Finite Group Databasebeta

← #6773674

Subgroups — #6773674

Order 512.

1441 conjugacy classes of subgroups.

The subgroup lattice has 1247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39066C211yesmaximal, characteristic
2#35579C211yesmaximal, characteristic, complemented
3#33102C211yesmaximal, characteristic, complemented
4#32374C211yesmaximal, characteristic, complemented
5#32231C211yesmaximal, characteristic, complemented
6#31574C211yesmaximal, characteristic, complemented
7#31573C211yesmaximal, characteristic, complemented
8#31475C211yesmaximal, characteristic, complemented
9#30951C211yesmaximal, characteristic, complemented
10#30827C211yesmaximal, characteristic, complemented
11#30807C211yesmaximal, characteristic, complemented
12#30149C211yesmaximal, characteristic, complemented
13#30071C211yesmaximal, characteristic, complemented
14#29516C211yesmaximal, characteristic, complemented
15#29406C211yesmaximal, characteristic, complemented
16#28783C211yesmaximal, characteristic, complemented
17#28665C211yesmaximal, characteristic, complemented
18#28207C211yesmaximal, characteristic, complemented
19#27874C211yesmaximal, characteristic, complemented
20#27594C211yesmaximal, characteristic, complemented
21#27279C211yesmaximal, characteristic
22#27254C211yesmaximal, characteristic
23#26439C211yesmaximal, characteristic, complemented
24#26345C211yesmaximal, characteristic, complemented
25#26066C211yesmaximal, characteristic, complemented
26#25968C211yesmaximal, characteristic, complemented
27#25952C211yesmaximal, characteristic, complemented
28#22593C211yesmaximal, characteristic, complemented
29#22220C211yesmaximal, characteristic, complemented
30#22126C211yesmaximal, characteristic, complemented
31#21065C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic, complemented
33C2×#490C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic, complemented
38C2×#427C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C22×#102C2211yescharacteristic
41#2860C2211yescharacteristic
42#2752—21no—
43#2705—21no—
44#2685—21no—
45#2685—21no—
46#2641C2211yescharacteristic
47#2624C2211yescharacteristic
48#2602—21no—
49#2588—21no—
50#2587—21no—
51#2585—21no—
52#2570C2211yescharacteristic, complemented
53#2556—21no—
54#2552C2211yescharacteristic, complemented
55#2552C2211yescharacteristic, complemented
56#2550C2211yescharacteristic, complemented
57#2534—21no—
58#2522—21no—
59#2512C2211yescharacteristic
60#2507—21no—
61#2467—21no—
62#2462—21no—
63#2454C2211yescharacteristic
64#2445C2211yescharacteristic
65#2445C2211yescharacteristic
66#2442C2211yescharacteristic
67#2441C2211yescharacteristic
68#2441C2211yescharacteristic
69#2441C2211yescharacteristic
70#2440C2211yescharacteristic
71#2433C2211yescharacteristic
72#2423—21no—
73#2418—21no—
74#2363C2211yescharacteristic
75D4×C22⋊C4C2211yescharacteristic
76#2330C2211yescharacteristic, complemented
77#2330C2211yescharacteristic, complemented
78#2319C2211yescharacteristic
79#2314C2211yescharacteristic
80#2309C2211yescharacteristic
81C4×C4⋊Q8C2211yescharacteristic, complemented
82C4×#127C2211yescharacteristic
83C4×#125C2211yescharacteristic, complemented
84#2298C2211yescharacteristic
85#2274C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2094C2211yescharacteristic
89#2094C2211yescharacteristic, complemented
90#2093C2211yescharacteristic
91#2093C2211yescharacteristic
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2059C2211yescharacteristic, complemented
116#2058C2211yescharacteristic, complemented
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic, complemented
125#2023C2211yescharacteristic
126#1992C2211yescharacteristic, complemented
127#1990C2211yescharacteristic, complemented
128#1989C2211yescharacteristic, complemented
129#1957C2211yescharacteristic
130#1957C2211yescharacteristic
131#1947C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1942C2211yescharacteristic, complemented
134#1942C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic, complemented
147#1926C2211yescharacteristic, complemented
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1925C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1918C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1895C2211yescharacteristic
171#1893C2211yescharacteristic
