Finite Group Databasebeta

← #6357528

Subgroups — #6357528

Order 512.

2198 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60947C211yesmaximal, characteristic, complemented
2#60804C211yesmaximal, characteristic, complemented
3#60798C211yesmaximal, characteristic, complemented
4C2×#3205C211yesmaximal, characteristic, complemented
5#60700C211yesmaximal, characteristic, complemented
6C2×#3138C211yesmaximal, characteristic, complemented
7#19729C214yesmaximal, complemented
8#19715C214yesmaximal, complemented
9#19682C212yesmaximal, complemented
10#19677C212yesmaximal, complemented
11#19676C212yesmaximal, complemented
12#19673C212yesmaximal, complemented
13#19635C212yesmaximal, complemented
14#19631C212yesmaximal, complemented
15#19627C212yesmaximal, complemented
16#19627C212yesmaximal, complemented
17#17327C211yesmaximal, characteristic, complemented
18#3444C2211yescharacteristic
19C2×#533C2211yescharacteristic
20C2×#532C2211yescharacteristic
21C22×#127C2211yescharacteristic
22#3248—22no—
23#3231C2212yescomplemented
24#3229C2211yescharacteristic, complemented
25#3226C2211yescharacteristic, complemented
26#3217—22no—
27#3217—22no—
28#3216—22no—
29#3215—22no—
30#3210C2214yescomplemented
31#3210C2212yescomplemented
32#3209C2211yescharacteristic, complemented
33#3209C2212yescomplemented
34#3208C2212yes—
35#3208C2212yescomplemented
36#3208C2212yescomplemented
37#3206C2211yescharacteristic, complemented
38#3205—22no—
39#3205—22no—
40#3205C2214yes—
41#3205C2212yes—
42#3205C2212yes—
43#3205C2212yes—
44#3205C2212yescomplemented
45#3190—22no—
46#3184C2212yescomplemented
47#3182C2212yescomplemented
48#3180—22no—
49#3171—22no—
50#3170C2212yescomplemented
51#3169C2212yescomplemented
52#3167C2212yescomplemented
53#3167C2212yescomplemented
54#3165C2211yescharacteristic, complemented
55#3152C2212yescomplemented
56#3151C2212yescomplemented
57#3151C2211yescharacteristic, complemented
58C2×#493C2212yes—
59#3141C2211yescharacteristic, complemented
60#3141C2212yescomplemented
61#3138—22no—
62#3138—22no—
63#3138C2212yes—
64#3138C2212yes—
65#3138C2214yescomplemented
66#3138C2212yescomplemented
67#3138C2211yescharacteristic, complemented
68C2×#490—22no—
69C2×#486C2212yes—
70C2×#486C2212yescomplemented
71C2×#486C2212yescomplemented
72#3108—22no—
73#3107—22no—
74#3055—22no—
75#3038—22no—
76#3037—22no—
77C2×#459—22no—
78#3007—22no—
79#3003—22no—
80C2×#447—22no—
81C4×AGL(1,ℤ/8)—22no—
82#2920C2211yescharacteristic
83C2×#431C2211yescharacteristic
84C2×#418—22no—
85C2×C4×M16C2211yescharacteristic
86#1722C2214yescomplemented
87#1721C2214yescomplemented
88#1721C2214yescomplemented
89#1720C2214yescomplemented
90#1720C2214yescomplemented
91#1720C2214yescomplemented
92#1719C2214yescomplemented
93#1717C2214yescomplemented
94#1717C2214yescomplemented
95#1717C2214yescomplemented
96#1717C2214yescomplemented
97#1715C2214yescomplemented
98#1711C2214yescomplemented
99#1709C2214yescomplemented
100#1709C2214yescomplemented
101#1706C2214yescomplemented
