106C24112yes—
704#106C24112yes—
705C4⋊C8C2412yes—
706C4⋊C8C2416yes—
707C4⋊C8C24112yes—
708C4⋊C8C24112yes—
709#103C2414yes—
710#103C2414yes—
711#103C24112yes—
712#103C24112yes—
713#102C24112yes—
714#102C24112yes—
715#102C24124yes—
716#102C24124yes—
717#102C24112yes—
718#102C24112yes—
719C22⋊C8C2412yes—
720C22⋊C8C2416yes—
721C22⋊C8C24112yes—
722C22⋊C8C24112yes—
723#97C2412yes—
724#97C2416yes—
725#97C24112yes—
726C4×C8C24112yes—
727C24—26no—
728C24C22×D413yes—
729#41—24no—
730#41—212no—
731#41—212no—
732#41—224no—
733#41—412no—
734#41—48no—
735#41—812no—
736#41—812no—
737#41—86no—
738#41—812no—
739#412−1+418yes—
740C2×Q8—24no—
741C2×Q8—21no—
742C2×Q8—23no—
743C2×Q8—21no—
744C2×Q8—23no—
745C2×Q8—21no—
746C2×Q8—23no—
747C2×Q8—26no—
748C2×Q8—26no—
749C2×Q8—26no—
750C2×Q8—26no—
751C2×Q8—26no—
752C2×Q8—86no—
753C2×Q8—86no—
754C2×Q8—86no—
755C2×Q8—86no—
756C2×Q8—86no—
757C2×Q8C22×D413yes—
758C2×Q8C22×D411yescharacteristic
759C2×Q8C2512yes—
760C2×D4—212no—
761C2×D4—26no—
762C2×D4—26no—
763C2×D4—26no—
764C2×D4—212no—
765C2×D4—26no—
766C2×D4—23no—
767C2×D4—23no—
768C2×D4—26no—
769C2×D4—26no—
770C2×D4—224no—
771C2×D4—424no—
772C2×D4—86no—
773C2×D4—86no—
774C2×D4—812no—
775C2×D4C22×D416yes—
776C2×D4C22×D413yes—
777C2×D4C22×D413yes—
778C2×D4C2516yes—
779C22×C4—212no—
780C22×C4—26no—
781C22×C4—26no—
782C22×C4—26no—
783C22×C4—26no—
784C22×C4—26no—
785C22×C4—26no—
786C22×C4—26no—
787C22×C4—26no—
788C22×C4—212no—
789C22×C4—46no—
790C22×C4—812no—
791C22×C4—83no—
792C22×C4C22×D413yes—
793C22×C4C22×D413yes—
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D413yes—
796C22×C4C22×D413yes—
797C22×C4C22×D413yes—
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D413yes—
800C22×C4C22×D413yes—
801C22×C4C22×D413yes—
802C22×C4C22×D413yes—
803C22×C4C22×D413yes—
804C22×C4C22×D413yes—
805C22×C4C22×D413yes—
806C22×C4C22×D413yes—
807C22×C4C2511yescharacteristic
808C22×C4C2513yes—
809C22×C4C2513yes—
810M16—224no—
811C2×C8—224no—
812C2×C8C25112yes—
813C2×C8C2514yes—
814C4⋊C4—26no—
815C4⋊C4—22no—
816C4⋊C4—26no—
817C4⋊C4—22no—
818C4⋊C4—23no—
819C4⋊C4—21no—
820C4⋊C4—23no—
821C4⋊C4—21no—
822C4⋊C4—23no—
823C4⋊C4—26no—
824C4⋊C4—26no—
825C4⋊C4—26no—
826C4⋊C4—26no—
827C4⋊C4—26no—
828C4⋊C4—26no—
829C4⋊C4—26no—
830C4⋊C4—26no—
831C4⋊C4—26no—
832C4⋊C4—212no—
833C4⋊C4—26no—
834C4⋊C4—26no—
835C4⋊C4—212no—
836C4⋊C4—26no—
837C4⋊C4—26no—
838C4⋊C4—26no—
839C4⋊C4—26no—
840C4⋊C4—21no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—26no—
846C4⋊C4—26no—
847C4⋊C4—26no—
848C4⋊C4C22×D413yes—
849C4⋊C4C22×D413yes—
850C4⋊C4C22×D413yes—
851C4⋊C4C22×D413yes—
852C4⋊C4C22×D416yes—
853C4⋊C4C22×D416yes—
