Finite Group Databasebeta

← #10575765

Subgroups — #10575765

Order 512.

5996 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62813C211yesmaximal, characteristic, complemented
2#62805C211yesmaximal, characteristic
3#60891C2112yesmaximal, complemented
4#60881C213yesmaximal, complemented
5#60880C213yesmaximal, complemented
6#60878C213yesmaximal, complemented
7#60878C213yesmaximal, complemented
8#60876C2112yesmaximal, complemented
9#60865C213yesmaximal, complemented
10#60862C213yesmaximal, complemented
11#60846C213yesmaximal, complemented
12C2×#3231C213yesmaximal, complemented
13#60667C211yesmaximal, characteristic, complemented
14#60665C211yesmaximal, characteristic, complemented
15#60623C211yesmaximal, characteristic, complemented
16#60623C211yesmaximal, characteristic, complemented
17#60524C214yesmaximal, complemented
18#60499C214yesmaximal, complemented
19#60127C211yesmaximal, characteristic, complemented
20#3523—21no—
21#3520—23no—
22#3518—21no—
23#3515—23no—
24#3511C2213yes—
25#3509C2213yes—
26#3504C2212yes—
27#3504C2216yes—
28#3503C2211yescharacteristic
29#3503C2213yes—
30#3503C2213yes—
31#3503C2211yescharacteristic
32#3503C2211yescharacteristic
33#3502—21no—
34#3502—21no—
35#3501—23no—
36#3501—23no—
37#3499C2211yescharacteristic
38#3495C2216yes—
39#3489C2212yes—
40#3482—21no—
41#3482—23no—
42Q8×#41—23no—
43Q8×#41—21no—
44Q8×#41—23no—
45Q8×#41—21no—
46Q8×#41—21no—
47#3475—23no—
48#3461C2216yes—
49#3458C2216yes—
50#3444C2213yes—
51C2×#533C2213yes—
52C2×#533C2213yes—
53C2×#533C2213yes—
54C4×2−1+4C2212yes—
55#3428C2212yes—
56C2×C4×#41C2211yescharacteristic
57#3244C22124yescomplemented
58#3243C22124yescomplemented
59#3242C22124yescomplemented
60#3242C22124yescomplemented
61#3240C22112yes—
62#3240C22112yescomplemented
63#3237C22112yes—
64#3236C22112yescomplemented
65#3233C22112yes—
66#3232C22112yescomplemented
67#3231C2213yes—
68#3231C2216yes—
69#3231C22112yes—
70#3231C2213yes—
71#3231C2216yescomplemented
72#3231C2216yescomplemented
73#3231C22112yescomplemented
74#3231C2216yescomplemented
75#3230C2213yescomplemented
76#3230C2216yescomplemented
77#3229C2213yescomplemented
78#3229C2216yescomplemented
79#3228C2211yescharacteristic
80#3228C2213yes—
81#3228C2216yescomplemented
82#3227C2213yescomplemented
83#3226C2213yescomplemented
84#3165C2213yescomplemented
85#3165C2213yescomplemented
86#3165C2213yescomplemented
87#3165C2213yescomplemented
88#3164C22112yescomplemented
89#3163C22112yescomplemented
90#3160C2213yescomplemented
91#3160C2213yescomplemented
92C2×#500C2213yescomplemented
93C2×#498C2213yescomplemented
94#3141C2213yescomplemented
95#3141C2213yescomplemented
96#3139C2213yescomplemented