102#1453C2214yescomplemented
103#1451C2212yescomplemented
104#1451C2212yescomplemented
105C8×M16C2212yescomplemented
106C8×M16C2212yescomplemented
107C22×#41—21no—
108C23×D4—21no—
109C23×D4—21no—
110C23×D4—21no—
111C2×#137—24no—
112C2×AGL(1,ℤ/8)—22no—
113C2×AGL(1,ℤ/8)—24no—
114C22×D8—24no—
115C22×M16D412yes—
116#533—21no—
117#533—21no—
118#533—21no—
119#533—21no—
120#533—21no—
121#533—21no—
122#533C2312yes—
123#533C2311yescharacteristic
124#533C2312yes—
125#533C2311yescharacteristic
126#533C2311yescharacteristic
127#532—21no—
128#532—21no—
129#532—21no—
130#532—21no—
131#532—21no—
132#532—21no—
133#532C2311yescharacteristic
134#532C2312yes—
135#532C2311yescharacteristic
136#532C2312yes—
137#532C2311yescharacteristic
138C2×C4⋊Q8C2311yescharacteristic
139C2×C4⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×#127—21no—
142C2×#127—21no—
143C2×#127—21no—
144C2×#127—21no—
145C2×#127—21no—
146C2×#127—21no—
147C2×#127—21no—
148C2×#127—21no—
149C2×#127—21no—
150C2×#127C2312yes—
151C2×#127C2312yes—
152C2×#127C2312yes—
153C2×#127C2311yescharacteristic
154#529—21no—
155#529—21no—
156#529—21no—
157#529—21no—
158#529—21no—
159#529—21no—
160C2×#125—21no—
161C2×#124—21no—
162#525—21no—
163#525—21no—
164#525—21no—
165C2×C22⋊Q8—21no—
166C2×C22⋊Q8—21no—
167C2×#121—21no—
168C2×#121—21no—
169C4×#41—21no—
170C4×#41—21no—
171C4×#41—21no—
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174C2×C4×D4—21no—
175C2×C4×D4—21no—
176C2×#117—21no—
177C22×C42C2311yescharacteristic
178#501—22no—
179#500C2312yescomplemented
180#500C2312yescomplemented
181#498C2312yescomplemented
182#498C2312yescomplemented
183#497—24no—
184#496—22no—
185#496—24no—
186#494C2314yescomplemented
187#494C2312yescomplemented
188#493—24no—
189#493C2314yes—
190#493C2314yes—
191#493C2314yes—
192#493C2312yescomplemented
193#492C2314yes—
194#492C2312yescomplemented
195#492C2314yescomplemented
196#492C2312yescomplemented
197#490—24no—
198#490—24no—
199#490—28no—
200#490—22no—
201#490—24no—
202#489—22no—
203#489—24no—
204#487C2312yescomplemented
205#487C2314yescomplemented
206#487C2312yescomplemented
207#487C2312yescomplemented
208#487C2312yescomplemented
209#486—24no—
210#486—24no—
211#486—24no—
212#486C2314yes—
213#486C2314yes—
214#486C2314yes—
215#486C2314yes—
216#486C2314yes—
217#486C2314yes—
218#486C2314yes—
219#486C2314yes—
220#486C2312yescomplemented
221#486C2312yescomplemented
222#486C2312yescomplemented
223#486C2314yescomplemented
224#486C2312yescomplemented
225#485—24no—
226#483—22no—
227#480—22no—
228#479—24no—
229#475—22no—
230#474—22no—
231#469—24no—
232#468—24no—
233#467—24no—
234#466—24no—
235#465—24no—
236#465—24no—
237#464—24no—
238#464—28no—
239#462—22no—
240#462—24no—
241#461—22no—
242#460—24no—
243#460—24no—
244#460—24no—
245#459—24no—
246#459—24no—
247#459—28no—
248#459—24no—
249#459—24no—
250#452—24no—
251#452—28no—
252#451—22no—
253#451—24no—
254#450—24no—
255#450—24no—
256#450—24no—
257#448—22no—
258#447—24no—
259#447—24no—
260#447—28no—
261#447—24no—
