Finite Group Databasebeta

← #10575764

Subgroups — #10575764

Order 512.

6184 conjugacy classes of subgroups.

The subgroup lattice has 1071 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62813C211yesmaximal, characteristic, complemented
2#62800C211yesmaximal, characteristic
3#60890C2112yesmaximal, complemented
4#60881C213yesmaximal, complemented
5#60880C213yesmaximal, complemented
6#60877C213yesmaximal, complemented
7#60877C213yesmaximal, complemented
8#60875C2112yesmaximal, complemented
9#60864C213yesmaximal, complemented
10#60862C213yesmaximal, complemented
11#60846C213yesmaximal, complemented
12C2×#3228C213yesmaximal, complemented
13#60667C211yesmaximal, characteristic, complemented
14#60665C211yesmaximal, characteristic, complemented
15#60622C211yesmaximal, characteristic, complemented
16#60622C211yesmaximal, characteristic, complemented
17#60523C214yesmaximal, complemented
18#60496C214yesmaximal, complemented
19#60127C211yesmaximal, characteristic, complemented
20#3522—21no—
21#3519—23no—
22#3517—21no—
23#3514—23no—
24#3511C2213yes—
25#3508C2213yes—
26#3504C2212yes—
27#3504C2216yescomplemented
28#3503C2211yescharacteristic
29#3503C2211yescharacteristic
30#3503C2211yescharacteristic
31#3503C2213yescomplemented
32#3503C2213yescomplemented
33#3502—21no—
34#3502—21no—
35#3501—23no—
36#3501—23no—
37#3498C2211yescharacteristic
38#3494C2216yes—
39#3488C2212yes—
40#3483—21no—
41#3481—23no—
42#3480—21no—
43Q8×#41—23no—
44Q8×#41—21no—
45Q8×#41—23no—
46Q8×#41—21no—
47D4×#41—23no—
48#3460C2216yes—
49#3458C2216yescomplemented
50#3444C2213yes—
51C2×#533C2213yescomplemented
52C2×#533C2213yescomplemented
53C2×#532C2213yes—
54C4×H(5,𝔽2)C2212yes—
55#3428C2212yes—
56C2×C4×#41C2211yescharacteristic
57#3244C22124yescomplemented
58#3243C22124yescomplemented
59#3241C22124yescomplemented
60#3241C22124yescomplemented
61#3240C22112yescomplemented
62#3240C22112yescomplemented
63#3235C22112yescomplemented
64#3234C22112yescomplemented
65#3233C22112yescomplemented
66#3232C22112yescomplemented
67#3231C2211yescharacteristic, complemented
68#3231C2213yescomplemented
69#3231C2216yescomplemented
70#3230C2213yescomplemented
71#3229C2213yescomplemented
72#3228C2213yescomplemented
73#3228C2216yescomplemented
74#3228C22112yescomplemented
75#3228C2216yescomplemented
76#3228C2216yescomplemented
77#3228C22112yescomplemented
78#3228C2213yescomplemented
79#3228C2216yescomplemented
80#3227C2213yescomplemented
81#3227C2216yescomplemented
82#3226C2213yescomplemented
83#3226C2216yescomplemented
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#3138C2213yescomplemented