97#3139C2213yescomplemented
98#3137C22112yescomplemented
99#3137C22112yescomplemented
100#3131C2213yescomplemented
101#3131C2213yescomplemented
102C2×#487C2213yescomplemented
103C2×#487C2213yescomplemented
104#3099C22112yes—
105#3098C22112yes—
106#3097C22112yes—
107#3097C22112yes—
108#3095C22112yes—
109#3093C22112yes—
110#3091C22112yes—
111C2×#485C22112yes—
112#3084C22112yescomplemented
113#3083C22112yescomplemented
114#3082C22112yescomplemented
115#3082C22112yescomplemented
116#3080C22112yescomplemented
117#3078C22112yescomplemented
118#3076C22112yescomplemented
119C2×#479C22112yescomplemented
120#2925C2216yes—
121#2924C2216yes—
122#2922C2213yes—
123#2922C2213yes—
124#2920C2213yes—
125C2×#431C2213yes—
126#2913C2214yes—
127#2912C2214yes—
128#2906C2212yes—
129#2898C2214yes—
130#2898C2214yes—
131#2880C2212yes—
132C4×#131C2211yescharacteristic
133C4×#131C2211yescharacteristic
134C2×2−1+4C2312yes—
135C22×#41C2311yescharacteristic
136C2×#131C2312yes—
137C2×#131C2312yes—
138Q82—21no—
139Q82—21no—
140Q82—23no—
141Q82—23no—
142Q82—21no—
143#557—21no—
144#557—21no—
145#557—23no—
146#557—23no—
147#557—22no—
148#557—22no—
149#557—26no—
150#557—26no—
151#557—23no—
152#557—21no—
153#557—23no—
154#556—23no—
155#556—23no—
156#556—23no—
157#556—26no—
158#555—23no—
159#554—23no—
160#554—23no—
161#554—23no—
162#554—23no—
163#554—23no—
164#554—26no—
165#554—26no—
166#554—23no—
167#554—26no—
168#554—26no—
169#554—212no—
170#554—26no—
171#554—212no—
172#554—26no—
173#554—26no—
174#553—26no—
175#552—26no—
176#552—26no—
177#552—212no—
178#552—26no—
179#552—26no—
180#551—212no—
181D4×Q8—22no—
182D4×Q8—21no—
183D4×Q8—21no—
184D4×Q8—23no—
185D4×Q8—23no—
186D4×Q8—23no—
187D4×Q8—26no—
188D4×Q8—26no—
189D4×Q8—23no—
190D4×Q8—23no—
191#548—22no—
192#548—26no—
193#547—26no—
194#547—23no—
195#547—23no—
196#547—23no—
197#546—26no—
198#544—26no—
199#544—26no—
200#544C2316yes—
201#544C2316yes—
202#544C2316yes—
203#544C2316yes—
204#544C2316yes—
205#544C23112yes—
206#544C23112yes—
207#543—212no—
208#542—26no—
209#542C23112yes—
210#541—26no—
211#541C23112yes—
212#539—212no—
213#537C2316yes—
214#536C2316yes—
215#536C2316yes—
216#533—26no—
217#533—212no—
218#533—26no—
219#533—26no—
220#533—23no—
221#533—23no—
222#533—23no—
223#533—23no—
224#533—23no—
225#533—23no—
226#533—23no—
227#533—23no—
228#533—23no—
229#533—23no—
230#533—23no—
231#533—23no—
232#533C2313yes—
233#533C2316yes—
234#533C2316yes—
235#533C2316yes—
236#533C2313yes—
237#533C2316yes—
238#533C2313yes—
239#533C2313yes—
240#533C2313yes—
241#533C2313yes—
242#533C2311yescharacteristic
243#533C2316yes—
244#533C2316yes—
245#533C2316yes—
246#533C2316yes—
247#532C2313yes—