262#447—24no—
263#442—24no—
264#440—24no—
265C4×Q16—24no—
266C4×SD16—24no—
267C4×SD16—24no—
268C4×D8—24no—
269#432D412yes—
270#432D412yes—
271#431D412yes—
272#431D412yes—
273#431C2311yescharacteristic
274#431C2311yescharacteristic
275#431C2312yes—
276#431C2312yes—
277#431C2312yes—
278#428—22no—
279#423D412yes—
280C2×C4⋊C8D412yes—
281#418—24no—
282#418—24no—
283#418—28no—
284#418—22no—
285#418—24no—
286#417—22no—
287#417—24no—
288C2×#102—24no—
289C2×#102—24no—
290C2×#102—24no—
291#407D412yes—
292C2×C22⋊C8D412yes—
293C4×M16D412yes—
294C4×M16D412yes—
295C4×M16C2311yescharacteristic
296C4×M16C2311yescharacteristic
297C4×M16C2312yes—
298C4×M16C2312yes—
299C2×#97D412yes—
300C2×C4×C8C2312yes—
301C2×C4×C8C2312yes—
302#322C2314yescomplemented
303#322C2314yescomplemented
304#322C2314yescomplemented
305C82C2314yescomplemented
306C25—41no—
307C2×#41—21no—
308C2×#41—21no—
309C2×#41—22no—
310C2×#41—21no—
311C2×#41—22no—
312C2×#41—41no—
313C2×#41—41no—
314C2×#41—84no—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8—21no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—48no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—41no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4—41no—
341C22×D4—84no—
342C22×D4—84no—
343C23×C4—41no—
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347#137—88no—
348AGL(1,ℤ/8)—48no—
349AGL(1,ℤ/8)—88no—
350C2×Q16—28no—
351C2×Q16—24no—
352C2×SD16—24no—
353C2×SD16—28no—
354C2×SD16—28no—
355C2×SD16—24no—
356C2×D8—24no—
357C2×D8—28no—
358C2×D8—28no—
359C2×D8—28no—
360C2×D8—88no—
361C2×M16—44no—
362C2×M16C2×D412yes—
363C2×M16C2×D412yes—
364C2×M16C2×D414yes—
365C2×M16C2×D414yes—
366C22×C8C2×D414yes—
367C22×C8C2×D414yes—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C2412yes—
378C4⋊Q8C2412yes—
379C4⋊Q8C2412yes—
380C4⋊Q8C2411yescharacteristic
381C4⋊Q8C2411yescharacteristic
382C4⋊Q8C2411yescharacteristic
383#127—22no—
384#127—22no—
385#127—22no—
386#127—22no—
387#127—22no—
388#127—22no—
389#127—22no—
390#127—22no—
391#127—22no—
392#127—21no—
393#127—21no—
394#127—21no—
395#127—41no—
396#127—41no—
397#127—41no—
398#127—41no—
399#127—41no—
400#127—41no—
401#127C2414yes—
402#127C2412yes—
403#127C2411yescharacteristic
404#126—41no—
405#126—41no—
406#125—22no—
407#125—22no—
408#125—21no—
409#125—21no—
410#125—21no—
411#125—41no—
412#125—41no—
413#124—22no—
414#124—22no—
415#124—21no—
416#124—21no—
417#124—21no—
418#124—41no—
419#124—41no—
420#123—41no—
421#123—41no—
422#123—41no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8—21no—
433C22⋊Q8—41no—
434C22⋊Q8—41no—
435C22⋊Q8—41no—
436C22⋊Q8—41no—
437#121—22no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—21no—
442#121—21no—
443#121—21no—
444#121—21no—
445#121—21no—
446#121—21no—
447#121—41no—
448#121—41no—
449#121—41no—
450#121—41no—
451#120—41no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—21no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8—21no—
460C4×Q8—21no—
461C4×Q8—21no—
462C4×Q8—41no—
463C4×Q8—41no—
