Finite Group Databasebeta

← #7624971

Subgroups — #7624971

Order 512.

1184 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62379C211yesmaximal, characteristic, complemented
2#62377C211yesmaximal, characteristic, complemented
3#33970C211yesmaximal, characteristic, complemented
4#33970C211yesmaximal, characteristic, complemented
5#33964C211yesmaximal, characteristic, complemented
6#33961C211yesmaximal, characteristic, complemented
7#33955C211yesmaximal, characteristic, complemented
8#33955C211yesmaximal, characteristic, complemented
9#33953C211yesmaximal, characteristic, complemented
10#33947C211yesmaximal, characteristic, complemented
11#33944C211yesmaximal, characteristic, complemented
12#33943C211yesmaximal, characteristic, complemented
13#33940C211yesmaximal, characteristic, complemented
14#33938C211yesmaximal, characteristic, complemented
15#33937C211yesmaximal, characteristic, complemented
16#33933C211yesmaximal, characteristic, complemented
17#33932C211yesmaximal, characteristic, complemented
18#33928C211yesmaximal, characteristic, complemented
19#33829C211yesmaximal, characteristic, complemented
20#33825C211yesmaximal, characteristic, complemented
21#33824C211yesmaximal, characteristic, complemented
22#33823C211yesmaximal, characteristic, complemented
23#33816C211yesmaximal, characteristic, complemented
24#33813C211yesmaximal, characteristic, complemented
25#33750C211yesmaximal, characteristic, complemented
26#33744C211yesmaximal, characteristic, complemented
27#33744C211yesmaximal, characteristic, complemented
28#33743C211yesmaximal, characteristic, complemented
29#33739C211yesmaximal, characteristic, complemented
30#33737C211yesmaximal, characteristic, complemented
31#33476C211yesmaximal, characteristic, complemented
32#3557—21no—
33#3554—21no—
34#3396C2211yescharacteristic
35#3396C2211yescharacteristic
36#3396C2211yescharacteristic
37#3396C2211yescharacteristic
38#3396C2211yescharacteristic
39#3393C2211yescharacteristic
40#3393C2211yescharacteristic
41#3391C2211yescharacteristic
42#3383C2211yescharacteristic
43#3383C2211yescharacteristic
44#3383C2211yescharacteristic
45#3380C2211yescharacteristic
46#3380C2211yescharacteristic
47#3380C2211yescharacteristic
48#3380C2211yescharacteristic
49Q8×D8C2211yescharacteristic
50#3376—21no—
51#3376—21no—
52#3373—21no—
53#3371—21no—
54#3371—21no—
55#3370—21no—
56#3370—21no—
57#3368—21no—
58#3263—21no—
59#3260—21no—
60#3257—21no—
61#3257—21no—
62#3256—21no—
63#3251—21no—
64#3177C2211yescharacteristic
65#3176C2211yescharacteristic
66#3176C2211yescharacteristic
67#3176C2211yescharacteristic
68#3175C2211yescharacteristic
69#3175C2211yescharacteristic
70#3175C2211yescharacteristic
71#3175C2211yescharacteristic
72#3169C2211yescharacteristic
73#3168C2211yescharacteristic
74#3168C2211yescharacteristic
75#3168C2211yescharacteristic
76#2960C2211yescharacteristic
77#2255C2211yescharacteristic
78#2255C2211yescharacteristic
79#2255C2211yescharacteristic
80#2253C2211yescharacteristic
81#2253C2211yescharacteristic