248#532C2311yescharacteristic
249#532C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256#529—212no—
257#529—26no—
258#529—23no—
259#529—23no—
260#529—23no—
261#529—23no—
262#529C2316yes—
263#529C2316yes—
264C2×#125—23no—
265C2×#125C2316yes—
266C2×#125C2316yes—
267#525—23no—
268#525—23no—
269#525C2316yes—
270C2×C22⋊Q8—23no—
271C2×C22⋊Q8—23no—
272C2×C22⋊Q8—23no—
273C2×C22⋊Q8—23no—
274C2×C22⋊Q8—23no—
275C2×C22⋊Q8C2316yes—
276#520—26no—
277#520C2316yes—
278#520C2316yes—
279#520C2316yes—
280#520C2312yes—
281#520C2312yes—
282#520C2312yes—
283#519—22no—
284#519—22no—
285#519C2316yes—
286#518—26no—
287C4×#41—26no—
288C4×#41—22no—
289C4×#41—26no—
290C4×#41—23no—
291C4×#41—23no—
292C4×#41D413yes—
293C4×#41D411yescharacteristic
294C4×#41D413yes—
295C4×#41D411yescharacteristic
296C4×#41C2316yes—
297C4×#41C2311yescharacteristic
298C4×#41C2311yescharacteristic
299C4×#41C2313yes—
300C4×#41C2313yes—
301C2×C4×Q8—22no—
302C2×C4×Q8—23no—
303C2×C4×Q8—23no—
304C2×C4×Q8—23no—
305C2×C4×Q8—23no—
306C2×C4×Q8—23no—
307C2×C4×Q8D411yescharacteristic
308C2×C4×Q8D411yescharacteristic
309C2×C4×Q8C2316yes—
310C2×C4×D4D413yes—
311C2×C4×D4D413yes—
312C2×#117—23no—
313C2×#117C2316yes—
314C2×#117C2316yes—
315C2×#117C2313yes—
316C22×C42C2313yes—
317#501C23112yes—
318#501C23112yes—
319#501C23112yes—
320#501C23112yes—
321#500C2313yes—
322#500C23112yes—
323#500C2316yes—
324#500C2311yescharacteristic
325#500C2313yes—
326#500C2313yes—
327#499C23112yes—
328#499C23112yes—
329#498C2313yes—
330#498C23112yes—
331#498C2316yes—
332#498C2311yescharacteristic
333#498C2313yes—
334#498C2313yes—
335#491C23112yes—
336#491C23112yes—
337#489C23112yes—
338#489C23112yes—
339#488C23112yes—
340#488C23112yes—
341#487C2313yes—
342#487C2313yes—
343#487C23112yes—
344#487C23112yes—
345#487C2316yes—
346#487C2316yes—
347#487C2313yes—
348#487C2313yes—
349#486C2311yescharacteristic
350#486C2311yescharacteristic
351#486C2313yes—
352#486C2313yes—
353#485C23112yes—
354#485C23124yes—
355#485C23124yes—
356#485C23124yes—
357#485C23112yes—
358#485C23124yes—
359#484C23112yes—
360#484C23124yes—
361#483C23112yes—
362#483C23124yes—
363#482C2314yes—
364#482C23112yes—
365#482C23124yes—
366#481C23112yes—
367#480C23112yes—
368#479C23112yes—
369#479C23124yes—
370#479C23124yes—
371#479C23124yes—
372#479C23112yes—
373#479C23124yes—
374#478C2314yes—
375#478C23112yes—
376#478C23124yes—
377#477C23112yes—
378#477C23124yes—
379#476C23112yes—
380#475C23112yes—
381#475C23124yes—
382#474C23112yes—
383#433C23112yes—
384#433C23112yes—
385#432C2316yes—
386#432C2316yes—
387#431C2311yescharacteristic
388#431C2313yes—
389#431C2313yes—
390#431C2313yes—
391#431C2316yes—
392#431C2316yes—