464C4×Q8—41no—
465C4×Q8—41no—
466C4×D4—22no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—41no—
477C4×D4—41no—
478C4×D4—41no—
479C4×D4—41no—
480C4×D4—41no—
481C4×D4—41no—
482C4×D4—41no—
483C4×D4—41no—
484C4×D4—41no—
485C4×D4—41no—
486#117—22no—
487#117—22no—
488#117—21no—
489#117—21no—
490#117—21no—
491#117—41no—
492#117—41no—
493#117—41no—
494#117—41no—
495#117—41no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C42—41no—
508C2×C42—41no—
509C2×C42C2×D411yescharacteristic
510C2×C42C2×D411yescharacteristic
511C2×C42C2×D411yescharacteristic
512C2×C42C2×D411yescharacteristic
513C2×C42C2×D411yescharacteristic
514C2×C42C2×D411yescharacteristic
515C2×C42C2×D411yescharacteristic
516C2×C42C2×D411yescharacteristic
517C2×C42C2×D411yescharacteristic
518C2×C42C2411yescharacteristic
519C2×C42C2411yescharacteristic
520C2×C42C2411yescharacteristic
521#107—24no—
522#107—24no—
523#106—24no—
524#106—24no—
525C4⋊C8C2×D412yes—
526C4⋊C8C2×D412yes—
527C4⋊C8C2×D414yes—
528C4⋊C8C2×D414yes—
529C4⋊C8C2×D414yes—
530#103—24no—
531#103—28no—
532#103—24no—
533#103—24no—
534#103—24no—
535#102—28no—
536#102—28no—
537#102—28no—
538#102—28no—
539#102—28no—
540#102—28no—
541#102—24no—
542#102—28no—
543#102—24no—
544#102—24no—
545#102—28no—
546#102—28no—
547#102—24no—
548C22⋊C8C2×D412yes—
549C22⋊C8C2×D412yes—
550C22⋊C8C2×D414yes—
551C22⋊C8C2×D414yes—
552C22⋊C8C2×D414yes—
553#97C2×D414yes—
554#97C2×D412yes—
555#97C2×D412yes—
556#97C2×D414yes—
557C4×C8C2×D414yes—
558C4×C8C2×D414yes—
559C4×C8C2412yes—
560C4×C8C2412yes—
561C4×C8C2414yes—
562C4×C8C2412yes—
563C4×C8C2412yes—
564C24—41no—
565C24—42no—
566C24—42no—
567C24—42no—
568C24—84no—
569C24—84no—
570C24—84no—
571C24#12711yescharacteristic
572#41—44no—
573#41—44no—
574#41—48no—
575#41—82no—
576#41—84no—
577#41—84no—
578#41—84no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—21no—
584C2×Q8—22no—
585C2×Q8—41no—
586C2×Q8—41no—
587C2×Q8—41no—
588C2×Q8—44no—
589C2×Q8—82no—
590C2×Q8—82no—
591C2×D4—24no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—44no—
601C2×D4—48no—
602C2×D4—48no—
603C2×D4—48no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—48no—
623C2×D4—48no—
624C2×D4—84no—
625C2×D4—84no—
626C2×D4—84no—
627C2×D4—84no—
628C2×D4—82no—
629C2×D4—84no—
630C2×D4—84no—
631C2×D4—84no—
632C2×D4—84no—
633C2×D4—84no—
634C2×D4—84no—
635C2×D4—84no—
636C2×D4—84no—
637C2×D4—84no—
638C2×D4—84no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—42no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—84no—
651C22×C4#12711yescharacteristic
652C22×C4#12711yescharacteristic
653C22×C4#12711yescharacteristic
654C22×C4#12711yescharacteristic
655C22×C4#12711yescharacteristic
656C22×C4#12711yescharacteristic
657C22×C4#12711yescharacteristic
658C22×C4#12711yescharacteristic
659C22×C4#12711yescharacteristic
660C22×C4C22×D411yescharacteristic
661C22×C4C22×D411yescharacteristic
662C22×C4C22×D411yescharacteristic
663C22×C4C22×D411yescharacteristic
664C22×C4C22×D411yescharacteristic