82#2252C2211yescharacteristic
83#2250C2211yescharacteristic
84#2250C2211yescharacteristic
85#2250C2211yescharacteristic
86#2249C2211yescharacteristic
87#2249C2211yescharacteristic
88#2248C2211yescharacteristic
89#2245C2211yescharacteristic
90#2244C2211yescharacteristic
91#2244C2211yescharacteristic
92#2243C2211yescharacteristic
93#2243C2211yescharacteristic
94#2243C2211yescharacteristic
95#2242C2211yescharacteristic
96#2242C2211yescharacteristic
97#2242C2211yescharacteristic
98#2242C2211yescharacteristic
99#2240C2211yescharacteristic
100#2240C2211yescharacteristic
101#2229C2211yescharacteristic
102#2229C2211yescharacteristic
103#2229C2211yescharacteristic
104#2229C2211yescharacteristic
105#2228C2211yescharacteristic
106#2228C2211yescharacteristic
107#2228C2211yescharacteristic
108#2228C2211yescharacteristic
109#2228C2211yescharacteristic
110#2228C2211yescharacteristic
111#2228C2211yescharacteristic
112#2228C2211yescharacteristic
113#2228C2211yescharacteristic
114#2228C2211yescharacteristic
115#2227C2211yescharacteristic
116#2227C2211yescharacteristic
117#2226C2211yescharacteristic
118#2226C2211yescharacteristic
119#2226C2211yescharacteristic
120#2226C2211yescharacteristic
121#2225C2211yescharacteristic
122#2225C2211yescharacteristic
123#2225C2211yescharacteristic
124#2224C2211yescharacteristic
125#2220C2211yescharacteristic
126#2220C2211yescharacteristic
127#2220C2211yescharacteristic
128#2220C2211yescharacteristic
129#2219C2211yescharacteristic
130#2218C2211yescharacteristic
131#2218C2211yescharacteristic
132#2218C2211yescharacteristic
133#2217C2211yescharacteristic
134#2217C2211yescharacteristic
135#2217C2211yescharacteristic
136#2217C2211yescharacteristic
137#2216C2211yescharacteristic
138#2215C2211yescharacteristic
139#2215C2211yescharacteristic
140#2215C2211yescharacteristic
141#2211C2211yescharacteristic
142#2211C2211yescharacteristic
143#2211C2211yescharacteristic
144#2211C2211yescharacteristic
145#2211C2211yescharacteristic
146#2211C2211yescharacteristic
147#2210C2211yescharacteristic
148#2210C2211yescharacteristic
149#2210C2211yescharacteristic
150#2210C2211yescharacteristic
151#2210C2211yescharacteristic
152#2210C2211yescharacteristic
153#2210C2211yescharacteristic
154#2210C2211yescharacteristic
155#2209C2211yescharacteristic
156#2208C2211yescharacteristic
157#2207C2211yescharacteristic
158#2207C2211yescharacteristic
159#2206C2211yescharacteristic
160#2206C2211yescharacteristic
161#2206C2211yescharacteristic
162#2206C2211yescharacteristic
163#2206C2211yescharacteristic
164#2206C2211yescharacteristic
165#2183C2211yescharacteristic
166#2183C2211yescharacteristic
167#2183C2211yescharacteristic
168#2183C2211yescharacteristic
169#2183C2211yescharacteristic
170#2183C2211yescharacteristic
171Q8×C16C2211yescharacteristic
172Q8×C16C2211yescharacteristic
173#2177C2211yescharacteristic
174#2177C2211yescharacteristic
175#2177C2211yescharacteristic
176#2176C2211yescharacteristic
177#2175C2211yescharacteristic
178#2175C2211yescharacteristic
179#2175C2211yescharacteristic