172#1875C2211yescharacteristic
173#1874C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1853C2211yescharacteristic
184#1851C2211yescharacteristic
185#1850C2211yescharacteristic
186#1845C2211yescharacteristic, complemented
187#1840C2211yescharacteristic, complemented
188#1831C2211yescharacteristic, complemented
189#1818C2211yescharacteristic
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1768C2211yescharacteristic, complemented
198#1753C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1744C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#123—21no—
217C2×#123—21no—
218C2×C22⋊Q8—21no—
219C2×#121C2311yescharacteristic
220C2×#120—21no—
221C2×#120—21no—
222C2×C4×Q8—21no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C22⋊C4—21no—
233#499—42no—
234#490—42no—
235#486—24no—
236#478—24no—
237#478—42no—
238#478—42no—
239#427—42no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260#418—42no—
261C2×#102—24no—
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#400—21no—
293#400—21no—
294#399—21no—
295#399—21no—
296#399—21no—
297#399—21no—
298#399—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#395—21no—
315#395—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#392—21no—
327#392—21no—
328#391—21no—
329#391—21no—
330#390—21no—
331#390—21no—
332#390—21no—
333#390—21no—
334#390—21no—
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388D411yescharacteristic
380#388D411yescharacteristic
381#388D411yescharacteristic
382#388D411yescharacteristic
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387D411yescharacteristic
397#387D411yescharacteristic
398#387D411yescharacteristic
399#387D411yescharacteristic
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#384—21no—
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#379—21no—
424#379—21no—
425#379—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445#376C2311yescharacteristic
446C43C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×D4—22no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2411yescharacteristic
509C2×M16—22no—
510C2×M16—41no—
511C2×M16—41no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525#127—22no—
526#127—41no—
527#127—41no—
528#127—41no—
529#126—82no—
530#126—82no—
531#125—22no—
532#125—22no—
533#125—22no—
534#125—41no—
535#125—41no—
536#125—41no—
537#125—41no—
538#125—41no—
539#125—82no—
540#123—82no—
541#123—82no—
542C22⋊Q8—82no—
543#121—22no—
544#121—22no—
545#120—82no—
546#120—82no—
547C4×Q8—82no—
548C4×D4—22no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—82no—
555C4×D4—82no—
556#117—22no—
557#117—22no—
558#117—22no—
559#117—41no—
560#117—41no—
561#117—41no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—82no—
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42C2×D411yescharacteristic
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673#107—22no—
674#107—22no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#106—22no—
682#106—22no—
683#106—22no—
684#106—41no—
685#106—41no—
686#106—41no—
687#106—41no—
688#106—41no—
689C4⋊C8—22no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102#4114yes—
717C22⋊C8—22no—
718C22⋊C8—22no—
719#97—41no—
720C4×C8—22no—
721C4×C8—41no—
722C4×C8—41no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762C24—21no—
763C24—21no—
764C24—21no—
765C24—42no—
766C24—42no—
767C24—81no—
768C24—81no—
769C24—81no—
770C24—81no—
771C24—81no—
772C24C22×D411yescharacteristic
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—81no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—82no—
803C2×D4—82no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4C2×#4112yes—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C42−1+412yes—
859C22×C42−1+412yes—
860C22×C4C2511yescharacteristic
861M16—82no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—44no—
886C2×C8C2×#4112yes—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
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—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4C2×#4112yes—
951C4⋊C4H(5,𝔽2)12yes—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C42—22no—
990C42—22no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—41no—
1004C42—41no—
1005C42—42no—
1006C42—81no—
1007C42—81no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42—81no—
1012C42—81no—
