Finite Group Databasebeta

← #7625124

Subgroups — #7625124

Order 512.

1209 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62490C211yesmaximal, characteristic, complemented
2#62432C211yesmaximal, characteristic, complemented
3#33944C211yesmaximal, characteristic, complemented
4#33943C211yesmaximal, characteristic, complemented
5#33941C211yesmaximal, characteristic, complemented
6#33939C211yesmaximal, characteristic, complemented
7#33896C211yesmaximal, characteristic, complemented
8#33895C211yesmaximal, characteristic, complemented
9#33894C211yesmaximal, characteristic, complemented
10#33893C211yesmaximal, characteristic, complemented
11#33888C211yesmaximal, characteristic, complemented
12#33887C211yesmaximal, characteristic, complemented
13#33887C211yesmaximal, characteristic, complemented
14#33882C211yesmaximal, characteristic, complemented
15#33880C211yesmaximal, characteristic, complemented
16#33879C211yesmaximal, characteristic, complemented
17#33879C211yesmaximal, characteristic, complemented
18#33874C211yesmaximal, characteristic, complemented
19#33808C211yesmaximal, characteristic, complemented
20#33808C211yesmaximal, characteristic, complemented
21#33806C211yesmaximal, characteristic, complemented
22#33791C211yesmaximal, characteristic, complemented
23#33791C211yesmaximal, characteristic, complemented
24#33784C211yesmaximal, characteristic, complemented
25#33750C211yesmaximal, characteristic, complemented
26#33745C211yesmaximal, characteristic, complemented
27#33745C211yesmaximal, characteristic, complemented
28#33705C211yesmaximal, characteristic, complemented
29#33703C211yesmaximal, characteristic, complemented
30#33703C211yesmaximal, characteristic, complemented
31#33481C211yesmaximal, characteristic, complemented
32#3565—21no—
33#3552—21no—
34#3398—21no—
35#3395C2211yescharacteristic
36#3393C2211yescharacteristic
37#3388—21no—
38#3383C2211yescharacteristic
39#3380C2211yescharacteristic
40#3351—21no—
41#3350—21no—
42#3348—21no—
43#3342C2211yescharacteristic
44#3341C2211yescharacteristic
45#3339C2211yescharacteristic
46#3339C2211yescharacteristic
47#3336C2211yescharacteristic
48#3336C2211yescharacteristic
49D4×Q16C2211yescharacteristic
50D4×Q16C2211yescharacteristic
51D4×Q16C2211yescharacteristic
52#3285C2211yescharacteristic
53#3285C2211yescharacteristic
54#3283C2211yescharacteristic
55#3276—21no—
56#3270—21no—
57#3270—21no—
58#3244—21no—
59#3244—21no—
60#3240—21no—
61#3223—21no—
62#3223—21no—
63#3218—21no—
64#3177C2211yescharacteristic
65#3177C2211yescharacteristic
66#3175C2211yescharacteristic
67#3175C2211yescharacteristic
68#3168C2211yescharacteristic
69#3168C2211yescharacteristic
70#3164C2211yescharacteristic
71#3164C2211yescharacteristic
72#3160C2211yescharacteristic
73#3156C2211yescharacteristic
74#3156C2211yescharacteristic
75C2×#494C2211yescharacteristic
76#2966C2211yescharacteristic
77#2255C2211yescharacteristic
78#2255C2211yescharacteristic
79#2253C2211yescharacteristic
80#2251C2211yescharacteristic
81#2251C2211yescharacteristic
82#2249C2211yescharacteristic
83#2245C2211yescharacteristic
84#2245C2211yescharacteristic