180#2175C2211yescharacteristic
181#2175C2211yescharacteristic
182#2175C2211yescharacteristic
183#2175C2211yescharacteristic
184#2175C2211yescharacteristic
185C4×Q32C2211yescharacteristic
186C4×SD32C2211yescharacteristic
187C4×SD32C2211yescharacteristic
188C4×SD32C2211yescharacteristic
189C4×SD32C2211yescharacteristic
190C4×SD32C2211yescharacteristic
191C4×SD32C2211yescharacteristic
192C4×D16C2211yescharacteristic
193C4×D16C2211yescharacteristic
194C4×D16C2211yescharacteristic
195C4×D16C2211yescharacteristic
196C4×D16C2211yescharacteristic
197#2151C2211yescharacteristic
198#2151C2211yescharacteristic
199C2×C4⋊C16C2211yescharacteristic
200#2108C2211yescharacteristic
201#2108C2211yescharacteristic
202C4×M32C2211yescharacteristic
203#563—41no—
204#563—41no—
205#562—41no—
206#562—41no—
207#559—21no—
208#559—21no—
209#559—21no—
210#559—21no—
211#559—21no—
212#557—21no—
213#557—21no—
214#557—21no—
215#556—21no—
216#556—21no—
217#554—21no—
218#554—21no—
219#554—21no—
220#554—21no—
221#552—41no—
222#552—41no—
223#550—21no—
224D4×Q8—21no—
225#548—41no—
226#547—41no—
227#542—21no—
228#542—21no—
229#542—21no—
230#542—21no—
231#542—41no—
232#542—41no—
233#542—41no—
234#541—21no—
235#540—21no—
236#540—21no—
237#540—21no—
238#539—41no—
239#539—41no—
240#539—41no—
241#539—41no—
242#536—41no—
243#533D411yescharacteristic
244#532—21no—
245#529—21no—
246#529—21no—
247#529—21no—
248C2×Q32C2311yescharacteristic
249C2×Q32C2311yescharacteristic
250C2×SD32C2311yescharacteristic
251C2×SD32C2311yescharacteristic
252C2×SD32C2311yescharacteristic
253C2×SD32C2311yescharacteristic
254C2×SD32C2311yescharacteristic
255C2×SD32C2311yescharacteristic
256C2×SD32C2311yescharacteristic
257C2×SD32C2311yescharacteristic
258C2×D16C2311yescharacteristic
259C2×D16C2311yescharacteristic
260C2×D16C2311yescharacteristic
261C2×D16C2311yescharacteristic
262C2×D16C2311yescharacteristic
263C2×D16C2311yescharacteristic
264C2×M32C2311yescharacteristic
265C2×M32C2311yescharacteristic
266C22×C16C2311yescharacteristic
267C22×C16C2311yescharacteristic
268#500C2311yescharacteristic
269#500C2311yescharacteristic
270#500C2311yescharacteristic
271#500C2311yescharacteristic
272#500C2311yescharacteristic
273#499C2311yescharacteristic
274#499C2311yescharacteristic
275#499C2311yescharacteristic
276#499C2311yescharacteristic
277#499C2311yescharacteristic
278#499C2311yescharacteristic
279#499C2311yescharacteristic
280#495C2311yescharacteristic
281#495C2311yescharacteristic
282#495C2311yescharacteristic
283#495C2311yescharacteristic
284#495C2311yescharacteristic
285#495C2311yescharacteristic
286#495C2311yescharacteristic
287#494C2311yescharacteristic
288#493C2311yescharacteristic
289#493C2311yescharacteristic
290#493C2311yescharacteristic
291#493C2311yescharacteristic
292#491—21no—
293#490—21no—
294#490—21no—
295#490—21no—
296#489—21no—
297#489—21no—
298#489—21no—
299#489—21no—
300#488—21no—
301#488—21no—
302#488—21no—
303#486—21no—
304#479—21no—
305#479—21no—
306#479—21no—
307#479—21no—
308#479—21no—
309#479—21no—
310#478—21no—
311#478—21no—