393#431C2316yes—
394#428C23112yes—
395#428C23112yes—
396#428C23112yes—
397#428C23112yes—
398#427C23112yes—
399#427C23112yes—
400C2×#107C23112yes—
401C2×#106C23112yes—
402#424C2316yes—
403#424C2316yes—
404#423C2316yes—
405C2×C4⋊C8C2316yes—
406#419C23112yes—
407#419C23112yes—
408#417C23112yes—
409#417C23112yes—
410#416C23112yes—
411#416C23112yes—
412C2×#103C23112yes—
413C2×#103C23112yes—
414#408C2316yes—
415#408C2316yes—
416#407C2316yes—
417C2×C22⋊C8C2316yes—
418#405C2316yes—
419#405C2316yes—
420C4×M16C2313yes—
421C4×M16C2313yes—
422C2×C4×C8C2313yes—
423C2×C4×C8C2313yes—
4242−1+4—216no—
425C2×#41—28no—
426C2×#41—26no—
427C2×#41—21no—
428C2×#41—23no—
429C2×#41C2×D413yes—
430C2×#41C2×D411yescharacteristic
431C2×#41C2416yes—
432C2×#41C2413yes—
433C2×#41C2411yescharacteristic
434C22×Q8—22no—
435C22×Q8—23no—
436C22×Q8—23no—
437C22×Q8—23no—
438C22×Q8—23no—
439C22×Q8—23no—
440C22×Q8C2×D411yescharacteristic
441C22×Q8C2416yes—
442C22×D4C2×D413yes—
443C23×C4C2×D413yes—
444C23×C4C2×D413yes—
445C23×C4C2413yes—
446#131—28no—
447#131—28no—
448C2×M16C2416yes—
449C2×M16C2416yes—
450C22×C8C2416yes—
451C22×C8C2416yes—
452C4⋊Q8—26no—
453C4⋊Q8—26no—
454C4⋊Q8—26no—
455C4⋊Q8—26no—
456C4⋊Q8—26no—
457C4⋊Q8—212no—
458C4⋊Q8—26no—
459C4⋊Q8—212no—
460C4⋊Q8—23no—
461C4⋊Q8—23no—
462C4⋊Q8—23no—
463C4⋊Q8—23no—
464C4⋊Q8—23no—
465C4⋊Q8—23no—
466C4⋊Q8—23no—
467C4⋊Q8—23no—
468C4⋊Q8—23no—
469C4⋊Q8—23no—
470C4⋊Q8—23no—
471C4⋊Q8—23no—
472C4⋊Q8C2413yes—
473C4⋊Q8C2416yes—
474C4⋊Q8C2413yes—
475C4⋊Q8C2411yescharacteristic
476C4⋊Q8C2413yes—
477C4⋊Q8C2411yescharacteristic
478C4⋊Q8C2413yes—
479C4⋊Q8C2416yes—
480C4⋊Q8C2416yes—
481C4⋊Q8C2416yes—
482C4⋊Q8C2416yes—
483C4⋊Q8C2416yes—
484C4⋊Q8C2411yescharacteristic
485#127C2411yescharacteristic
486#126—212no—
487#126—212no—
488#126—212no—
489#126—26no—
490#126—26no—
491#125—212no—
492#125—26no—
493#125—212no—
494#125—26no—
495#125—26no—
496#125—26no—
497#125—212no—
498#125—26no—
499#125—212no—
500#125—23no—
501#125—26no—
502#125—26no—
503#125—26no—
504#125—26no—
505#125—26no—
506#125—26no—
507#125—26no—
508#125—23no—
509#125C2416yes—
510#125C2412yes—
511#125C24112yes—
512#125C2416yes—
513#125C2416yes—
514#125C2416yes—
515#124—26no—
516#124—212no—
517#124—21no—
518#124—23no—
519#124C2416yes—
520#123—212no—
521#123—26no—
522#123—26no—
523#123—26no—
524#123—212no—
525#123—212no—
526C22⋊Q8—26no—
527C22⋊Q8—23no—
528C22⋊Q8—21no—
529C22⋊Q8—23no—
530C22⋊Q8—21no—
531C22⋊Q8—23no—
532C22⋊Q8—26no—
533C22⋊Q8—26no—
534C22⋊Q8—26no—
535C22⋊Q8—26no—
536C22⋊Q8—26no—
537C22⋊Q8—26no—
538C22⋊Q8—23no—
539C22⋊Q8—23no—
540C22⋊Q8—23no—
541C22⋊Q8—23no—
542C22⋊Q8—26no—
543C22⋊Q8—26no—
544C22⋊Q8—26no—
545C22⋊Q8—26no—