97#3138C2213yescomplemented
98#3136C22112yescomplemented
99#3136C22112yescomplemented
100#3131C2213yescomplemented
101#3131C2213yescomplemented
102C2×#486C2213yescomplemented
103C2×#486C2213yescomplemented
104#3099C22112yescomplemented
105#3098C22112yescomplemented
106#3096C22112yescomplemented
107#3096C22112yescomplemented
108#3094C22112yescomplemented
109#3093C22112yescomplemented
110#3091C22112yescomplemented
111C2×#482C22112yescomplemented
112#3084C22112yescomplemented
113#3083C22112yescomplemented
114#3081C22112yescomplemented
115#3081C22112yescomplemented
116#3080C22112yescomplemented
117#3077C22112yescomplemented
118#3076C22112yescomplemented
119C2×#478C22112yescomplemented
120#2925C2216yescomplemented
121#2924C2216yescomplemented
122#2922C2213yescomplemented
123#2922C2213yescomplemented
124#2920C2213yescomplemented
125C2×#431C2213yescomplemented
126#2913C2214yes—
127#2912C2214yes—
128#2906C2212yes—
129#2897C2214yes—
130#2897C2214yes—
131#2880C2212yes—
132C4×#131C2211yescharacteristic
133C4×#131C2211yescharacteristic
134C2×H(5,𝔽2)C2312yes—
135C22×#41—23no—
136C22×#41C2311yescharacteristic
137C2×#131C2312yes—
138C2×#131C2312yes—
139#559—23no—
140#559—23no—
141Q82—21no—
142Q82—21no—
143Q82—23no—
144Q82—23no—
145Q82—21no—
146#557—21no—
147#557—21no—
148#557—23no—
149#557—23no—
150#557—22no—
151#557—22no—
152#557—26no—
153#557—26no—
154#557—21no—
155#556—23no—
156#555—23no—
157#555—26no—
158#554—23no—
159#554—23no—
160#554—23no—
161#554—26no—
162#554—26no—
163#554—23no—
164#554—23no—
165#554—26no—
166#554—26no—
167#554—212no—
168#554—26no—
169#554—212no—
170#554—26no—
171#554—23no—
172#553—26no—
173#553—26no—
174#553—26no—
175#551—212no—
176#550—22no—
177#550—21no—
178#550—21no—
179#550—23no—
180#550—23no—
181D4×Q8—23no—
182D4×Q8—23no—
183D4×Q8—23no—
184D4×Q8—26no—
185D4×Q8—26no—
186D4×Q8—23no—
187D4×Q8—23no—
188#548—22no—
189#548—26no—
190#547—23no—
191#547—26no—
192#546—26no—
193#546—26no—
194#546—26no—
195#546—212no—
196D42—26no—
197D42—23no—
198D42—23no—
199#544—26no—
200#544—26no—
201#544C2316yes—
202#544C2316yes—
203#544C2316yes—
204#544C2316yes—
205#544C2316yes—
206#544C23112yes—
207#544C23112yes—
208#543—212no—
209#542—26no—
210#542C23112yes—
211#540—26no—
212#540C23112yes—
213#538—212no—
214#537C2316yes—
215#535C2316yes—
216#535C2316yes—
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#533C2311yescharacteristic
229#533C2313yes—
230#533C2316yes—
231#533C2313yes—
232#533C2313yes—
233#533C2313yes—
234#533C2313yes—
235#533C2311yescharacteristic
236#533C2316yes—
237#533C2316yes—
238#533C2316yes—
239#533C2316yes—
240#532—26no—
