Finite Group Databasebeta

← #24918327

Subgroups — #24918327

Order 10624.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128270C211yesmaximal, characteristic, complemented
2#19128267C211yesmaximal, characteristic, complemented
3#19128028C211yesmaximal, characteristic, complemented
4#19128027C211yesmaximal, characteristic, complemented
5#19128025C211yesmaximal, characteristic, complemented
6#19127955C211yesmaximal, characteristic, complemented
7#19127953C211yesmaximal, characteristic, complemented
8#19127938C211yesmaximal, characteristic, complemented
9#19127936C211yesmaximal, characteristic, complemented
10#19127837C211yesmaximal, characteristic, complemented
11#19127836C211yesmaximal, characteristic, complemented
12#19127836C211yesmaximal, characteristic, complemented
13#19127834C211yesmaximal, characteristic, complemented
14#19127666C211yesmaximal, characteristic, complemented
15#482×C83C211yesmaximal, characteristic, complemented
16C2×#13050590C2211yescharacteristic
17C22×D332C2211yescharacteristic, complemented
18C2×D4×D83C2211yescharacteristic, complemented
19C2×D664C2211yescharacteristic
20C2×D664C2211yescharacteristic
21C2×#13050575C2211yescharacteristic
22C2×#13050575C2211yescharacteristic
23C2×#13050573C2211yescharacteristic, complemented
24C2×C8×D83C2211yescharacteristic, complemented
25#14581789—21no—
26#14581788—21no—
27#14581780—21no—
28#14581778—21no—
29#14581767C2211yescharacteristic
30#14581767C2211yescharacteristic
31#14581767C2211yescharacteristic, complemented
32#14581767C2211yescharacteristic, complemented
33#14581767C2211yescharacteristic, complemented
34#14581766C2211yescharacteristic
35#14581763C2211yescharacteristic, complemented
36#14581762—21no—
37#14581762—21no—
38#14581762—21no—
39#14581760—21no—
40#14581750C2211yescharacteristic, complemented
41#14581725C2211yescharacteristic, complemented
42#14581723C2211yescharacteristic, complemented
43#14581714C2211yescharacteristic, complemented
44#14581714C2211yescharacteristic, complemented
45#14581712C2211yescharacteristic, complemented
46#14581712C2211yescharacteristic, complemented
47#14581712C2211yescharacteristic, complemented
48#14581712C2211yescharacteristic, complemented
49C22⋊(C83⋊C8)C2211yescharacteristic, complemented
50(C2×D83)⋊C8C2211yescharacteristic, complemented
51(C2×D83)⋊C8C2211yescharacteristic, complemented
52#121×C83C2211yescharacteristic
53#117×C83C2211yescharacteristic, complemented
54#107×C83C2211yescharacteristic, complemented
55#106×C83C2211yescharacteristic, complemented
56#102×C83C2211yescharacteristic, complemented
57#102×C83C2211yescharacteristic, complemented
58C22⋊C8×C83C2211yescharacteristic, complemented
59C23×D83—21no—
60C23×D83—21no—
61#13050590—41no—
62#13050590—41no—
63C2×Dic166D411yescharacteristic
64C2×D332—21no—
65C2×D332—21no—
66C2×D332—21no—
67C2×D332—21no—
68C2×D332—21no—
69C2×D332—21no—
70C2×D332—41no—
71C2×D332—41no—
72C2×D332D411yescharacteristic
73C2×D332C2311yescharacteristic
74C2×D332C2311yescharacteristic
75C2×D332C2311yescharacteristic
76C2×C22⋊D83—21no—
77C2×C22⋊D83—21no—
78C2×C22⋊D83—21no—
79C2×C22⋊D83D411yescharacteristic
80C2×C22⋊D83D411yescharacteristic
81D4×D83—41no—
82D4×D83—41no—
83C2×C4×D83C2311yescharacteristic
84C2×C4×D83C2311yescharacteristic
85D664—41no—
86D664—41no—
87#13050575—41no—
88#13050575—41no—
89#13050573—41no—
90C2×C83⋊C8C2311yescharacteristic
91C2×C83⋊C8C2311yescharacteristic
92C8×D83—41no—
93C4⋊Dic83C2311yescharacteristic
94C22⋊Dic83—21no—
95(C2×D83)⋊C4—21no—
96(C2×D83)⋊C4—21no—
97(C2×D83)⋊C4—21no—
98(C2×D83)⋊C4—21no—
99(C2×D83)⋊C4—21no—
100(C2×D83)⋊C4—21no—
101(C2×D83)⋊C4—21no—
102C4×Dic83—21no—
103C2×D4×C83—21no—
104C2×D4×C83C2311yescharacteristic