546C22⋊Q8—26no—
547C22⋊Q8—26no—
548C22⋊Q8—26no—
549C22⋊Q8—26no—
550C22⋊Q8—26no—
551C22⋊Q8—23no—
552C22⋊Q8—23no—
553C22⋊Q8—23no—
554C22⋊Q8—26no—
555C22⋊Q8—26no—
556C22⋊Q8—212no—
557C22⋊Q8—212no—
558C22⋊Q8—212no—
559C22⋊Q8—212no—
560C22⋊Q8—212no—
561C22⋊Q8—212no—
562C22⋊Q8—212no—
563C22⋊Q8—212no—
564C22⋊Q8—212no—
565C22⋊Q8—212no—
566C22⋊Q8C2416yes—
567C22⋊Q8C24112yes—
568C22⋊Q8C2416yes—
569#121—212no—
570#121—26no—
571#121—21no—
572#121—23no—
573#121—23no—
574#121—23no—
575#121C2412yes—
576#121C2416yes—
577#120—26no—
578C4×Q8—22no—
579C4×Q8—26no—
580C4×Q8—26no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—26no—
584C4×Q8—26no—
585C4×Q8—23no—
586C4×Q8—21no—
587C4×Q8—23no—
588C4×Q8—21no—
589C4×Q8—23no—
590C4×Q8—26no—
591C4×Q8—26no—
592C4×Q8—26no—
593C4×Q8—26no—
594C4×Q8—26no—
595C4×Q8—26no—
596C4×Q8—26no—
597C4×Q8—26no—
598C4×Q8—23no—
599C4×Q8—23no—
600C4×Q8—23no—
601C4×Q8—23no—
602C4×Q8—26no—
603C4×Q8—26no—
604C4×Q8—26no—
605C4×Q8—26no—
606C4×Q8—26no—
607C4×Q8—26no—
608C4×Q8—26no—
609C4×Q8—23no—
610C4×Q8—23no—
611C4×Q8—23no—
612C4×Q8C2×D411yescharacteristic
613C4×Q8C2×D411yescharacteristic
614C4×Q8C2×D413yes—
615C4×Q8C2×D413yes—
616C4×Q8C2×D411yescharacteristic
617C4×Q8C2×D411yescharacteristic
618C4×Q8C2×D413yes—
619C4×Q8C2×D413yes—
620C4×Q8C2416yes—
621C4×Q8C24112yes—
622C4×Q8C2416yes—
623C4×D4—212no—
624C4×D4—212no—
625C4×D4—26no—
626C4×D4—26no—
627C4×D4—26no—
628C4×D4—26no—
629C4×D4—26no—
630C4×D4—26no—
631C4×D4—26no—
632C4×D4—26no—
633C4×D4—26no—
634C4×D4—26no—
635C4×D4—26no—
636C4×D4—212no—
637C4×D4—21no—
638C4×D4—23no—
639C4×D4—23no—
640C4×D4—23no—
641C4×D4C2×D413yes—
642C4×D4C2×D413yes—
643C4×D4C2×D413yes—
644C4×D4C2×D416yes—
645C4×D4C2×D416yes—
646C4×D4C2×D413yes—
647C4×D4C2×D413yes—
648C4×D4C2×D413yes—
649C4×D4C2×D413yes—
650C4×D4C2×D416yes—
651C4×D4C2×D416yes—
652C4×D4C2×D413yes—
653C4×D4C2412yes—
654C4×D4C2416yes—
655#117—23no—
656#117—26no—
657#117—26no—
658#117—26no—
659#117—26no—
660#117—26no—
661#117—26no—
662#117—26no—
663#117—23no—
664#117—26no—
665#117—212no—
666#117—26no—
667#117—26no—
668#117—26no—
669#117C2×D413yes—
670#117C2×D416yes—
671#117C2×D413yes—
672#117C2416yes—
673#117C2412yes—
674#117C2416yes—
675#117C2416yes—
676#117C24112yes—
677#117C2416yes—
678#117C2413yes—
679#117C2413yes—
680#117C2416yes—
681C2×C4⋊C4—23no—
682C2×C4⋊C4—23no—
683C2×C4⋊C4—26no—
684C2×C4⋊C4—26no—
685C2×C4⋊C4—26no—
686C2×C4⋊C4—26no—
687C2×C4⋊C4—23no—
688C2×C4⋊C4—23no—
689C2×C4⋊C4—23no—
690C2×C4⋊C4—23no—
691C2×C4⋊C4—23no—
692C2×C4⋊C4—26no—
693C2×C4⋊C4—26no—
694C2×C4⋊C4—26no—
695C2×C4⋊C4C2×D413yes—
696C2×C4⋊C4C2×D413yes—
697C2×C4⋊C4C2416yes—
698C2×C4⋊C4C2416yes—
699C2×C4⋊C4C2416yes—
700C2×C4⋊C4C2416yes—