854C4⋊C4C2516yes—
855C4⋊C4C2512yes—
856C4⋊C4C2516yes—
857C4⋊C4C2512yes—
858C4⋊C4C2516yes—
859C4⋊C4C2512yes—
860C22⋊C4—26no—
861C22⋊C4—22no—
862C22⋊C4—26no—
863C22⋊C4—212no—
864C22⋊C4—26no—
865C22⋊C4—26no—
866C22⋊C4—22no—
867C22⋊C4—26no—
868C22⋊C4—26no—
869C22⋊C4—26no—
870C22⋊C4—212no—
871C22⋊C4—26no—
872C22⋊C4—212no—
873C22⋊C4—26no—
874C22⋊C4—26no—
875C22⋊C4—26no—
876C22⋊C4C22×D416yes—
877C22⋊C4C22×D416yes—
878C22⋊C4C22×D416yes—
879C22⋊C4C22×D416yes—
880C42—22no—
881C42—26no—
882C42—22no—
883C42—26no—
884C42—26no—
885C42—212no—
886C42—26no—
887C42—26no—
888C42C22×D413yes—
889C42C22×D411yescharacteristic
890C42C22×D411yescharacteristic
891C42C22×D413yes—
892C42C22×D413yes—
893C42C22×D413yes—
894C42C22×D413yes—
895C42C22×D413yes—
896C42C22×D413yes—
897C42C22×D413yes—
898C42C22×D413yes—
899C42C22×D413yes—
900C42C2513yes—
901C42C2511yescharacteristic
902C42C2511yescharacteristic
903C42C2513yes—
904C23—26no—
905C23—26no—
906C23—43no—
907C23—43no—
908C23—412no—
909C23—86no—
910C23—86no—
911C23C23×D411yescharacteristic
912C23C23×D413yes—
913C23C23×D413yes—
914Q8—26no—
915Q8—24no—
916Q8—46no—
917Q8—42no—
918Q8—46no—
919Q8—42no—
920Q8—46no—
921Q8—42no—
922Q8—86no—
923Q8—86no—
924Q8—86no—
925Q8—86no—
926Q8—86no—
927Q8#53614yes—
928D4—212no—
929D4—212no—
930D4—26no—
931D4—46no—
932D4—46no—
933D4—412no—
934D4—412no—
935D4—412no—
936D4—86no—
937D4—86no—
938D4—812no—
939D4—86no—
940D4#536112yes—
941C2×C4—26no—
942C2×C4—22no—
943C2×C4—26no—
944C2×C4—26no—
945C2×C4—22no—
946C2×C4—26no—
947C2×C4—26no—
948C2×C4—26no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—26no—
952C2×C4—22no—
953C2×C4—26no—
954C2×C4—22no—
955C2×C4—26no—
956C2×C4—43no—
957C2×C4—43no—
958C2×C4—43no—
959C2×C4—41no—
960C2×C4—43no—
961C2×C4—43no—
962C2×C4—43no—
963C2×C4—43no—
964C2×C4—43no—
965C2×C4—412no—
966C2×C4—412no—
967C2×C4—812no—
968C2×C4—86no—
969C2×C4—86no—
970C2×C4—86no—
971C2×C4—86no—
972C2×C4—86no—
973C2×C4—86no—
974C2×C4C23×D411yescharacteristic
975C2×C4C23×D413yes—
976C2×C4C23×D413yes—
977C2×C4C23×D411yescharacteristic
978C2×C4C23×D411yescharacteristic
979C2×C4C23×D411yescharacteristic
980C2×C4C23×D413yes—
981C2×C4C23×D413yes—
982C2×C4C23×D413yes—
983C2×C4C23×D411yescharacteristic
984C2×C4C23×D413yes—
985C2×C4C2×2−1+4112yes—
986C2×C4C2611yescharacteristic
987C8—24no—
988C8—212no—
989C22—23no—
990C22—23no—
991C22—21no—
992C22—23no—
993C22—21no—
994C22—23no—
995C22—21no—
996C22—23no—
997C22—46no—
998C22—46no—
999C22—46no—
1000C22—86no—
1001C22—1612no—
1002C22C2×#53616yes—
1003C22C24×D411yescharacteristic
1004C4—21no—
1005C4—23no—
1006C4—23no—
1007C4—21no—
1008C4—21no—
1009C4—23no—
1010C4—23no—