85#2245C2211yescharacteristic
86#2245C2211yescharacteristic
87#2245C2211yescharacteristic
88#2245C2211yescharacteristic
89#2245C2211yescharacteristic
90#2245C2211yescharacteristic
91#2243C2211yescharacteristic
92#2243C2211yescharacteristic
93#2243C2211yescharacteristic
94#2243C2211yescharacteristic
95#2242C2211yescharacteristic
96#2242C2211yescharacteristic
97#2242C2211yescharacteristic
98#2242C2211yescharacteristic
99#2241C2211yescharacteristic
100#2241C2211yescharacteristic
101#2241C2211yescharacteristic
102#2241C2211yescharacteristic
103#2241C2211yescharacteristic
104#2241C2211yescharacteristic
105#2237C2211yescharacteristic
106#2237C2211yescharacteristic
107#2237C2211yescharacteristic
108#2237C2211yescharacteristic
109#2237C2211yescharacteristic
110#2237C2211yescharacteristic
111#2236C2211yescharacteristic
112#2236C2211yescharacteristic
113#2235C2211yescharacteristic
114#2235C2211yescharacteristic
115#2234C2211yescharacteristic
116#2234C2211yescharacteristic
117#2229C2211yescharacteristic
118#2229C2211yescharacteristic
119#2229C2211yescharacteristic
120#2229C2211yescharacteristic
121#2229C2211yescharacteristic
122#2229C2211yescharacteristic
123#2228C2211yescharacteristic
124#2228C2211yescharacteristic
125#2227C2211yescharacteristic
126#2227C2211yescharacteristic
127#2225C2211yescharacteristic
128#2225C2211yescharacteristic
129#2220C2211yescharacteristic
130#2220C2211yescharacteristic
131#2220C2211yescharacteristic
132#2220C2211yescharacteristic
133#2219C2211yescharacteristic
134#2219C2211yescharacteristic
135#2219C2211yescharacteristic
136#2218C2211yescharacteristic
137#2217C2211yescharacteristic
138#2217C2211yescharacteristic
139#2216C2211yescharacteristic
140#2216C2211yescharacteristic
141#2211C2211yescharacteristic
142#2211C2211yescharacteristic
143#2210C2211yescharacteristic
144#2210C2211yescharacteristic
145#2209C2211yescharacteristic
146#2209C2211yescharacteristic
147#2209C2211yescharacteristic
148#2209C2211yescharacteristic
149#2208C2211yescharacteristic
150#2208C2211yescharacteristic
151#2208C2211yescharacteristic
152#2208C2211yescharacteristic
153#2189C2211yescharacteristic
154#2189C2211yescharacteristic
155#2188C2211yescharacteristic
156#2188C2211yescharacteristic
157#2188C2211yescharacteristic
158#2188C2211yescharacteristic
159#2186C2211yescharacteristic
160#2186C2211yescharacteristic
161#2185C2211yescharacteristic
162#2185C2211yescharacteristic
163#2185C2211yescharacteristic
164#2185C2211yescharacteristic
165#2183C2211yescharacteristic
166#2183C2211yescharacteristic
167#2177C2211yescharacteristic
168#2176C2211yescharacteristic
169#2176C2211yescharacteristic
170#2176C2211yescharacteristic
171#2175C2211yescharacteristic
172#2175C2211yescharacteristic
173#2175C2211yescharacteristic
174#2175C2211yescharacteristic
175C4×Q32C2211yescharacteristic
176C4×Q32C2211yescharacteristic
177C4×SD32C2211yescharacteristic
178C4×SD32C2211yescharacteristic
179#2169C2211yescharacteristic
180#2169C2211yescharacteristic
181#2168C2211yescharacteristic
182#2168C2211yescharacteristic
183#2168C2211yescharacteristic
184#2168C2211yescharacteristic