312#478—21no—
313#478—21no—
314#478—21no—
315#478—21no—
316#478—21no—
317#478—21no—
318#476—21no—
319#476—21no—
320#476—21no—
321#476—21no—
322#475—21no—
323#475—21no—
324#475—21no—
325#474—21no—
326#474—21no—
327#474—21no—
328#470—21no—
329#469—21no—
330#469—21no—
331#469—21no—
332#468—21no—
333#468—21no—
334#468—21no—
335#468—21no—
336#467C2311yescharacteristic
337#467C2311yescharacteristic
338#467C2311yescharacteristic
339#466—21no—
340#466C2311yescharacteristic
341#466C2311yescharacteristic
342#466C2311yescharacteristic
343#466C2311yescharacteristic
344#466C2311yescharacteristic
345#465—21no—
346#465—21no—
347#465—21no—
348#464—21no—
349#464—21no—
350#464—21no—
351#464—21no—
352#463—21no—
353#463—21no—
354#463—21no—
355#463—21no—
356#463—21no—
357#463—21no—
358#463—21no—
359#463—21no—
360#463—21no—
361#463—21no—
362#461—21no—
363#461—21no—
364#460—21no—
365#460—21no—
366#460—21no—
367#460—21no—
368#460—21no—
369#459—21no—
370#459—21no—
371#459—21no—
372#446D411yescharacteristic
373#446D411yescharacteristic
374#446D411yescharacteristic
375#446D411yescharacteristic
376C8×Q8C2311yescharacteristic
377C8×Q8C2311yescharacteristic
378C8×Q8C2311yescharacteristic
379C8×Q8C2311yescharacteristic
380#442—21no—
381#442—21no—
382#442—21no—
383#441—21no—
384#440—21no—
385#440—21no—
386#440—21no—
387#440—21no—
388C4×Q16C2311yescharacteristic
389C4×Q16C2311yescharacteristic
390C4×Q16C2311yescharacteristic
391C4×Q16C2311yescharacteristic
392C4×Q16C2311yescharacteristic
393C4×Q16C2311yescharacteristic
394C4×Q16C2311yescharacteristic
395C4×Q16C2311yescharacteristic
396C4×Q16C2311yescharacteristic
397C4×SD16—21no—
398C4×SD16—21no—
399C4×SD16—21no—
400C4×D8—21no—
401C4×D8C2311yescharacteristic
402C4×D8C2311yescharacteristic
403C4×D8C2311yescharacteristic
404C4×D8C2311yescharacteristic
405C4×D8C2311yescharacteristic
406C4×D8C2311yescharacteristic
407C4×D8C2311yescharacteristic
408C4×D8C2311yescharacteristic
409C4×D8C2311yescharacteristic
410C4×D8C2311yescharacteristic
411C4×D8C2311yescharacteristic
412C4×D8C2311yescharacteristic
413C4×D8C2311yescharacteristic
414C4×D8C2311yescharacteristic
415C4×D8C2311yescharacteristic
416#424D411yescharacteristic
417#424D411yescharacteristic
418#423D411yescharacteristic
419#405C2311yescharacteristic
420#405C2311yescharacteristic
421C2×C4×C8C2311yescharacteristic
422#367C2311yescharacteristic
423#367C2311yescharacteristic
424#367C2311yescharacteristic
425#367C2311yescharacteristic
426#367C2311yescharacteristic
427#367C2311yescharacteristic
428#367C2311yescharacteristic
429#367C2311yescharacteristic
430#366C2311yescharacteristic
431#366C2311yescharacteristic
432#366C2311yescharacteristic
433#366C2311yescharacteristic
434#366C2311yescharacteristic
435#366C2311yescharacteristic
436#366C2311yescharacteristic
437#366C2311yescharacteristic
438C4⋊C16C2311yescharacteristic
439C4⋊C16C2311yescharacteristic
440C4⋊C16C2311yescharacteristic
441C4⋊C16C2311yescharacteristic
442C4⋊C16C2311yescharacteristic
443C4⋊C16C2311yescharacteristic
444C4⋊C16C2311yescharacteristic