241#532—23no—
242#532—23no—
243#532—23no—
244#532—23no—
245#532C2313yes—
246#532C2313yes—
247#532C2316yes—
248#532C2316yes—
249#532C2316yes—
250#532C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×#127C2313yes—
257#529—26no—
258#529—23no—
259#529—23no—
260#529—23no—
261#529—23no—
262#529C2316yes—
263#529C2316yes—
264C2×#125C2316yes—
265C2×#125C2316yes—
266C2×#124—23no—
267#525—23no—
268#525—23no—
269#525—212no—
270#525C2316yes—
271C2×C22⋊Q8—23no—
272C2×C22⋊Q8—23no—
273C2×C22⋊Q8—23no—
274C2×C22⋊Q8—23no—
275C2×#121—23no—
276C2×#121C2316yes—
277#520—22no—
278#520C2316yes—
279#520C2316yes—
280#520C2316yes—
281#520C2312yes—
282#520C2312yes—
283#520C2312yes—
284#519—22no—
285#518—26no—
286#518—26no—
287#518C2316yes—
288C4×#41—26no—
289C4×#41—22no—
290C4×#41—22no—
291C4×#41—23no—
292C4×#41—23no—
293C4×#41D413yes—
294C4×#41D411yescharacteristic
295C4×#41D413yes—
296C4×#41D411yescharacteristic
297C4×#41C2316yes—
298C4×#41C2311yescharacteristic
299C4×#41C2311yescharacteristic
300C4×#41C2313yes—
301C4×#41C2313yes—
302C2×C4×Q8—23no—
303C2×C4×Q8—23no—
304C2×C4×Q8—23no—
305C2×C4×Q8—23no—
306C2×C4×Q8D411yescharacteristic
307C2×C4×Q8D411yescharacteristic
308C2×C4×D4—26no—
309C2×C4×D4—23no—
310C2×C4×D4D413yes—
311C2×C4×D4D413yes—
312C2×C4×D4C2316yes—
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#490C23112yes—
336#490C23112yes—
337#489C23112yes—
338#489C23112yes—
339#488C23112yes—
340#488C23112yes—
341#487C2311yescharacteristic
342#487C2311yescharacteristic
343#487C2313yes—
344#487C2313yes—
345#486C2313yes—
346#486C2313yes—
347#486C23112yes—
348#486C23112yes—
349#486C2316yes—
350#486C2316yes—
351#486C2313yes—
352#486C2313yes—
353#485C2314yes—
354#485C23112yes—
355#485C23124yes—
356#484C23112yes—
357#483C23112yes—
358#482C23112yes—
359#482C23124yes—
360#482C23124yes—
361#482C23124yes—
362#482C23112yes—
363#482C23124yes—
364#481C23112yes—
365#481C23124yes—
366#480C23112yes—
367#480C23124yes—
368#479C2314yes—
369#479C23112yes—
370#479C23124yes—
371#478C23112yes—
372#478C23124yes—
373#478C23124yes—
374#478C23124yes—
375#478C23112yes—
376#478C23124yes—
377#477C23112yes—
378#476C23112yes—
379#476C23124yes—
380#475C23112yes—
381#474C23112yes—
382#474C23124yes—
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#418C23112yes—
407#418C23112yes—
408#417C23112yes—
409#417C23112yes—
410#416C23112yes—
411#416C23112yes—
412C2×#102C23112yes—
413C2×#102C23112yes—
414#408C2316yes—
415#408C2316yes—
416#407C2316yes—
417C2×C22⋊C8C2316yes—
418#405C2316yes—
419#405C2316yes—
420C4×M16C2313yes—
421C4×M16C2313yes—
422C2×C4×C8C2313yes—
423C2×C4×C8C2313yes—