105C22×C4×C83C2311yescharacteristic
106C2×C8×C83C2311yescharacteristic
107C2×C8×C83C2311yescharacteristic
108C4⋊C4×C83C2311yescharacteristic
109C4⋊C4×C83C2311yescharacteristic
110C4⋊C4×C83C2311yescharacteristic
111C22⋊C4×C83—21no—
112C22⋊C4×C83—21no—
113C42×C83—21no—
114C23×C83—21no—
115C23×C83C2×D411yescharacteristic
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—21no—
119C22×D83—42no—
120C22×D83—42no—
121C22×D83—81no—
122C22×D83—81no—
123C22×D83—81no—
124C22×D83—81no—
125C22×D83C2×D411yescharacteristic
126C22×D83C2×D411yescharacteristic
127D4×C83—21no—
128D4×C83—21no—
129D4×C83—81no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83C2×D411yescharacteristic
136C2×C4×C83C2411yescharacteristic
137C22⋊D83—41no—
138C22⋊D83—41no—
139C22⋊D83—42no—
140C22⋊D83—81no—
141C22⋊D83—81no—
142C2×Dic83—21no—
143C2×Dic83C2×D411yescharacteristic
144C2×Dic83C2×D411yescharacteristic
145D332—21no—
146D332—21no—
147D332—21no—
148D332—21no—
149D332—21no—
150D332—21no—
151D332—41no—
152D332—42no—
153D332—81no—
154D332—81no—
155D332—81no—
156D332—81no—
157D332—81no—
158C4×D83—21no—
159C4×D83—21no—
160C4×D83—21no—
161C4×D83—21no—
162Dic166—41no—
163C8×C83—21no—
164C8×C83—21no—
165C83⋊C8—21no—
166C83⋊C8—21no—
167C22×C83—21no—
168C22×C83—21no—
169C22×C83—21no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83C22×D411yescharacteristic
174C2×D83—21no—
175C2×D83—21no—
176C2×D83—21no—
177C2×D83—21no—
178C2×D83—21no—
179C2×D83—21no—
180C2×D83—41no—
181C2×D83—41no—
182C2×D83—41no—
183C2×D83—41no—
184C2×D83—41no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—41no—
189C2×D83—84no—
190C2×D83—84no—
191C4×C83—21no—
192C4×C83—41no—
193C4×C83—41no—
194C4×C83—41no—
195C4×C83H(5,𝔽2)11yescharacteristic
196C4×C83H(5,𝔽2)11yescharacteristic
197Dic83—21no—
198Dic83—21no—
199Dic83—41no—
200C2×C83—41no—
201C2×C83—81no—
202C2×C83#53411yescharacteristic
203C2×C83#57611yescharacteristic
204C2×C83#57611yescharacteristic
205D83—41no—
206D83—41no—
207D83—81no—
208D83—81no—
209D83—81no—
210#3199—831nomaximal, Sylow
211C83#319911yescharacteristic, complemented, Sylow
212#535—831no—
213#535—831no—
214#482—831no—
215#482—831no—
216#482—831no—
217#482D8311yescharacteristic, complemented
218#469—831no—
219#469—831no—
220#466—831no—
221#466—831no—
222#447—831no—
223#447—831no—
224#447—831no—
225#447—831no—
226#408—831no—
227C2×#41—831no—
228C22×D4—831no—
229C22×D4—831no—
230C2×D8—831no—
231C2×D8—831no—
232C2×D8—831no—
233C2×D8—831no—
234C2×M16—831no—
235C22×C8—831no—
236#127—1661no—
237#127—1661no—
238#124—1661no—
239#124—1661no—
240#121—831no—
241#121—831no—
242#121—831no—
243#121—831no—
244#121—831no—
245#121—831no—
246#121—831no—
247#121C2×D8311yescharacteristic
248#120—1661no—
249#120—1661no—
250#120—1661no—
251#120—1661no—
252#117—831no—
253#117C2×D8311yescharacteristic, complemented
254#107—831no—
255#107C2×D8311yescharacteristic, complemented
256#106—831no—
257#106C2×D8311yescharacteristic, complemented
258#102—831no—
259#102—831no—
260#102—831no—
261#102—831no—
262#102—831no—
263#102—831no—
264#102C2×D8311yescharacteristic, complemented
265#102C2×D8311yescharacteristic, complemented
266C22⋊C8—831no—
267C22⋊C8—831no—
268C22⋊C8—831no—
269C22⋊C8C2×D8311yescharacteristic, complemented
270C24—1661no—
271C24—1661no—
272#41—3321no—
273#41—3321no—
274C2×Q8—831no—
275C2×D4—21no—
276C2×D4—3321no—
277C2×D4—3321no—
278C2×D4—3321no—
279C2×D4—3321no—
280C2×D4—831no—
281C2×D4—831no—
282C2×D4—831no—
283C2×D4—831no—
284C2×D4—831no—
285C2×D4—831no—
286C2×D4—1661no—
287C2×D4—1661no—
288C2×D4—1661no—
289C2×D4—1661no—
290C2×D4—1661no—
291C2×D4—1661no—
292C2×D4—1661no—
293C2×D4—1661no—
294C2×D4—1661no—
295C2×D4C22×D8311yescharacteristic
296C22×C4—831no—