445C4⋊C16C2311yescharacteristic
446C4⋊C16C2311yescharacteristic
447C4⋊C16C2311yescharacteristic
448C4⋊C16C2311yescharacteristic
449C4⋊C16C2311yescharacteristic
450#358C2311yescharacteristic
451#358C2311yescharacteristic
452#358C2311yescharacteristic
453#358C2311yescharacteristic
454#358C2311yescharacteristic
455#358C2311yescharacteristic
456#358C2311yescharacteristic
457#358C2311yescharacteristic
458#358C2311yescharacteristic
459#358C2311yescharacteristic
460#358C2311yescharacteristic
461#358C2311yescharacteristic
462#357C2311yescharacteristic
463#357C2311yescharacteristic
464#357C2311yescharacteristic
465#357C2311yescharacteristic
466#357C2311yescharacteristic
467#357C2311yescharacteristic
468#357C2311yescharacteristic
469#357C2311yescharacteristic
470#357C2311yescharacteristic
471#357C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478#357C2311yescharacteristic
479#357C2311yescharacteristic
480#357C2311yescharacteristic
481#357C2311yescharacteristic
482#346C2311yescharacteristic
483#346C2311yescharacteristic
484#346C2311yescharacteristic
485#346C2311yescharacteristic
486#346C2311yescharacteristic
487#346C2311yescharacteristic
488C4×C16C2311yescharacteristic
489C4×C16C2311yescharacteristic
490C4×C16C2311yescharacteristic
491C4×C16C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—41no—
497C2×Q16—21no—
498C2×Q16C2411yescharacteristic
499C2×Q16C2411yescharacteristic
500C2×Q16C2411yescharacteristic
501C2×SD16—21no—
502C2×SD16—21no—
503C2×SD16—21no—
504C2×SD16—21no—
505C2×SD16—21no—
506C2×SD16—21no—
507C2×SD16—21no—
508C2×D8—21no—
509C2×D8—21no—
510C2×D8—21no—
511C2×D8—21no—
512C2×D8C2411yescharacteristic
513C2×D8C2411yescharacteristic
514C2×D8C2411yescharacteristic
515C2×D8C2411yescharacteristic
516C2×D8C2411yescharacteristic
517C2×M16C2×D411yescharacteristic
518C2×M16C2×D411yescharacteristic
519C22×C8C2×D411yescharacteristic
520C22×C8C2411yescharacteristic
521C4⋊Q8—21no—
522C4⋊Q8—21no—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8D811yescharacteristic
531C4⋊Q8D811yescharacteristic
532#127—21no—
533#127—21no—
534#127—21no—
535#127—21no—
536#126—41no—
537#126—41no—
538#126—41no—
539#126—41no—
540#126—41no—
541#126—41no—
542#126—41no—
543#126—41no—
544#126—41no—
545#126—41no—
546#126—41no—
547#126—41no—
548#126—41no—
549#125—21no—
550#125—21no—
551#125—21no—
552#125—21no—
553#125—21no—
554#125—21no—
555#125—21no—
556#125—41no—
557#125—41no—
558#125—41no—
559#125—41no—
560#125—41no—
561#125—41no—
562#125—41no—
563#125—41no—
564#125D811yescharacteristic
565#125D811yescharacteristic
566#124—21no—
567#124—21no—
568#124—21no—
569#124—21no—
570#124—21no—
571#124—21no—
572#124—21no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#123—41no—
584#123—41no—
585#123—41no—
586#123—41no—
587#123—41no—
588#123—41no—
589#123—41no—
590#123—41no—
591#123—41no—
592#123—41no—
593#123—41no—
594#123—41no—
595#123—41no—
596#123—41no—
597#123—41no—
598#123—41no—
599#123—41no—
600#123—41no—
601#123—41no—
602#123—41no—
603#123—41no—
604#123—41no—