424H(5,𝔽2)—216no—
425C2×#41—28no—
426C2×#41—22no—
427C2×#41—23no—
428C2×#41—23no—
429C2×#41—26no—
430C2×#41—26no—
431C2×#41—26no—
432C2×#41—812no—
433C2×#41C2×D413yes—
434C2×#41C2×D411yescharacteristic
435C2×#41C2416yes—
436C2×#41C2413yes—
437C2×#41C2411yescharacteristic
438C22×Q8—23no—
439C22×Q8—23no—
440C22×Q8—23no—
441C22×Q8—23no—
442C22×Q8—23no—
443C22×Q8C2×D411yescharacteristic
444C22×D4—26no—
445C22×D4—26no—
446C22×D4—23no—
447C22×D4—23no—
448C22×D4C2×D413yes—
449C22×D4C2416yes—
450C23×C4—26no—
451C23×C4C2×D413yes—
452C23×C4C2×D413yes—
453C23×C4C2413yes—
454#131—28no—
455#131—28no—
456C2×M16C2416yes—
457C2×M16C2416yes—
458C22×C8C2416yes—
459C22×C8C2416yes—
460C4⋊Q8—26no—
461C4⋊Q8—26no—
462C4⋊Q8—26no—
463C4⋊Q8—26no—
464C4⋊Q8—26no—
465C4⋊Q8—212no—
466C4⋊Q8—212no—
467C4⋊Q8—23no—
468C4⋊Q8—23no—
469C4⋊Q8—23no—
470C4⋊Q8—23no—
471C4⋊Q8—23no—
472C4⋊Q8—23no—
473C4⋊Q8—23no—
474C4⋊Q8—23no—
475C4⋊Q8—23no—
476C4⋊Q8—23no—
477C4⋊Q8C2411yescharacteristic
478C4⋊Q8C2413yes—
479C4⋊Q8C2411yescharacteristic
480C4⋊Q8C2413yes—
481C4⋊Q8C2411yescharacteristic
482C4⋊Q8C2413yes—
483C4⋊Q8C2416yes—
484C4⋊Q8C2416yes—
485C4⋊Q8C2416yes—
486C4⋊Q8C2416yes—
487C4⋊Q8C2416yes—
488C4⋊Q8C2411yescharacteristic
489#127—26no—
490#127—23no—
491#127—23no—
492#127C2413yes—
493#127C2416yes—
494#126—212no—
495#126—26no—
496#126—26no—
497#125—26no—
498#125—26no—
499#125—26no—
500#125—26no—
501#125—26no—
502#125—212no—
503#125—212no—
504#125—26no—
505#125—26no—
506#125—26no—
507#125—26no—
508#125—21no—
509#125—23no—
510#125C2416yes—
511#125C2412yes—
512#125C24112yes—
513#125C2416yes—
514#125C2416yes—
515#125C2416yes—
516#124—26no—
517#124—212no—
518#124—23no—
519#124—26no—
520#124—26no—
521#124—26no—
522#124—23no—
523#124C2416yes—
524#123—26no—
525#123—26no—
526#123—26no—
527#123—212no—
528#123—212no—
529#123—212no—
530C22⋊Q8—26no—
531C22⋊Q8—23no—
532C22⋊Q8—21no—
533C22⋊Q8—23no—
534C22⋊Q8—21no—
535C22⋊Q8—26no—
536C22⋊Q8—26no—
537C22⋊Q8—26no—
538C22⋊Q8—26no—
539C22⋊Q8—23no—
540C22⋊Q8—23no—
541C22⋊Q8—26no—
542C22⋊Q8—23no—
543C22⋊Q8—23no—
544C22⋊Q8—26no—
545C22⋊Q8—26no—
546C22⋊Q8—26no—
547C22⋊Q8—26no—
548C22⋊Q8—26no—
549C22⋊Q8—21no—
550C22⋊Q8—23no—
551C22⋊Q8—23no—
552C22⋊Q8—23no—
553C22⋊Q8—212no—
554C22⋊Q8—212no—
555C22⋊Q8—212no—
556C22⋊Q8—212no—
557C22⋊Q8—212no—
558C22⋊Q8—212no—
559C22⋊Q8—212no—
560C22⋊Q8—212no—
561C22⋊Q8—212no—
562C22⋊Q8—212no—
563C22⋊Q8C2412yes—
564C22⋊Q8C2416yes—
565#121—212no—
566#121—26no—
567#121—23no—
568#121—26no—
569#121—26no—
570#121—26no—
571#121—26no—
572#121—26no—
573#121—23no—
574#121—23no—
575#121—23no—
576#121—26no—
577#121—26no—
578#121—212no—