185#2164C2211yescharacteristic
186#2164C2211yescharacteristic
187#2163C2211yescharacteristic
188#2141C2211yescharacteristic
189#2141C2211yescharacteristic
190#2141C2211yescharacteristic
191#2141C2211yescharacteristic
192#2141C2211yescharacteristic
193#2141C2211yescharacteristic
194#2139C2211yescharacteristic
195#2139C2211yescharacteristic
196#2138C2211yescharacteristic
197#2138C2211yescharacteristic
198C2×#358C2211yescharacteristic
199C2×#358C2211yescharacteristic
200#2108C2211yescharacteristic
201#2108C2211yescharacteristic
202C4×M32C2211yescharacteristic
203C2×#137—21no—
204C2×#137—21no—
205C2×#135C2311yescharacteristic
206C2×#135C2311yescharacteristic
207C22×Q16—21no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212#563—41no—
213#563—41no—
214#563—41no—
215#562—41no—
216#557—21no—
217#557—21no—
218#556—21no—
219#556—21no—
220#556—41no—
221#555—21no—
222#554—21no—
223#554—41no—
224#553—21no—
225#553—21no—
226#553—41no—
227#552—21no—
228#552—21no—
229#552—41no—
230D4×Q8—21no—
231D4×Q8—21no—
232D4×Q8—21no—
233#548—21no—
234#548—21no—
235#547—21no—
236#544—21no—
237#544—21no—
238#544—41no—
239#542—21no—
240#542—21no—
241#542—41no—
242#542—41no—
243#542—41no—
244#541—21no—
245#541—21no—
246#541—41no—
247#539—41no—
248#539—41no—
249#539—41no—
250#536—21no—
251#536—21no—
252#533—21no—
253C2×C4⋊Q8—21no—
254#529—21no—
255#529—21no—
256#529D411yescharacteristic
257C2×Q32C2311yescharacteristic
258C2×Q32C2311yescharacteristic
259C2×Q32C2311yescharacteristic
260C2×Q32C2311yescharacteristic
261C2×Q32C2311yescharacteristic
262C2×SD32C2311yescharacteristic
263C2×SD32C2311yescharacteristic
264C2×SD32C2311yescharacteristic
265C2×SD32C2311yescharacteristic
266C2×SD32C2311yescharacteristic
267C2×SD32C2311yescharacteristic
268C2×D16C2311yescharacteristic
269C2×M32C2311yescharacteristic
270C2×M32C2311yescharacteristic
271C2×M32C2311yescharacteristic
272C2×M32C2311yescharacteristic
273C22×C16C2311yescharacteristic
274C22×C16C2311yescharacteristic
275#501—21no—
276#501—21no—
277#501—21no—
278#501—21no—
279#500C2311yescharacteristic
280#500C2311yescharacteristic
281#500C2311yescharacteristic
282#500C2311yescharacteristic
283#499—21no—
284#499C2311yescharacteristic
285#499C2311yescharacteristic
286#499C2311yescharacteristic
287#499C2311yescharacteristic
288#499C2311yescharacteristic
289#499C2311yescharacteristic
290#498—21no—
291#497—21no—
292#497—21no—
293#497—21no—
294#497—21no—
295#495C2311yescharacteristic
296#495C2311yescharacteristic
297#495C2311yescharacteristic
298#495C2311yescharacteristic
299#494—21no—
300#494—21no—
301#494C2311yescharacteristic
302#494C2311yescharacteristic
303#494C2311yescharacteristic
304#494C2311yescharacteristic
305#494C2311yescharacteristic
306#494C2311yescharacteristic
307#491—21no—
308#491—21no—
309#489—21no—
310#489—21no—
311#488—21no—
312#488—21no—
313#485—21no—
314#485—21no—
315#485—21no—
316#485—21no—
317#483—21no—
318#483—21no—
319#482—21no—
320#482—21no—
321#482—21no—
322#482—21no—
323#481—21no—
324#481—21no—
325#479—21no—
326#479—21no—
327#479—21no—
328#479—21no—
329#478—21no—
330#478—21no—
331#478—21no—