701C2×C4⋊C4C2416yes—
702C2×C22⋊C4—26no—
703C2×C22⋊C4—26no—
704C2×C22⋊C4—26no—
705C2×C22⋊C4C2×D416yes—
706C2×C42—26no—
707C2×C42—26no—
708C2×C42—26no—
709C2×C42—26no—
710C2×C42C2×D413yes—
711C2×C42C2×D413yes—
712C2×C42C2×D413yes—
713C2×C42C2×D413yes—
714C2×C42C2×D413yes—
715C2×C42C2×D413yes—
716C2×C42C2413yes—
717C2×C42C2413yes—
718C2×C42C2413yes—
719C2×C42C2413yes—
720C2×C42C2413yes—
721C2×C42C2411yescharacteristic
722#107C24112yes—
723#107C24124yes—
724#107C2414yes—
725#107C24112yes—
726#107C24112yes—
727#106C24112yes—
728#106C24124yes—
729#106C2414yes—
730#106C24112yes—
731#106C24112yes—
732C4⋊C8C2412yes—
733C4⋊C8C2416yes—
734C4⋊C8C2416yes—
735C4⋊C8C2416yes—
736C4⋊C8C24112yes—
737#103C24112yes—
738#103C24112yes—
739#103C24124yes—
740#103C24124yes—
741#103C24112yes—
742#103C24112yes—
743#102C2414yes—
744#102C2414yes—
745#102C24112yes—
746#102C24112yes—
747C22⋊C8C2412yes—
748C22⋊C8C2416yes—
749C22⋊C8C2416yes—
750C22⋊C8C2416yes—
751C22⋊C8C24112yes—
752#97C2416yes—
753#97C2416yes—
754C4×C8C2411yescharacteristic
755C4×C8C2411yescharacteristic
756C4×C8C2413yes—
757C4×C8C2413yes—
758C4×C8C2416yes—
759C4×C8C2416yes—
760C24C22×D413yes—
761#41—24no—
762#41—212no—
763#41—212no—
764#41—224no—
765#41—44no—
766#41—424no—
767#41—86no—
768#412−1+418yes—
769C2×Q8—24no—
770C2×Q8—21no—
771C2×Q8—26no—
772C2×Q8—23no—
773C2×Q8—21no—
774C2×Q8—23no—
775C2×Q8—23no—
776C2×Q8—21no—
777C2×Q8—26no—
778C2×Q8—26no—
779C2×Q8—26no—
780C2×Q8—26no—
781C2×Q8—26no—
782C2×Q8—224no—
783C2×Q8—48no—
784C2×Q8—86no—
785C2×Q8—86no—
786C2×Q8—86no—
787C2×Q8—86no—
788C2×Q8—86no—
789C2×Q8C22×D413yes—
790C2×Q8C22×D411yescharacteristic
791C2×Q8C2516yes—
792C2×D4—212no—
793C2×D4—22no—
794C2×D4—26no—
795C2×D4—26no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4C22×D416yes—
799C2×D4C22×D413yes—
800C2×D4C22×D413yes—
801C2×D4C2512yes—
802C22×C4—212no—
803C22×C4—26no—
804C22×C4—26no—
805C22×C4—26no—
806C22×C4—26no—
807C22×C4—26no—
808C22×C4—26no—
809C22×C4—22no—
810C22×C4—26no—
811C22×C4—26no—
812C22×C4—46no—
813C22×C4—46no—
814C22×C4C22×D413yes—
815C22×C4C22×D413yes—
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D413yes—
819C22×C4C22×D413yes—
820C22×C4C22×D413yes—
821C22×C4C22×D413yes—
822C22×C4C22×D413yes—
823C22×C4C22×D413yes—
824C22×C4C22×D413yes—
825C22×C4C22×D413yes—
826C22×C4C22×D413yes—
827C22×C4C22×D413yes—
828C22×C4C22×D413yes—
829C22×C4C2511yescharacteristic
830C22×C4C2513yes—
831C22×C4C2513yes—
832M16—212no—
833M16—212no—
834C2×C8—212no—
835C2×C8—212no—
836C2×C8C2512yes—
837C2×C8C2512yes—
838C2×C8C2516yes—
839C2×C8C2516yes—
840C4⋊C4—26no—
841C4⋊C4—22no—
842C4⋊C4—26no—
843C4⋊C4—22no—
844C4⋊C4—23no—
845C4⋊C4—21no—