579#121—212no—
580#121C2416yes—
581#121C24112yes—
582#121C2416yes—
583#120—26no—
584#120—212no—
585#120—212no—
586C4×Q8—26no—
587C4×Q8—26no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—23no—
592C4×Q8—21no—
593C4×Q8—23no—
594C4×Q8—21no—
595C4×Q8—26no—
596C4×Q8—26no—
597C4×Q8—26no—
598C4×Q8—26no—
599C4×Q8—26no—
600C4×Q8—26no—
601C4×Q8—23no—
602C4×Q8—23no—
603C4×Q8—23no—
604C4×Q8—23no—
605C4×Q8—26no—
606C4×Q8—26no—
607C4×Q8—26no—
608C4×Q8—26no—
609C4×Q8—21no—
610C4×Q8—23no—
611C4×Q8—23no—
612C4×Q8—23no—
613C4×Q8C2×D411yescharacteristic
614C4×Q8C2×D411yescharacteristic
615C4×Q8C2×D413yes—
616C4×Q8C2×D413yes—
617C4×Q8C2×D411yescharacteristic
618C4×Q8C2×D411yescharacteristic
619C4×Q8C2×D413yes—
620C4×Q8C2×D413yes—
621C4×Q8C2412yes—
622C4×Q8C2416yes—
623C4×D4—26no—
624C4×D4—212no—
625C4×D4—212no—
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—26no—
637C4×D4—26no—
638C4×D4—212no—
639C4×D4—23no—
640C4×D4—26no—
641C4×D4—26no—
642C4×D4—26no—
643C4×D4—26no—
644C4×D4—26no—
645C4×D4—23no—
646C4×D4—23no—
647C4×D4—23no—
648C4×D4C2×D413yes—
649C4×D4C2×D413yes—
650C4×D4C2×D416yes—
651C4×D4C2×D413yes—
652C4×D4C2×D416yes—
653C4×D4C2×D413yes—
654C4×D4C2×D413yes—
655C4×D4C2×D413yes—
656C4×D4C2×D416yes—
657C4×D4C2×D416yes—
658C4×D4C2×D413yes—
659C4×D4C2×D413yes—
660C4×D4C2416yes—
661C4×D4C24112yes—
662C4×D4C2416yes—
663#117—26no—
664#117—26no—
665#117—26no—
666#117—26no—
667#117—21no—
668#117—23no—
669#117—26no—
670#117—26no—
671#117—26no—
672#117—26no—
673#117C2×D416yes—
674#117C2×D413yes—
675#117C2×D413yes—
676#117C2416yes—
677#117C2412yes—
678#117C2416yes—
679#117C2416yes—
680#117C24112yes—
681#117C2416yes—
682#117C2413yes—
683#117C2413yes—
684#117C2416yes—
685C2×C4⋊C4—23no—
686C2×C4⋊C4—26no—
687C2×C4⋊C4—26no—
688C2×C4⋊C4—26no—
689C2×C4⋊C4—26no—
690C2×C4⋊C4—23no—
691C2×C4⋊C4—23no—
692C2×C4⋊C4—23no—
693C2×C4⋊C4—23no—
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⋊C4—26no—
706C2×C22⋊C4—212no—
707C2×C22⋊C4C2×D416yes—
708C2×C42—26no—
709C2×C42—26no—
710C2×C42—26no—
711C2×C42C2×D413yes—
712C2×C42C2×D413yes—
713C2×C42C2×D413yes—
714C2×C42C2×D413yes—
715C2×C42C2×D413yes—
716C2×C42C2×D413yes—
717C2×C42C2413yes—
718C2×C42C2413yes—
719C2×C42C2413yes—
720C2×C42C2413yes—
721C2×C42C2413yes—
722C2×C42C2411yescharacteristic
723#107C24112yes—
724#107C24124yes—
725#107C2414yes—
726#107C24112yes—
727#107C24112yes—
728#106C24112yes—
729#106C24124yes—
730#106C2414yes—
731#106C24112yes—
732#106C24112yes—
733C4⋊C8C2412yes—
734C4⋊C8C2416yes—
735C4⋊C8C2416yes—
736C4⋊C8C2416yes—
737C4⋊C8C24112yes—
738#103C2414yes—
739#103C2414yes—
740#103C24112yes—
741#103C24112yes—