665C22×C4C22×D411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C22×D411yescharacteristic
669Q16—84no—
670Q16—88no—
671SD16—48no—
672SD16—84no—
673SD16—88no—
674SD16—88no—
675D8—48no—
676D8—88no—
677D8—88no—
678D8—88no—
679M16—24no—
680M16—24no—
681M16—28no—
682M16—44no—
683C2×C8—44no—
684C2×C8—44no—
685C2×C8C22×D414yes—
686C2×C8C22×D414yes—
687C2×C8C22×D414yes—
688C2×C8C22×D414yes—
689C2×C8C22×D418yes—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—41no—
703C4⋊C4—41no—
704C4⋊C4—41no—
705C4⋊C4—41no—
706C4⋊C4—41no—
707C4⋊C4—41no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—41no—
715C4⋊C4—41no—
716C4⋊C4—41no—
717C4⋊C4—41no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—41no—
721C22⋊C4—41no—
722C22⋊C4—41no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—41no—
728C22⋊C4—41no—
729C22⋊C4—41no—
730C22⋊C4—41no—
731C22⋊C4—41no—
732C22⋊C4—41no—
733C42—41no—
734C42—41no—
735C42—41no—
736C42—42no—
737C42—42no—
738C42#12711yescharacteristic
739C42#12711yescharacteristic
740C42#12711yescharacteristic
741C42#12711yescharacteristic
742C42#12711yescharacteristic
743C42#12711yescharacteristic
744C42C22×D411yescharacteristic
745C42C22×D411yescharacteristic
746C42C22×D411yescharacteristic
747C42C22×D411yescharacteristic
748C42C22×D411yescharacteristic
749C42C22×D411yescharacteristic
750C42C22×D411yescharacteristic
751C42C22×D411yescharacteristic
752C42C22×D411yescharacteristic
753C42C2511yescharacteristic
754C23—22no—
755C23—22no—
756C23—41no—
757C23—41no—
758C23—42no—
759C23—44no—
760C23—82no—
761C23—84no—
762C23—84no—
763C23—84no—
764C23—82no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—82no—
771C23—84no—
772C23—1616no—
773C23C2×#12711yescharacteristic
774C23C2×#12711yescharacteristic
775C23C2×#12711yescharacteristic
776Q8—44no—
777Q8—42no—
778Q8—42no—
779Q8—42no—
780Q8—44no—
781Q8—44no—
782Q8—82no—
783Q8—82no—
784Q8—82no—
785D4—44no—
786D4—48no—
787D4—42no—
788D4—42no—
789D4—44no—
790D4—48no—
791D4—42no—
792D4—48no—
793D4—44no—
794D4—82no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800D4—84no—
801D4—84no—
802D4—82no—
803D4—84no—
804D4—82no—
805D4—82no—
806D4—84no—
807D4—82no—
808D4—82no—
809D4—84no—
810D4—84no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—84no—
834C2×C4—82no—
835C2×C4—82no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4—82no—
839C2×C4—84no—
840C2×C4—82no—
841C2×C4C2×#12711yescharacteristic
842C2×C4C2×#12711yescharacteristic
843C2×C4C2×#12711yescharacteristic
844C2×C4C2×#12711yescharacteristic
845C2×C4C2×#12711yescharacteristic
846C2×C4C2×#12711yescharacteristic
847C2×C4C2×#12711yescharacteristic
848C2×C4C2×#12711yescharacteristic
849C2×C4C2×#12711yescharacteristic
850C2×C4#57514yes—
851C2×C4#57614yes—
852C2×C4C23×D411yescharacteristic
853C2×C4C23×D411yescharacteristic
854C2×C4C23×D411yescharacteristic
855C8—24no—
856C8—24no—
857C8—24no—
858C8—24no—
859C8—28no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—44no—
868C22—81no—
869C22—84no—
870C22—82no—
871C22—82no—
872C22—81no—