332#478—21no—
333#476—21no—
334#476—21no—
335#475—21no—
336#475—21no—
337#470—21no—
338#470—21no—
339#468—21no—
340#468—21no—
341#467C2311yescharacteristic
342#467C2311yescharacteristic
343#467C2311yescharacteristic
344#467C2311yescharacteristic
345#467C2311yescharacteristic
346#467C2311yescharacteristic
347#467C2311yescharacteristic
348#467C2311yescharacteristic
349#466C2311yescharacteristic
350#466C2311yescharacteristic
351#466C2311yescharacteristic
352#466C2311yescharacteristic
353#465—21no—
354#465—21no—
355#464—21no—
356#464—21no—
357#464—21no—
358#464—21no—
359#462—21no—
360#462—21no—
361#462—21no—
362#462—21no—
363#462—21no—
364#462—21no—
365#461—21no—
366#461—21no—
367#452—21no—
368#452—21no—
369#452—21no—
370#452—21no—
371#451—21no—
372#451—21no—
373#451—21no—
374#451—21no—
375#451—21no—
376#451—21no—
377#448—21no—
378#448—21no—
379#446D411yescharacteristic
380C8×Q8C2311yescharacteristic
381#441—21no—
382#441—21no—
383#440—21no—
384#440—21no—
385C4×Q16C2311yescharacteristic
386C4×Q16C2311yescharacteristic
387C4×Q16C2311yescharacteristic
388C4×Q16C2311yescharacteristic
389C4×Q16C2311yescharacteristic
390C4×Q16C2311yescharacteristic
391C4×Q16C2311yescharacteristic
392C4×Q16C2311yescharacteristic
393C4×SD16—21no—
394C4×SD16—21no—
395C4×D8C2311yescharacteristic
396C4×D8C2311yescharacteristic
397C4×D8C2311yescharacteristic
398C4×D8C2311yescharacteristic
399#436D411yescharacteristic
400#435D411yescharacteristic
401#435D411yescharacteristic
402C8×D4C2311yescharacteristic
403C8×D4C2311yescharacteristic
404C8×D4C2311yescharacteristic
405#433D411yescharacteristic
406#433D411yescharacteristic
407#432D411yescharacteristic
408#428—21no—
409#428—21no—
410#427—21no—
411#427C2311yescharacteristic
412#427C2311yescharacteristic
413#427C2311yescharacteristic
414#427C2311yescharacteristic
415C2×#107C2311yescharacteristic
416C2×#107C2311yescharacteristic
417#405C2311yescharacteristic
418#405C2311yescharacteristic
419C2×C4×C8C2311yescharacteristic
420#367C2311yescharacteristic
421#367C2311yescharacteristic
422#367C2311yescharacteristic
423#367C2311yescharacteristic
424#367C2311yescharacteristic
425#367C2311yescharacteristic
426#366C2311yescharacteristic
427#366C2311yescharacteristic
428#366C2311yescharacteristic
429#366C2311yescharacteristic
430#366C2311yescharacteristic
431#366C2311yescharacteristic
432C4⋊C16C2311yescharacteristic
433C4⋊C16C2311yescharacteristic
434C4⋊C16C2311yescharacteristic
435C4⋊C16C2311yescharacteristic
436C4⋊C16C2311yescharacteristic
437C4⋊C16C2311yescharacteristic
438#358C2311yescharacteristic
439#358C2311yescharacteristic
440#358C2311yescharacteristic
441#358C2311yescharacteristic
442#358C2311yescharacteristic
443#358C2311yescharacteristic
444#358C2311yescharacteristic
445#358C2311yescharacteristic
446#358C2311yescharacteristic
447#358C2311yescharacteristic
448#358C2311yescharacteristic
449#358C2311yescharacteristic
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#358C2311yescharacteristic
463#358C2311yescharacteristic
464#358C2311yescharacteristic
465#358C2311yescharacteristic
466#358C2311yescharacteristic