605#123—41no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622C22⋊Q8—41no—
623C22⋊Q8—41no—
624C22⋊Q8—41no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8D811yescharacteristic
631C22⋊Q8D811yescharacteristic
632C22⋊Q8D811yescharacteristic
633C22⋊Q8D811yescharacteristic
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—41no—
640#121—41no—
641#121—41no—
642#121—41no—
643#121—41no—
644#121—41no—
645#121—41no—
646#121—41no—
647#121—41no—
648#121—41no—
649C4×Q8—21no—
650C4×Q8—21no—
651C4×Q8—21no—
652C4×Q8—21no—
653C4×Q8—21no—
654C4×Q8—21no—
655C4×Q8—21no—
656C4×Q8—21no—
657C4×Q8—21no—
658C4×Q8—41no—
659C4×Q8—41no—
660C4×Q8—41no—
661C4×Q8C2×D411yescharacteristic
662C4×Q8C2×D411yescharacteristic
663C4×Q8C2×D411yescharacteristic
664C4×Q8C2×D411yescharacteristic
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4—21no—
674C4×D4—21no—
675C4×D4—21no—
676C4×D4—21no—
677C4×D4—21no—
678C4×D4—21no—
679C4×D4—21no—
680C4×D4—41no—
681C4×D4—41no—
682C4×D4—41no—
683C4×D4—41no—
684C4×D4—41no—
685C4×D4—41no—
686C4×D4—41no—
687C4×D4—41no—
688C4×D4—41no—
689#117—41no—
690#117—41no—
691#117—41no—
692#117—41no—
693#117—41no—
694#117C2×D411yescharacteristic
695#117C2×D411yescharacteristic
696C2×C4⋊C4—41no—
697C2×C4⋊C4—41no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4—41no—
700C2×C42C2×D411yescharacteristic
701Q32—41no—
702Q32—41no—
703SD32—22no—
704SD32—22no—
705SD32—22no—
706SD32—41no—
707SD32—41no—
708SD32—41no—
709SD32—41no—
710SD32—41no—
711D16—22no—
712D16—41no—
713D16—41no—
714D16—41no—
715D16—41no—
716D16—41no—
717M32—22no—
718M32—41no—
719C2×C16—41no—
720C2×C16—41no—
721C2×C16C2411yescharacteristic
722C2×C16C2411yescharacteristic
723C2×C16C2411yescharacteristic
724C2×C16C2411yescharacteristic
725C2×C16C2411yescharacteristic
726C2×C16C2411yescharacteristic
727C2×C16C2411yescharacteristic
728C2×C16C2411yescharacteristic
729#107—21no—
730#107—21no—
731#107—21no—
732#107—21no—
733#107—21no—
734#107C2411yescharacteristic
735#107C2411yescharacteristic
736#107C2411yescharacteristic
737#107C2411yescharacteristic
738#107C2411yescharacteristic
739#107C2411yescharacteristic
740#107C2411yescharacteristic
741#107C2411yescharacteristic
742#106—21no—
743#106—21no—
744#106—21no—
745#106—21no—
746#106—21no—
747#106—21no—
748#106—21no—
749C4⋊C8C2×D411yescharacteristic
750C4⋊C8C2×D411yescharacteristic
751C4⋊C8C2×D411yescharacteristic
752C4⋊C8C2×D411yescharacteristic
753C4⋊C8C2×D411yescharacteristic
754C4⋊C8C2×D411yescharacteristic
755C4⋊C8C2×D411yescharacteristic
756C4⋊C8C2×D411yescharacteristic
757C4⋊C8C2×D411yescharacteristic
758C4⋊C8C2×D411yescharacteristic
759C4⋊C8C2×D411yescharacteristic
760C4⋊C8C2×D411yescharacteristic
761#103—21no—
762#103—21no—
763#103—21no—
764#103—21no—
765#103—21no—
766#103—21no—
767#103—21no—
768#103—21no—
769#103—21no—
770#103—21no—
771#103—21no—
772#103—21no—
773#102—21no—
774#102—21no—
775#102—21no—
776#102—21no—
777#102—21no—
778#102—21no—
779#102—21no—
780#102—21no—
781#102—21no—
782#102—21no—
783#102—21no—
784#102—21no—
785#102—21no—
786#102—21no—
787#102—21no—
788#102—21no—