873C22—84no—
874C22—81no—
875C22—84no—
876C22—82no—
877C22—164no—
878C22—168no—
879C22—168no—
880C22—168no—
881C22#315312yes—
882C22#315512yes—
883C22C22×#12711yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—81no—
892C4—82no—
893C4—81no—
894C4—82no—
895C4—81no—
896C4—82no—
897C4#315312yes—
898C4#315512yes—
899C4C2×#57512yes—
900C4C2×#57612yes—
901C4#358512yes—
902C2—22no—
903C2—22no—
904C2—41no—
905C2—161no—
906C2—162no—
907C2—164no—
908C2C2×#315311yescharacteristic
909C2C2×#315511yescharacteristic
910C2#6064411yescharacteristic
subgroupG/H
center, socleC22C22×#127
commutator, Frattini, cosocleC42C25
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60947C2semidirect
2. #60804C2semidirect
3. #60798C2semidirect
4. C2×#3205C2semidirect
5. #60700C2semidirect
6. C2×#3138C2semidirect
7. #19729C2semidirect
8. #19715C2semidirect
9. #19682C2semidirect
10. #19677C2semidirect
11. #19676C2semidirect
12. #19673C2semidirect
13. #19635C2semidirect
14. #19631C2semidirect
15. #19627C2semidirect
16. #19627C2semidirect
17. #17327C2semidirect
23. #3231C22semidirect
24. #3229C22semidirect
25. #3226C22semidirect
30. #3210C22semidirect
31. #3210C22semidirect
32. #3209C22semidirect
33. #3209C22semidirect
35. #3208C22semidirect
36. #3208C22semidirect
37. #3206C22semidirect
44. #3205C22semidirect
46. #3184C22semidirect
47. #3182C22semidirect
50. #3170C22semidirect
51. #3169C22semidirect
52. #3167C22semidirect
53. #3167C22semidirect
54. #3165C22semidirect
55. #3152C22semidirect
56. #3151C22semidirect
57. #3151C22semidirect
59. #3141C22semidirect
60. #3141C22semidirect
65. #3138C22semidirect
66. #3138C22semidirect
67. #3138C22semidirect
70. C2×#486C22semidirect
71. C2×#486C22semidirect
86. #1722C22semidirect
87. #1721C22semidirect
88. #1721C22semidirect
89. #1720C22semidirect
90. #1720C22semidirect
91. #1720C22semidirect
92. #1719C22semidirect
93. #1717C22semidirect
94. #1717C22semidirect
95. #1717C22semidirect
96. #1717C22semidirect
97. #1715C22semidirect
98. #1711C22semidirect
99. #1709C22semidirect
100. #1709C22semidirect
101. #1706C22semidirect
102. #1453C22semidirect
103. #1451C22semidirect
104. #1451C22semidirect
105. C8×M16C22semidirect
106. C8×M16C22semidirect
179. #500C23semidirect
180. #500C23semidirect
181. #498C23semidirect
182. #498C23semidirect
186. #494C23semidirect
187. #494C23semidirect
192. #493C23semidirect
194. #492C23semidirect
195. #492C23semidirect
196. #492C23semidirect
204. #487C23semidirect
205. #487C23semidirect
206. #487C23semidirect
207. #487C23semidirect
208. #487C23semidirect
220. #486C23semidirect
221. #486C23semidirect
222. #486C23semidirect
223. #486C23semidirect
224. #486C23semidirect
302. #322C23semidirect
303. #322C23semidirect
304. #322C23semidirect
305. C82C23semidirect

Maximal subgroups

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

subgroupindex
#609472
#608042
#607982
C2×#32052
#607002
C2×#31382
#197292
#197152
#196822
#196772
#196762
#196732
#196352
#196312
#196272
#173272