467#358C2311yescharacteristic
468#358C2311yescharacteristic
469#358C2311yescharacteristic
470#357C2311yescharacteristic
471#357C2311yescharacteristic
472#357C2311yescharacteristic
473#357C2311yescharacteristic
474#357C2311yescharacteristic
475#357C2311yescharacteristic
476#357C2311yescharacteristic
477#357C2311yescharacteristic
478C22⋊C16C2311yescharacteristic
479C22⋊C16C2311yescharacteristic
480C22⋊C16C2311yescharacteristic
481C22⋊C16C2311yescharacteristic
482C22⋊C16C2311yescharacteristic
483C22⋊C16C2311yescharacteristic
484#346C2311yescharacteristic
485#346C2311yescharacteristic
486#346C2311yescharacteristic
487#346C2311yescharacteristic
488#346C2311yescharacteristic
489#346C2311yescharacteristic
490C4×C16C2311yescharacteristic
491C4×C16C2311yescharacteristic
492C4×C16C2311yescharacteristic
493C4×C16C2311yescharacteristic
494C2×#41—21no—
495C2×#41—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500#137—82no—
501#137—82no—
502#135—41no—
503#135—41no—
504#135—41no—
505#135—41no—
506C2×Q16—21no—
507C2×Q16—21no—
508C2×Q16—21no—
509C2×Q16—21no—
510C2×Q16—21no—
511C2×Q16—21no—
512C2×Q16—21no—
513C2×Q16—21no—
514C2×Q16—21no—
515C2×Q16—21no—
516C2×Q16—41no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—82no—
525C2×Q16C2411yescharacteristic
526C2×Q16C2411yescharacteristic
527C2×Q16C2411yescharacteristic
528C2×Q16C2411yescharacteristic
529C2×Q16C2411yescharacteristic
530C2×Q16C2411yescharacteristic
531C2×SD16—21no—
532C2×SD16—21no—
533C2×SD16—21no—
534C2×SD16—21no—
535C2×SD16—21no—
536C2×SD16—21no—
537C2×D8C2411yescharacteristic
538C2×D8C2411yescharacteristic
539C2×M16C2×D411yescharacteristic
540C2×M16C2×D411yescharacteristic
541C22×C8C2×D411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C4⋊Q8—21no—
546C4⋊Q8—21no—
547C4⋊Q8—21no—
548C4⋊Q8—21no—
549C4⋊Q8—21no—
550C4⋊Q8—21no—
551C4⋊Q8—21no—
552C4⋊Q8—21no—
553C4⋊Q8—21no—
554C4⋊Q8—21no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563#126—41no—
564#126—41no—
565#126—41no—
566#126—41no—
567#126—41no—
568#126—41no—
569#126—41no—
570#126—41no—
571#126—41no—
572#126—41no—
573#126—41no—
574#126—41no—
575#126—41no—
576#126—41no—
577#126—41no—
578#126—41no—
579#126D811yescharacteristic
580#126D811yescharacteristic
581#125—21no—
582#125—21no—
583#125—21no—
584#125—21no—
585#125—21no—
586#125—21no—
587#125—41no—
588#125—41no—
589#125—41no—
590#125—41no—
591#125—41no—
592#125—41no—
593#125—41no—
594#125—41no—
595#125—41no—
596#125—41no—
597#125—41no—
598#125—41no—
599#125—41no—
600#125D811yescharacteristic
601#124—21no—
602#124—21no—
603#124—21no—
604#124—21no—
605#124—41no—
606#124—41no—
607#124—41no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124D811yescharacteristic
613#123—41no—
614#123—41no—
615#123—41no—
616#123—41no—
617#123—41no—
618#123—41no—
619#123—41no—
620#123—41no—
621#123—41no—
622#123—41no—
623#123—41no—
624#123—41no—
625#123—41no—
626#123—41no—
627#123D811yescharacteristic
628#123D811yescharacteristic
629C22⋊Q8—21no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—21no—
635C22⋊Q8—21no—
636C22⋊Q8—21no—
637C22⋊Q8—41no—
638C22⋊Q8—41no—
639C22⋊Q8—41no—
640C22⋊Q8—41no—