742#102C24112yes—
743#102C24112yes—
744#102C24124yes—
745#102C24124yes—
746#102C24112yes—
747#102C24112yes—
748C22⋊C8C2412yes—
749C22⋊C8C2416yes—
750C22⋊C8C2416yes—
751C22⋊C8C2416yes—
752C22⋊C8C24112yes—
753#97C2416yes—
754#97C2416yes—
755C4×C8C2411yescharacteristic
756C4×C8C2411yescharacteristic
757C4×C8C2413yes—
758C4×C8C2413yes—
759C4×C8C2416yes—
760C4×C8C2416yes—
761C24—26no—
762C24C22×D413yes—
763#41—24no—
764#41—212no—
765#41—212no—
766#41—224no—
767#41—412no—
768#41—48no—
769#41—86no—
770#41—812no—
771#41—812no—
772#41—812no—
773#412−1+418yes—
774C2×Q8—24no—
775C2×Q8—21no—
776C2×Q8—23no—
777C2×Q8—21no—
778C2×Q8—23no—
779C2×Q8—21no—
780C2×Q8—23no—
781C2×Q8—26no—
782C2×Q8—26no—
783C2×Q8—26no—
784C2×Q8—26no—
785C2×Q8—26no—
786C2×Q8—86no—
787C2×Q8—86no—
788C2×Q8—86no—
789C2×Q8—86no—
790C2×Q8—86no—
791C2×Q8C22×D413yes—
792C2×Q8C22×D411yescharacteristic
793C2×Q8C2512yes—
794C2×D4—212no—
795C2×D4—26no—
796C2×D4—26no—
797C2×D4—26no—
798C2×D4—212no—
799C2×D4—26no—
800C2×D4—23no—
801C2×D4—23no—
802C2×D4—26no—
803C2×D4—26no—
804C2×D4—224no—
805C2×D4—424no—
806C2×D4—86no—
807C2×D4—86no—
808C2×D4—812no—
809C2×D4C22×D416yes—
810C2×D4C22×D413yes—
811C2×D4C22×D413yes—
812C2×D4C2516yes—
813C22×C4—212no—
814C22×C4—26no—
815C22×C4—26no—
816C22×C4—26no—
817C22×C4—26no—
818C22×C4—26no—
819C22×C4—26no—
820C22×C4—26no—
821C22×C4—26no—
822C22×C4—212no—
823C22×C4—46no—
824C22×C4—46no—
825C22×C4—812no—
826C22×C4C22×D413yes—
827C22×C4C22×D413yes—
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D413yes—
831C22×C4C22×D413yes—
832C22×C4C22×D413yes—
833C22×C4C22×D413yes—
834C22×C4C22×D413yes—
835C22×C4C22×D413yes—
836C22×C4C22×D413yes—
837C22×C4C22×D413yes—
838C22×C4C22×D413yes—
839C22×C4C22×D413yes—
840C22×C4C22×D413yes—
841C22×C4C2511yescharacteristic
842C22×C4C2513yes—
843C22×C4C2513yes—
844M16—212no—
845M16—212no—
846C2×C8—212no—
847C2×C8—212no—
848C2×C8C2512yes—
849C2×C8C2512yes—
850C2×C8C2516yes—
851C2×C8C2516yes—
852C4⋊C4—26no—
853C4⋊C4—22no—
854C4⋊C4—26no—
855C4⋊C4—22no—
856C4⋊C4—23no—
857C4⋊C4—21no—
858C4⋊C4—23no—
859C4⋊C4—21no—
860C4⋊C4—23no—
861C4⋊C4—26no—
862C4⋊C4—26no—
863C4⋊C4—26no—
864C4⋊C4—26no—
865C4⋊C4—26no—
866C4⋊C4—26no—
867C4⋊C4—26no—
868C4⋊C4—212no—
869C4⋊C4—26no—
870C4⋊C4—26no—
871C4⋊C4—212no—
872C4⋊C4—26no—
873C4⋊C4—26no—
874C4⋊C4—26no—
875C4⋊C4—26no—
876C4⋊C4—26no—
877C4⋊C4—26no—
878C4⋊C4—21no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—26no—
884C4⋊C4—26no—
885C4⋊C4—26no—
886C4⋊C4C22×D413yes—
887C4⋊C4C22×D413yes—
888C4⋊C4C22×D413yes—
889C4⋊C4C22×D413yes—
890C4⋊C4C22×D416yes—
891C4⋊C4C22×D416yes—
892C4⋊C4C2516yes—