789#102—21no—
790#102—21no—
791#102—21no—
792#102—21no—
793#97C2×D411yescharacteristic
794#97C2×D411yescharacteristic
795#97C2×D411yescharacteristic
796#97C2×D411yescharacteristic
797C4×C8C2×D411yescharacteristic
798C4×C8C2×D411yescharacteristic
799C4×C8C2411yescharacteristic
800C4×C8C2411yescharacteristic
801C4×C8C2411yescharacteristic
802C4×C8C2411yescharacteristic
803C4×C8C2411yescharacteristic
804C4×C8C2411yescharacteristic
805#41—162no—
806#41—162no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—41no—
811C2×Q8—41no—
812C2×Q8—41no—
813C2×Q8—41no—
814C2×Q8—41no—
815C2×Q8—162no—
816C2×Q8C2×D811yescharacteristic
817C2×Q8C2×D811yescharacteristic
818C2×Q8C2×D811yescharacteristic
819C2×Q8C2×D811yescharacteristic
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—41no—
826C2×D4—41no—
827C2×D4—41no—
828C2×D4—41no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—41no—
837C2×D4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—41no—
853C22×C4C2×D811yescharacteristic
854C22×C4C2×D811yescharacteristic
855C22×C4C22×D411yescharacteristic
856Q16—21no—
857Q16—21no—
858Q16—21no—
859Q16—21no—
860Q16—21no—
861Q16—21no—
862Q16—81no—
863SD16—81no—
864SD16—81no—
865SD16—81no—
866SD16—81no—
867SD16—81no—
868SD16—81no—
869SD16—81no—
870D8—21no—
871D8—21no—
872D8—21no—
873D8—21no—
874D8—21no—
875D8—21no—
876D8—21no—
877D8—21no—
878D8—21no—
879D8—21no—
880D8—81no—
881D8—81no—
882D8—81no—
883D8—81no—
884M16—41no—
885M16—41no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—41no—
889C2×C8C22×D411yescharacteristic
890C2×C8C22×D411yescharacteristic
891C2×C8C22×D411yescharacteristic
892C2×C8C22×D411yescharacteristic
893C2×C8C22×D411yescharacteristic
894C2×C8C22×D411yescharacteristic
895C2×C8C22×D411yescharacteristic
896C2×C8C2511yescharacteristic
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4C2×D811yescharacteristic
939C4⋊C4C2×D811yescharacteristic
940C4⋊C4C2×D811yescharacteristic
941C4⋊C4C2×D811yescharacteristic
942C4⋊C4C2×D811yescharacteristic
943C4⋊C4C2×D811yescharacteristic
944C4⋊C4C2×D811yescharacteristic
945C4⋊C4C2×D811yescharacteristic
946C4⋊C4C2×D811yescharacteristic
947C4⋊C4C2×D811yescharacteristic
948C4⋊C4C2×D811yescharacteristic
949C4⋊C4C2×D811yescharacteristic
950C4⋊C4C2×D811yescharacteristic
951C4⋊C4C2×D811yescharacteristic
952C4⋊C4C2×D811yescharacteristic
953C4⋊C4C2×D811yescharacteristic
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—41no—
964C22⋊C4—41no—
965C22⋊C4—41no—
966C22⋊C4—41no—
967C22⋊C4—41no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4C2×D811yescharacteristic
992C22⋊C4C2×D811yescharacteristic
993C22⋊C4C2×D811yescharacteristic
994C22⋊C4C2×D811yescharacteristic
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42C2×D811yescharacteristic
1005C42C2×D811yescharacteristic
1006C42C22×D411yescharacteristic
1007C42C22×D411yescharacteristic
1008C42C22×D411yescharacteristic
1009C42C22×D411yescharacteristic
1010C42C22×D411yescharacteristic
1011C42C22×D411yescharacteristic
1012C16—21no—
1013C16—21no—
1014C16—21no—
1015C16—21no—