641C22⋊Q8—41no—
642C22⋊Q8—41no—
643C22⋊Q8—41no—
644C22⋊Q8—41no—
645C22⋊Q8—41no—
646C22⋊Q8—41no—
647C22⋊Q8—41no—
648C22⋊Q8—41no—
649C22⋊Q8—41no—
650C22⋊Q8—41no—
651C22⋊Q8—41no—
652C22⋊Q8—41no—
653C22⋊Q8—41no—
654C22⋊Q8—41no—
655C22⋊Q8—41no—
656C22⋊Q8—41no—
657C22⋊Q8—41no—
658C22⋊Q8—41no—
659C22⋊Q8—41no—
660C22⋊Q8—41no—
661C22⋊Q8D811yescharacteristic
662#121—21no—
663#121—21no—
664#121—21no—
665#121—21no—
666#121—41no—
667#121—41no—
668#121—41no—
669#121—41no—
670#121—41no—
671#121—41no—
672#121D811yescharacteristic
673C4×Q8—21no—
674C4×Q8—21no—
675C4×Q8—21no—
676C4×Q8—21no—
677C4×Q8—21no—
678C4×Q8—21no—
679C4×Q8—21no—
680C4×Q8—21no—
681C4×Q8—41no—
682C4×Q8—41no—
683C4×Q8—41no—
684C4×Q8—41no—
685C4×Q8—41no—
686C4×Q8C2×D411yescharacteristic
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690C4×D4—21no—
691C4×D4—41no—
692C4×D4—41no—
693C4×D4—41no—
694C4×D4—41no—
695C4×D4—41no—
696C4×D4—41no—
697C4×D4—41no—
698C4×D4—41no—
699C4×D4—41no—
700C4×D4C2×D411yescharacteristic
701C4×D4C2×D411yescharacteristic
702C4×D4C2×D411yescharacteristic
703#117—21no—
704#117—21no—
705#117—21no—
706#117—21no—
707#117—41no—
708#117—41no—
709#117—41no—
710#117—41no—
711#117—41no—
712#117—41no—
713#117C2×D411yescharacteristic
714#117C2×D411yescharacteristic
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—41no—
718C2×C4⋊C4—41no—
719C2×C4⋊C4—41no—
720C2×C4⋊C4—41no—
721C2×C42C2×D411yescharacteristic
722Q32—41no—
723Q32—41no—
724Q32—41no—
725Q32—41no—
726Q32—41no—
727SD32—41no—
728SD32—41no—
729SD32—41no—
730SD32—41no—
731SD32—41no—
732SD32—41no—
733D16—41no—
734M32—41no—
735M32—41no—
736M32—41no—
737M32—41no—
738C2×C16—41no—
739C2×C16—41no—
740C2×C16C2411yescharacteristic
741C2×C16C2411yescharacteristic
742C2×C16C2411yescharacteristic
743C2×C16C2411yescharacteristic
744C2×C16C2411yescharacteristic
745C2×C16C2411yescharacteristic
746C2×C16C2411yescharacteristic
747C2×C16C2411yescharacteristic
748#107—21no—
749#107—21no—
750#107—21no—
751#107—21no—
752#107—21no—
753#107—21no—
754#107C2411yescharacteristic
755#107C2411yescharacteristic
756#107C2411yescharacteristic
757#107C2411yescharacteristic
758#107C2411yescharacteristic
759#107C2411yescharacteristic
760#107C2411yescharacteristic
761#107C2411yescharacteristic
762#106—21no—
763#106—21no—
764#106—21no—
765#106—21no—
766#106—21no—
767#106—21no—
768#106—21no—
769#106—21no—
770#106—21no—
771#106—21no—
772C4⋊C8C2×D411yescharacteristic
773C4⋊C8C2×D411yescharacteristic
774C4⋊C8C2×D411yescharacteristic
775C4⋊C8C2×D411yescharacteristic
776C4⋊C8C2×D411yescharacteristic
777C4⋊C8C2×D411yescharacteristic
778#103—21no—
779#103—21no—
780#103—21no—
781#103—21no—
782#103—21no—
783#103—21no—
784#103—21no—
785#103—21no—
786#103—21no—
787#103—21no—
788#103—21no—
789#103—21no—
790#103—21no—
791#103—21no—
792#103—21no—
793#103—21no—
794#102—21no—
795#102—21no—
796#102—21no—
797#102—21no—
798#102—21no—
799#102—21no—
800#102—21no—
801#102—21no—
802C22⋊C8C2×D411yescharacteristic
803C22⋊C8C2×D411yescharacteristic
804C22⋊C8C2×D411yescharacteristic
805C22⋊C8C2×D411yescharacteristic
806C22⋊C8C2×D411yescharacteristic
807C22⋊C8C2×D411yescharacteristic