1011C4—21no—
1012C4—23no—
1013C4—46no—
1014C4—46no—
1015C4—42no—
1016C4—42no—
1017C4—46no—
1018C4—42no—
1019C4—42no—
1020C4C2×#53616yes—
1021C4#358512yes—
1022C4C22×2−1+412yes—
1023C2—26no—
1024C2—43no—
1025C2—41no—
1026C2—86no—
1027C2C22×#53611yescharacteristic
1028C2C2×#358511yescharacteristic
1029C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#62800C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62813C2semidirect
3. #60892C2semidirect
4. #60888C2semidirect
5. #60886C2semidirect
6. #60883C2semidirect
7. #60875C2semidirect
8. #60864C2semidirect
9. #60863C2semidirect
10. #60854C2semidirect
11. C2×#3235C2semidirect
12. #60668C2semidirect
13. #60626C2semidirect
14. #60523C2semidirect
15. #60495C2semidirect
16. #60494C2semidirect
17. #60128C2semidirect
25. #3504C22semidirect
29. #3503C22semidirect
30. #3503C22semidirect
47. #3458C22semidirect
49. C2×#533C22semidirect
50. C2×#533C22semidirect
55. #3244C22semidirect
56. #3243C22semidirect
57. #3241C22semidirect
58. #3241C22semidirect
59. #3240C22semidirect
60. #3239C22semidirect
61. #3238C22semidirect
62. #3237C22semidirect
63. #3237C22semidirect
64. #3237C22semidirect
65. #3236C22semidirect
66. #3235C22semidirect
67. #3235C22semidirect
68. #3235C22semidirect
69. #3235C22semidirect
70. #3235C22semidirect
71. #3235C22semidirect
72. #3235C22semidirect
73. #3234C22semidirect
74. #3234C22semidirect
75. #3233C22semidirect
76. #3233C22semidirect
77. #3228C22semidirect
78. #3227C22semidirect
79. #3226C22semidirect
80. #3166C22semidirect
81. #3165C22semidirect
82. #3164C22semidirect
83. #3163C22semidirect
84. #3162C22semidirect
85. C2×#501C22semidirect
86. #3142C22semidirect
87. #3138C22semidirect
88. #3136C22semidirect
89. #3136C22semidirect
90. #3135C22semidirect
91. C2×#490C22semidirect
92. #3099C22semidirect
93. #3098C22semidirect
94. #3096C22semidirect
95. #3096C22semidirect
96. #3094C22semidirect
97. #3093C22semidirect
98. #3091C22semidirect
99. C2×#482C22semidirect
100. #3084C22semidirect
101. #3083C22semidirect
102. #3081C22semidirect
103. #3081C22semidirect
104. #3079C22semidirect
105. #3079C22semidirect
106. #3077C22semidirect
107. #3077C22semidirect
108. #3076C22semidirect
109. #3076C22semidirect
110. C2×#476C22semidirect
111. C2×#474C22semidirect
112. #2925C22semidirect
113. #2924C22semidirect
114. #2923C22semidirect
115. #2920C22semidirect
116. C2×#432C22semidirect

Maximal subgroups

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

subgroupindex
#628132
#628002
#608922
#608882
#608862
#608832
#608752
#608642
#608632
#608542
C2×#32352
#606682
#606262
#605232
#604952
#604942
#601282