297C22×C4—831no—
298C22×C4C22×D8311yescharacteristic
299D8—3321no—
300D8—3321no—
301D8—3321no—
302D8—3321no—
303M16—3321no—
304C2×C8—3321no—
305C2×C8—831no—
306C2×C8—831no—
307C2×C8C22×D8311yescharacteristic
308C2×C8C22×D8311yescharacteristic
309C4⋊C4—831no—
310C4⋊C4C22×D8311yescharacteristic
311C4⋊C4C22×D8311yescharacteristic
312C4⋊C4C22×D8311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—1661no—
316C22⋊C4—1661no—
317C22⋊C4—1661no—
318C22⋊C4—1661no—
319C22⋊C4—1661no—
320C22⋊C4—1661no—
321C22⋊C4—1661no—
322C22⋊C4—1661no—
323C42—21no—
324C42—1661no—
325C23—21no—
326C23—3322no—
327C23—3322no—
328C23—831no—
329C23—831no—
330C23—6641no—
331C23—6641no—
332C23—6641no—
333C23—6641no—
334C23—1661no—
335C23—1661no—
336C23—1661no—
337C23D4×D8311yescharacteristic
338Q8—3321no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—3322no—
343D4—3321no—
344D4—3321no—
345D4—3321no—
346D4—3322no—
347D4—6641no—
348D4—6641no—
349D4—6641no—
350D4—6641no—
351D4—6641no—
352D4—6641no—
353D4—6641no—
354D4—1661no—
355D4—1661no—
356D4—1661no—
357D4—1661no—
358D4—1661no—
359D4—1661no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—831no—
366C2×C4—831no—
367C2×C4—1661no—
368C2×C4—1661no—
369C2×C4—1661no—
370C2×C4—1661no—
371C2×C4—1661no—
372C2×C4D4×D8311yescharacteristic
373C2×C4C23×D8311yescharacteristic
374C8—21no—
375C8—21no—
376C8—1661no—
377C8—1661no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—3321no—
385C22—3321no—
386C22—3321no—
387C22—3321no—
388C22—3321no—
389C22—3321no—
390C22—3321no—
391C22—3321no—
392C22—3321no—
393C22—6644no—
394C22—6644no—
395C22—1661no—
396C22—1661no—
397C22—1661no—
398C22—1661no—
399C22—1661no—
400C22—1661no—
401C22C2×D4×D8311yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—3321no—
407C4—1661no—
408C4—1661no—
409C4#1458183811yescharacteristic
410C4#1458183811yescharacteristic
411C2—41no—
412C2—81no—
413C2—3321no—
414C2—3321no—
415C2—6641no—
416C2—6641no—
417C2—6641no—
418C2#1912826211yescharacteristic
419C2#1912850311yescharacteristic
420C2#1912850511yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#482×C83C2
socleC22×C83C22×D4
hypercenter#482D83
hypocenterC83#3199
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #19128270C2semidirect
2. #19128267C2semidirect
3. #19128028C2semidirect
4. #19128027C2semidirect
5. #19128025C2semidirect
6. #19127955C2semidirect
7. #19127953C2semidirect
8. #19127938C2semidirect
9. #19127936C2semidirect
10. #19127837C2semidirect
11. #19127836C2semidirect
12. #19127836C2semidirect
13. #19127834C2semidirect
14. #19127666C2semidirect
15. #482×C83C2semidirect
17. C22×D332C22semidirect
18. C2×D4×D83C22semidirect
23. C2×#13050573C22semidirect
24. C2×C8×D83C22semidirect
31. #14581767C22semidirect
32. #14581767C22semidirect
33. #14581767C22semidirect
35. #14581763C22semidirect
40. #14581750C22semidirect
41. #14581725C22semidirect
42. #14581723C22semidirect
43. #14581714C22semidirect
44. #14581714C22semidirect
45. #14581712C22semidirect
46. #14581712C22semidirect
47. #14581712C22semidirect
48. #14581712C22semidirect
49. C22⋊(C83⋊C8)C22semidirect
50. (C2×D83)⋊C8C22semidirect
51. (C2×D83)⋊C8C22semidirect
53. #117×C83C22semidirect
54. #107×C83C22semidirect
55. #106×C83C22semidirect
56. #102×C83C22semidirect
57. #102×C83C22semidirect
58. C22⋊C8×C83C22semidirect
211. C83#3199semidirect
217. #482D83semidirect
253. #117C2×D83semidirect
255. #107C2×D83semidirect
257. #106C2×D83semidirect
264. #102C2×D83semidirect
265. #102C2×D83semidirect
269. C22⋊C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191282702
#191282672
#191280282
#191280272
#191280252
#191279552
#191279532
#191279382
#191279362
#191278372
#191278362
#191278342
#191276662
#482×C832
#319983