808#97C2×D411yescharacteristic
809#97C2×D411yescharacteristic
810#97C2×D411yescharacteristic
811#97C2×D411yescharacteristic
812C4×C8C2×D411yescharacteristic
813C4×C8C2×D411yescharacteristic
814C4×C8C2411yescharacteristic
815C4×C8C2411yescharacteristic
816C4×C8C2411yescharacteristic
817C4×C8C2411yescharacteristic
818#41—81no—
819#41—81no—
820#41—81no—
821#41—81no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—41no—
829C2×Q8—41no—
830C2×Q8—41no—
831C2×Q8—41no—
832C2×Q8—41no—
833C2×Q8—41no—
834C2×Q8—41no—
835C2×Q8—41no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8C2×D811yescharacteristic
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4C2×D811yescharacteristic
854C2×D4C2×D811yescharacteristic
855C2×D4C2×D811yescharacteristic
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4C2×D811yescharacteristic
869C22×C4C2×D811yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873Q16—21no—
874Q16—21no—
875Q16—21no—
876Q16—21no—
877Q16—21no—
878Q16—21no—
879Q16—21no—
880Q16—21no—
881Q16—21no—
882Q16—21no—
883Q16—21no—
884Q16—21no—
885Q16—42no—
886Q16—42no—
887Q16—81no—
888Q16—81no—
889Q16—81no—
890Q16—81no—
891Q16—81no—
892Q16—81no—
893Q16—81no—
894Q16—81no—
895SD16—42no—
896SD16—42no—
897SD16—81no—
898SD16—81no—
899SD16—81no—
900SD16—81no—
901D8—21no—
902D8—21no—
903D8—21no—
904D8—21no—
905M16—22no—
906M16—22no—
907C2×C8—22no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8C22×D411yescharacteristic
915C2×C8C22×D411yescharacteristic
916C2×C8C22×D411yescharacteristic
917C2×C8C22×D411yescharacteristic
918C2×C8C22×D411yescharacteristic
919C2×C8C22×D411yescharacteristic
920C2×C8C22×D411yescharacteristic
921C2×C8C2511yescharacteristic
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
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⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4C2×D811yescharacteristic
977C4⋊C4C2×D811yescharacteristic
978C4⋊C4C2×D811yescharacteristic
979C4⋊C4C2×D811yescharacteristic
980C4⋊C4C2×D811yescharacteristic
981C4⋊C4C2×D811yescharacteristic
982C4⋊C4C2×D811yescharacteristic
983C4⋊C4C2×D811yescharacteristic
984C4⋊C4C2×D811yescharacteristic
985C4⋊C4C2×D811yescharacteristic
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—41no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4C2×D811yescharacteristic
1015C22⋊C4C2×D811yescharacteristic
1016C22⋊C4C2×D811yescharacteristic
1017C22⋊C4C2×D811yescharacteristic
1018C22⋊C4C2×D811yescharacteristic
1019C22⋊C4C2×D811yescharacteristic
1020C22⋊C4C2×D811yescharacteristic
1021C22⋊C4C2×D811yescharacteristic
1022C22⋊C4C2×D811yescharacteristic
1023C22⋊C4C2×D811yescharacteristic
1024C42—41no—
1025C42—41no—
1026C42—41no—
1027C42—41no—
1028C42—41no—
1029C42—41no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42C2×D811yescharacteristic
1037C42C2×D811yescharacteristic
1038C42C22×D411yescharacteristic
1039C42C22×D411yescharacteristic
1040C42C22×D411yescharacteristic
1041C42C22×D411yescharacteristic
1042C16—21no—
1043C16—21no—
1044C16—21no—
1045C16—21no—
1046C16—21no—
1047C16—21no—
1048C16—21no—
1049C16—21no—
1050C23—41no—
1051C23—41no—