893C4⋊C4C2512yes—
894C4⋊C4C2516yes—
895C4⋊C4C2512yes—
896C4⋊C4C2516yes—
897C4⋊C4C2512yes—
898C22⋊C4—26no—
899C22⋊C4—22no—
900C22⋊C4—26no—
901C22⋊C4—212no—
902C22⋊C4—26no—
903C22⋊C4—26no—
904C22⋊C4—22no—
905C22⋊C4—26no—
906C22⋊C4—26no—
907C22⋊C4—26no—
908C22⋊C4—212no—
909C22⋊C4—26no—
910C22⋊C4—212no—
911C22⋊C4—26no—
912C22⋊C4—26no—
913C22⋊C4—26no—
914C22⋊C4C22×D416yes—
915C22⋊C4C22×D416yes—
916C22⋊C4C22×D416yes—
917C22⋊C4C22×D416yes—
918C42—22no—
919C42—26no—
920C42—22no—
921C42—26no—
922C42—26no—
923C42—212no—
924C42—26no—
925C42—26no—
926C42C22×D413yes—
927C42C22×D411yescharacteristic
928C42C22×D411yescharacteristic
929C42C22×D413yes—
930C42C22×D413yes—
931C42C22×D413yes—
932C42C22×D413yes—
933C42C22×D413yes—
934C42C22×D413yes—
935C42C22×D413yes—
936C42C22×D413yes—
937C42C22×D413yes—
938C42C2511yescharacteristic
939C42C2513yes—
940C42C2511yescharacteristic
941C42C2513yes—
942C23—26no—
943C23—26no—
944C23—43no—
945C23—43no—
946C23—412no—
947C23—86no—
948C23—86no—
949C23C23×D411yescharacteristic
950C23C23×D413yes—
951C23C23×D413yes—
952Q8—26no—
953Q8—24no—
954Q8—46no—
955Q8—42no—
956Q8—42no—
957Q8—46no—
958Q8—42no—
959Q8—46no—
960Q8—86no—
961Q8—86no—
962Q8—86no—
963Q8—86no—
964Q8—86no—
965Q8#53614yes—
966D4—212no—
967D4—212no—
968D4—26no—
969D4—412no—
970D4—412no—
971D4—46no—
972D4—46no—
973D4—412no—
974D4—86no—
975D4—86no—
976D4—812no—
977D4—86no—
978D4#536112yes—
979C2×C4—26no—
980C2×C4—22no—
981C2×C4—26no—
982C2×C4—26no—
983C2×C4—22no—
984C2×C4—26no—
985C2×C4—26no—
986C2×C4—22no—
987C2×C4—26no—
988C2×C4—26no—
989C2×C4—26no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—26no—
993C2×C4—22no—
994C2×C4—26no—
995C2×C4—22no—
996C2×C4—26no—
997C2×C4—43no—
998C2×C4—43no—
999C2×C4—43no—
1000C2×C4—43no—
1001C2×C4—43no—
1002C2×C4—43no—
1003C2×C4—412no—
1004C2×C4—412no—
1005C2×C4—812no—
1006C2×C4—86no—
1007C2×C4—86no—
1008C2×C4—86no—
1009C2×C4—86no—
1010C2×C4—86no—
1011C2×C4—86no—
1012C2×C4C23×D411yescharacteristic
1013C2×C4C23×D413yes—
1014C2×C4C23×D411yescharacteristic
1015C2×C4C23×D413yes—
1016C2×C4C23×D411yescharacteristic
1017C2×C4C23×D413yes—
1018C2×C4C23×D413yes—
1019C2×C4C23×D413yes—
1020C2×C4C23×D411yescharacteristic
1021C2×C4C23×D411yescharacteristic
1022C2×C4C23×D413yes—
1023C2×C4C2×2−1+4112yes—
1024C2×C4C2611yescharacteristic
1025C8—22no—
1026C8—22no—
1027C8—26no—
1028C8—26no—
1029C22—23no—
1030C22—23no—
1031C22—21no—
1032C22—23no—
1033C22—21no—
1034C22—23no—
1035C22—21no—
1036C22—23no—
1037C22—46no—
1038C22—46no—
1039C22—46no—
1040C22—86no—
1041C22—1612no—
1042C22C2×#53616yes—
1043C22C24×D411yescharacteristic
1044C4—21no—
1045C4—23no—