846C4⋊C4—23no—
847C4⋊C4—21no—
848C4⋊C4—23no—
849C4⋊C4—23no—
850C4⋊C4—23no—
851C4⋊C4—26no—
852C4⋊C4—212no—
853C4⋊C4—26no—
854C4⋊C4—26no—
855C4⋊C4—26no—
856C4⋊C4—26no—
857C4⋊C4—212no—
858C4⋊C4—26no—
859C4⋊C4—26no—
860C4⋊C4—26no—
861C4⋊C4—26no—
862C4⋊C4—212no—
863C4⋊C4—212no—
864C4⋊C4—26no—
865C4⋊C4—26no—
866C4⋊C4—26no—
867C4⋊C4—26no—
868C4⋊C4—26no—
869C4⋊C4—26no—
870C4⋊C4—26no—
871C4⋊C4—26no—
872C4⋊C4—26no—
873C4⋊C4—21no—
874C4⋊C4—26no—
875C4⋊C4—26no—
876C4⋊C4—26no—
877C4⋊C4—26no—
878C4⋊C4C22×D413yes—
879C4⋊C4C22×D413yes—
880C4⋊C4C22×D416yes—
881C4⋊C4C22×D413yes—
882C4⋊C4C22×D413yes—
883C4⋊C4C22×D416yes—
884C4⋊C4C2512yes—
885C4⋊C4C2516yes—
886C4⋊C4C2512yes—
887C4⋊C4C2516yes—
888C4⋊C4C2516yes—
889C4⋊C4C2512yes—
890C22⋊C4—26no—
891C22⋊C4—22no—
892C22⋊C4—26no—
893C22⋊C4—212no—
894C22⋊C4—212no—
895C22⋊C4—26no—
896C22⋊C4—26no—
897C22⋊C4—26no—
898C22⋊C4—26no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—26no—
902C22⋊C4—26no—
903C22⋊C4—26no—
904C22⋊C4—26no—
905C22⋊C4C22×D416yes—
906C22⋊C4C22×D416yes—
907C22⋊C4C22×D416yes—
908C22⋊C4C22×D416yes—
909C42—26no—
910C42—26no—
911C42—22no—
912C42—26no—
913C42—212no—
914C42—26no—
915C42—212no—
916C42—26no—
917C42—26no—
918C42C22×D413yes—
919C42C22×D411yescharacteristic
920C42C22×D411yescharacteristic
921C42C22×D413yes—
922C42C22×D413yes—
923C42C22×D413yes—
924C42C22×D413yes—
925C42C22×D413yes—
926C42C22×D413yes—
927C42C22×D413yes—
928C42C22×D413yes—
929C42C22×D413yes—
930C42C2511yescharacteristic
931C42C2513yes—
932C42C2511yescharacteristic
933C42C2513yes—
934C23—26no—
935C23—22no—
936C23—43no—
937C23—43no—
938C23C23×D411yescharacteristic
939C23C23×D413yes—
940C23C23×D413yes—
941Q8—26no—
942Q8—212no—
943Q8—46no—
944Q8—42no—
945Q8—46no—
946Q8—46no—
947Q8—42no—
948Q8—42no—
949Q8—412no—
950Q8—86no—
951Q8—86no—
952Q8—86no—
953Q8—86no—
954Q8—86no—
955Q8#53614yes—
956D4—212no—
957D4—24no—
958D4—26no—
959D4—44no—
960D4—412no—
961D4—42no—
962D4—42no—
963D4—86no—
964D4#536112yes—
965C2×C4—26no—
966C2×C4—22no—
967C2×C4—26no—
968C2×C4—26no—
969C2×C4—22no—
970C2×C4—26no—
971C2×C4—26no—
972C2×C4—22no—
973C2×C4—26no—
974C2×C4—26no—
975C2×C4—26no—
976C2×C4—22no—
977C2×C4—26no—
978C2×C4—26no—
979C2×C4—26no—
980C2×C4—22no—
981C2×C4—26no—
982C2×C4—22no—
983C2×C4—43no—
984C2×C4—43no—
985C2×C4—43no—
986C2×C4—43no—
987C2×C4—43no—
988C2×C4—43no—
989C2×C4—44no—
990C2×C4—412no—
991C2×C4—412no—
992C2×C4—86no—
993C2×C4—86no—
994C2×C4—86no—
995C2×C4—86no—
996C2×C4—86no—
997C2×C4—86no—
998C2×C4C23×D411yescharacteristic
999C2×C4C23×D411yescharacteristic
1000C2×C4C23×D413yes—
1001C2×C4C23×D413yes—
1002C2×C4C23×D413yes—
1003C2×C4C23×D411yescharacteristic
1004C2×C4C23×D413yes—
1005C2×C4C23×D413yes—