1013C42—81no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—22no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—84no—
1042C23—84no—
1043C23—162no—
1044C23—162no—
1045C23—162no—
1046C23—162no—
1047C23—162no—
1048C23#53612yes—
1049C23C23×D411yescharacteristic
1050Q8—84no—
1051D4—22no—
1052D4—22no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—41no—
1062D4—41no—
1063D4—84no—
1064D4—84no—
1065D4—84no—
1066D4—162no—
1067D4—162no—
1068D4—162no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—162no—
1149C2×C4—162no—
1150C2×C4—162no—
1151C2×C4—162no—
1152C2×C4#53612yes—
1153C2×C4#57612yes—
1154C2×C4#57712yes—
1155C2×C4C22×#4111yescharacteristic
1156C2×C4C2×H(5,𝔽2)11yescharacteristic
1157C2×C4C2×2−1+411yescharacteristic
1158C2×C4C2×2−1+411yescharacteristic
1159C2×C4#58511yescharacteristic
1160C2×C4#58511yescharacteristic
1161C8—22no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C8—41no—
1166C8—41no—
1167C8—41no—
1168C8—41no—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—168no—
1198C22C2×#53611yescharacteristic
1199C22D4×#4111yescharacteristic
1200C22#348811yescharacteristic
1201C22C2×#57611yescharacteristic
1202C22C2×#57711yescharacteristic
1203C22#358411yescharacteristic
1204C22#358511yescharacteristic
1205C4—22no—
1206C4—22no—
1207C4—22no—
1208C4—41no—
1209C4—42no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—42no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4#349511yescharacteristic
1232C4#352011yescharacteristic
1233C4#356111yescharacteristic
1234C4#356411yescharacteristic
1235C2—42no—
1236C2—82no—
1237C2—161no—
1238C2—161no—
1239C2#3837011yescharacteristic
1240C2#6087711yescharacteristic
1241C2#6089011yescharacteristic
1242C2#6147111yescharacteristic
1243C2#6152111yescharacteristic
1244C2#6203711yescharacteristic
1245C2#6207011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35579C2semidirect
3. #33102C2semidirect
4. #32374C2semidirect
5. #32231C2semidirect
6. #31574C2semidirect
7. #31573C2semidirect
8. #31475C2semidirect
9. #30951C2semidirect
10. #30827C2semidirect
11. #30807C2semidirect
12. #30149C2semidirect
13. #30071C2semidirect
14. #29516C2semidirect
15. #29406C2semidirect
16. #28783C2semidirect
17. #28665C2semidirect
18. #28207C2semidirect
19. #27874C2semidirect
20. #27594C2semidirect
23. #26439C2semidirect
24. #26345C2semidirect
25. #26066C2semidirect
26. #25968C2semidirect
27. #25952C2semidirect
28. #22593C2semidirect
29. #22220C2semidirect
30. #22126C2semidirect
31. #21065C2semidirect
32. C2×#499C22semidirect
37. C2×#478C22semidirect
52. #2570C22semidirect
54. #2552C22semidirect
55. #2552C22semidirect
56. #2550C22semidirect
76. #2330C22semidirect
77. #2330C22semidirect
81. C4×C4⋊Q8C22semidirect
83. C4×#125C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
89. #2094C22semidirect
93. #2092C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2084C22semidirect
97. #2084C22semidirect
98. #2084C22semidirect
99. #2083C22semidirect
100. #2083C22semidirect
105. #2071C22semidirect
107. #2067C22semidirect
111. #2065C22semidirect
112. #2059C22semidirect
113. #2059C22semidirect
114. #2059C22semidirect
115. #2059C22semidirect
116. #2058C22semidirect
124. #2025C22semidirect
126. #1992C22semidirect
127. #1990C22semidirect
128. #1989C22semidirect
131. #1947C22semidirect
132. #1944C22semidirect
133. #1942C22semidirect
134. #1942C22semidirect
135. #1941C22semidirect
146. #1926C22semidirect
147. #1926C22semidirect
148. #1926C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
157. #1925C22semidirect
158. #1921C22semidirect
159. #1920C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1919C22semidirect
163. #1919C22semidirect
164. #1918C22semidirect
165. #1918C22semidirect
166. #1917C22semidirect
167. #1916C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
178. #1862C22semidirect
179. #1862C22semidirect
186. #1845C22semidirect
187. #1840C22semidirect
188. #1831C22semidirect
193. #1804C22semidirect
197. #1768C22semidirect
200. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#390662
#355792
#331022
#323742
#322312
#315742
#315732
#314752
#309512
#308272
#308072
#301492
#300712
#295162
#294062
#287832
#286652
#282072
#278742
#275942
#272792
#272542
#264392
#263452
#260662
#259682
#259522
#225932
#222202
#221262
#210652