1052C23C22×D811yescharacteristic
1053C23C22×D811yescharacteristic
1054C23C22×D811yescharacteristic
1055Q8—41no—
1056Q8—41no—
1057Q8—41no—
1058Q8—41no—
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—41no—
1064Q8—41no—
1065Q8—41no—
1066Q8—41no—
1067Q8—41no—
1068Q8—161no—
1069Q8—161no—
1070Q8—161no—
1071Q8—161no—
1072Q8—161no—
1073Q8—161no—
1074Q8—161no—
1075Q8—161no—
1076D4—41no—
1077D4—41no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—82no—
1084D4—161no—
1085D4—161no—
1086D4—161no—
1087D4—161no—
1088D4—161no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—82no—
1112C2×C4—161no—
1113C2×C4—161no—
1114C2×C4—161no—
1115C2×C4—161no—
1116C2×C4—161no—
1117C2×C4—161no—
1118C2×C4—161no—
1119C2×C4—161no—
1120C2×C4—161no—
1121C2×C4—161no—
1122C2×C4—161no—
1123C2×C4C22×D811yescharacteristic
1124C2×C4C22×D811yescharacteristic
1125C2×C4C22×D811yescharacteristic
1126C2×C4C22×D811yescharacteristic
1127C2×C4C22×D811yescharacteristic
1128C2×C4C22×D811yescharacteristic
1129C2×C4C22×D811yescharacteristic
1130C2×C4C22×D811yescharacteristic
1131C2×C4C22×D811yescharacteristic
1132C2×C4C22×D811yescharacteristic
1133C2×C4C22×D811yescharacteristic
1134C2×C4C23×D411yescharacteristic
1135C8—21no—
1136C8—21no—
1137C8—21no—
1138C8—21no—
1139C8—21no—
1140C8—21no—
1141C8#57712yes—
1142C8#58511yescharacteristic
1143C8#58511yescharacteristic
1144C22—21no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—21no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22C23×D811yescharacteristic
1160C4—21no—
1161C4—21no—
1162C4—21no—
1163C4—21no—
1164C4—21no—
1165C4—21no—
1166C4—21no—
1167C4—21no—
1168C4—21no—
1169C4—21no—
1170C4—21no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4#350011yescharacteristic
1186C4C2×#57711yescharacteristic
1187C2—41no—
1188C2—41no—
1189C2—41no—
1190C2—161no—
1191C2—161no—
1192C2#6252911yescharacteristic
1193C2#6263711yescharacteristic
1194C2#6263711yescharacteristic
subgroupG/H
center, socleC22C23×D8
commutator, Frattini, cosocleC2×C8C25
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #529 ◁ #2966 ◁ G
LECSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62490C2semidirect
2. #62432C2semidirect
3. #33944C2semidirect
4. #33943C2semidirect
5. #33941C2semidirect
6. #33939C2semidirect
7. #33896C2semidirect
8. #33895C2semidirect
9. #33894C2semidirect
10. #33893C2semidirect
11. #33888C2semidirect
12. #33887C2semidirect
13. #33887C2semidirect
14. #33882C2semidirect
15. #33880C2semidirect
16. #33879C2semidirect
17. #33879C2semidirect
18. #33874C2semidirect
19. #33808C2semidirect
20. #33808C2semidirect
21. #33806C2semidirect
22. #33791C2semidirect
23. #33791C2semidirect
24. #33784C2semidirect
25. #33750C2semidirect
26. #33745C2semidirect
27. #33745C2semidirect
28. #33705C2semidirect
29. #33703C2semidirect
30. #33703C2semidirect
31. #33481C2semidirect

Maximal subgroups

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

subgroupindex
#624902
#624322
#339442
#339432
#339412
#339392
#338962
#338952
#338942
#338932
#338882
#338872
#338822
#338802
#338792
#338742
#338082
#338062
#337912
#337842
#337502
#337452
#337052
#337032
#334812