1016C16—21no—
1017C16—21no—
1018C16—21no—
1019C162−1+412yes—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23C22×D811yescharacteristic
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—82no—
1037Q8—161no—
1038Q8—161no—
1039Q8—161no—
1040Q8—161no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—82no—
1052D4—161no—
1053D4—161no—
1054D4—161no—
1055D4—161no—
1056D4—161no—
1057D4—161no—
1058D4—161no—
1059D4—161no—
1060D4—161no—
1061D4—161no—
1062D4—161no—
1063D4—161no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—82no—
1080C2×C4—161no—
1081C2×C4—161no—
1082C2×C4—161no—
1083C2×C4—161no—
1084C2×C4—161no—
1085C2×C4—161no—
1086C2×C4—161no—
1087C2×C4—161no—
1088C2×C4—161no—
1089C2×C4—161no—
1090C2×C4—161no—
1091C2×C4—161no—
1092C2×C4—161no—
1093C2×C4—161no—
1094C2×C4C22×D811yescharacteristic
1095C2×C4C22×D811yescharacteristic
1096C2×C4C22×D811yescharacteristic
1097C2×C4C22×D811yescharacteristic
1098C2×C4C22×D811yescharacteristic
1099C2×C4C22×D811yescharacteristic
1100C2×C4C22×D811yescharacteristic
1101C2×C4C22×D811yescharacteristic
1102C2×C4C22×D811yescharacteristic
1103C2×C4C22×D811yescharacteristic
1104C2×C4C22×D811yescharacteristic
1105C2×C4C22×D811yescharacteristic
1106C2×C4C22×D811yescharacteristic
1107C2×C4C23×D411yescharacteristic
1108C8—21no—
1109C8—21no—
1110C8—21no—
1111C8—21no—
1112C8—21no—
1113C8—21no—
1114C8—21no—
1115C8C2×2−1+411yescharacteristic
1116C8#58511yescharacteristic
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22C23×D811yescharacteristic
1136C4—21no—
1137C4—21no—
1138C4—21no—
1139C4—21no—
1140C4—21no—
1141C4—21no—
1142C4—21no—
1143C4—21no—
1144C4—21no—
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4#349711yescharacteristic
1161C4#358411yescharacteristic
1162C2—41no—
1163C2—161no—
1164C2—161no—
1165C2—161no—
1166C2—161no—
1167C2—161no—
1168C2#6235911yescharacteristic
1169C2#6263511yescharacteristic
1170C2#6263611yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #533 ◁ #2960 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62379C2semidirect
2. #62377C2semidirect
3. #33970C2semidirect
4. #33970C2semidirect
5. #33964C2semidirect
6. #33961C2semidirect
7. #33955C2semidirect
8. #33955C2semidirect
9. #33953C2semidirect
10. #33947C2semidirect
11. #33944C2semidirect
12. #33943C2semidirect
13. #33940C2semidirect
14. #33938C2semidirect
15. #33937C2semidirect
16. #33933C2semidirect
17. #33932C2semidirect
18. #33928C2semidirect
19. #33829C2semidirect
20. #33825C2semidirect
21. #33824C2semidirect
22. #33823C2semidirect
23. #33816C2semidirect
24. #33813C2semidirect
25. #33750C2semidirect
26. #33744C2semidirect
27. #33744C2semidirect
28. #33743C2semidirect
29. #33739C2semidirect
30. #33737C2semidirect
31. #33476C2semidirect

Maximal subgroups

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

subgroupindex
#623792
#623772
#339702
#339642
#339612
#339552
#339532
#339472
#339442
#339432
#339402
#339382
#339372
#339332
#339322
#339282
#338292
#338252
#338242
#338232
#338162
#338132
#337502
#337442
#337432
#337392
#337372
#334762