1006C2×C4C23×D411yescharacteristic
1007C2×C4C23×D411yescharacteristic
1008C2×C4C23×D413yes—
1009C2×C4C2×2−1+4112yes—
1010C2×C4C2611yescharacteristic
1011C8—22no—
1012C8—22no—
1013C8—26no—
1014C8—26no—
1015C22—23no—
1016C22—23no—
1017C22—21no—
1018C22—23no—
1019C22—21no—
1020C22—23no—
1021C22—21no—
1022C22—23no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—86no—
1027C22C2×#53616yes—
1028C22C24×D411yescharacteristic
1029C4—21no—
1030C4—23no—
1031C4—23no—
1032C4—21no—
1033C4—23no—
1034C4—23no—
1035C4—21no—
1036C4—23no—
1037C4—46no—
1038C4—46no—
1039C4—42no—
1040C4—42no—
1041C4—46no—
1042C4—42no—
1043C4—46no—
1044C4C2×#53616yes—
1045C4#358412yes—
1046C4#358612yes—
1047C4C22×2−1+412yes—
1048C2—26no—
1049C2—43no—
1050C2—41no—
1051C2—82no—
1052C2C22×#53611yescharacteristic
1053C2C2×#358411yescharacteristic
1054C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#62805C2
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. #60891C2semidirect
4. #60881C2semidirect
5. #60880C2semidirect
6. #60878C2semidirect
7. #60878C2semidirect
8. #60876C2semidirect
9. #60865C2semidirect
10. #60862C2semidirect
11. #60846C2semidirect
12. C2×#3231C2semidirect
13. #60667C2semidirect
14. #60665C2semidirect
15. #60623C2semidirect
16. #60623C2semidirect
17. #60524C2semidirect
18. #60499C2semidirect
19. #60127C2semidirect
57. #3244C22semidirect
58. #3243C22semidirect
59. #3242C22semidirect
60. #3242C22semidirect
62. #3240C22semidirect
64. #3236C22semidirect
66. #3232C22semidirect
71. #3231C22semidirect
72. #3231C22semidirect
73. #3231C22semidirect
74. #3231C22semidirect
75. #3230C22semidirect
76. #3230C22semidirect
77. #3229C22semidirect
78. #3229C22semidirect
81. #3228C22semidirect
82. #3227C22semidirect
83. #3226C22semidirect
84. #3165C22semidirect
85. #3165C22semidirect
86. #3165C22semidirect
87. #3165C22semidirect
88. #3164C22semidirect
89. #3163C22semidirect
90. #3160C22semidirect
91. #3160C22semidirect
92. C2×#500C22semidirect
93. C2×#498C22semidirect
94. #3141C22semidirect
95. #3141C22semidirect
96. #3139C22semidirect
97. #3139C22semidirect
98. #3137C22semidirect
99. #3137C22semidirect
100. #3131C22semidirect
101. #3131C22semidirect
102. C2×#487C22semidirect
103. C2×#487C22semidirect
112. #3084C22semidirect
113. #3083C22semidirect
114. #3082C22semidirect
115. #3082C22semidirect
116. #3080C22semidirect
117. #3078C22semidirect
118. #3076C22semidirect
119. C2×#479C22semidirect

Maximal subgroups

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

subgroupindex
#628132
#628052
#608912
#608812
#608802
#608782
#608762
#608652
#608622
#608462
C2×#32312
#606672
#606652
#606232
#605242
#604992
#601272