1046C4—23no—
1047C4—21no—
1048C4—23no—
1049C4—23no—
1050C4—21no—
1051C4—23no—
1052C4—42no—
1053C4—46no—
1054C4—42no—
1055C4—46no—
1056C4—46no—
1057C4—42no—
1058C4—42no—
1059C4C2×#53616yes—
1060C4#358412yes—
1061C4#358512yes—
1062C4C22×2−1+412yes—
1063C2—26no—
1064C2—43no—
1065C2—41no—
1066C2—86no—
1067C2C22×#53611yescharacteristic
1068C2C2×#358411yescharacteristic
1069C2C2×#358511yescharacteristic
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. #60890C2semidirect
4. #60881C2semidirect
5. #60880C2semidirect
6. #60877C2semidirect
7. #60877C2semidirect
8. #60875C2semidirect
9. #60864C2semidirect
10. #60862C2semidirect
11. #60846C2semidirect
12. C2×#3228C2semidirect
13. #60667C2semidirect
14. #60665C2semidirect
15. #60622C2semidirect
16. #60622C2semidirect
17. #60523C2semidirect
18. #60496C2semidirect
19. #60127C2semidirect
27. #3504C22semidirect
31. #3503C22semidirect
32. #3503C22semidirect
49. #3458C22semidirect
51. C2×#533C22semidirect
52. C2×#533C22semidirect
57. #3244C22semidirect
58. #3243C22semidirect
59. #3241C22semidirect
60. #3241C22semidirect
61. #3240C22semidirect
62. #3240C22semidirect
63. #3235C22semidirect
64. #3234C22semidirect
65. #3233C22semidirect
66. #3232C22semidirect
67. #3231C22semidirect
68. #3231C22semidirect
69. #3231C22semidirect
70. #3230C22semidirect
71. #3229C22semidirect
72. #3228C22semidirect
73. #3228C22semidirect
74. #3228C22semidirect
75. #3228C22semidirect
76. #3228C22semidirect
77. #3228C22semidirect
78. #3228C22semidirect
79. #3228C22semidirect
80. #3227C22semidirect
81. #3227C22semidirect
82. #3226C22semidirect
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. #3138C22semidirect
97. #3138C22semidirect
98. #3136C22semidirect
99. #3136C22semidirect
100. #3131C22semidirect
101. #3131C22semidirect
102. C2×#486C22semidirect
103. C2×#486C22semidirect
104. #3099C22semidirect
105. #3098C22semidirect
106. #3096C22semidirect
107. #3096C22semidirect
108. #3094C22semidirect
109. #3093C22semidirect
110. #3091C22semidirect
111. C2×#482C22semidirect
112. #3084C22semidirect
113. #3083C22semidirect
114. #3081C22semidirect
115. #3081C22semidirect
116. #3080C22semidirect
117. #3077C22semidirect
118. #3076C22semidirect
119. C2×#478C22semidirect
120. #2925C22semidirect
121. #2924C22semidirect
122. #2922C22semidirect
123. #2922C22semidirect
124. #2920C22semidirect
125. C2×#431C22semidirect

Maximal subgroups

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

subgroupindex
#628132
#628002
#608902
#608812
#608802
#608772
#608752
#608642
#608622
#608462
C2×#32282
#606672
#606652
#606222
#605232
#604962
#601272