Finite Group Databasebeta

← #44543683

Subgroups — #44543683

Order 31936.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30630344C211yesmaximal, characteristic, complemented
2#30630344C211yesmaximal, characteristic, complemented
3#30630338C211yesmaximal, characteristic, complemented
4#30630337C211yesmaximal, characteristic, complemented
5#30630333C211yesmaximal, characteristic, complemented
6#30630332C211yesmaximal, characteristic, complemented
7#30630328C211yesmaximal, characteristic, complemented
8#30630323C211yesmaximal, characteristic, complemented
9#30630323C211yesmaximal, characteristic, complemented
10#30630322C211yesmaximal, characteristic, complemented
11#30630320C211yesmaximal, characteristic, complemented
12D4×Dic499C211yesmaximal, characteristic, complemented
13(C22⋊D499)⋊C4C211yesmaximal, characteristic, complemented
14C2×C22⋊Dic499C211yesmaximal, characteristic, complemented
15#120×C499C211yesmaximal, characteristic, complemented
16C2×Dic998C2211yescharacteristic, complemented
17C2×C22⋊D499C2211yescharacteristic
18C2×C22⋊D499C2211yescharacteristic
19C2×C22⋊D499C2211yescharacteristic
20C2×C22⋊D499C2211yescharacteristic, complemented
21C22×Dic499C2211yescharacteristic
22C22×Dic499C2211yescharacteristic
23C22×Dic499C2211yescharacteristic, complemented
24C2×C4×D499C2211yescharacteristic, complemented
25C4⋊Dic499C2211yescharacteristic, complemented
26C4⋊Dic499C2211yescharacteristic, complemented
27Dic499⋊C4C2211yescharacteristic, complemented
28Dic499⋊C4C2211yescharacteristic, complemented
29Dic499⋊C4C2211yescharacteristic, complemented
30Dic499⋊C4C2211yescharacteristic, complemented
31C22⋊Dic499C2211yescharacteristic
32C22⋊Dic499C2211yescharacteristic
33C22⋊Dic499C2211yescharacteristic
34C22⋊Dic499C2211yescharacteristic
35C22⋊Dic499C2211yescharacteristic
36C22⋊Dic499C2211yescharacteristic
37C22⋊Dic499C2211yescharacteristic
38C22⋊Dic499C2211yescharacteristic, complemented
39C22⋊Dic499C2211yescharacteristic, complemented
40(C2×D499)⋊C4C2211yescharacteristic, complemented
41(C2×D499)⋊C4C2211yescharacteristic, complemented
42C4×Dic499C2211yescharacteristic, complemented
43C4×Dic499C2211yescharacteristic, complemented
44C24×C499C2211yescharacteristic
45C2×D4×C499C2211yescharacteristic
46C2×D4×C499C2211yescharacteristic
47C2×D4×C499C2211yescharacteristic
48C22⋊C4×C499C2211yescharacteristic
49C22⋊C4×C499C2211yescharacteristic
50C22⋊C4×C499C2211yescharacteristic
51C22×D499C2311yescharacteristic
52Dic998—41no—
53C22⋊D499—22no—
54C22⋊D499—41no—
55C22⋊D499—41no—
56C22⋊D499—41no—
57C2×Dic499—41no—
58C2×Dic499—41no—
59C2×Dic499—41no—
60C2×Dic499C2311yescharacteristic
61C2×Dic499C2311yescharacteristic
62C2×Dic499C2311yescharacteristic
63C2×Dic499C2311yescharacteristic
64C2×Dic499C2311yescharacteristic
65C2×Dic499C2311yescharacteristic
66C2×Dic499C2311yescharacteristic
67C4×D499—41no—
68C23×C499—22no—
69C23×C499—41no—
70C23×C499—41no—
71C23×C499C2311yescharacteristic
72C23×C499C2311yescharacteristic
73C23×C499C2311yescharacteristic
74C23×C499C2311yescharacteristic
75D4×C499—22no—
76D4×C499—41no—
77D4×C499—41no—
78C2×C4×C499C2311yescharacteristic
79C2×C4×C499C2311yescharacteristic
80C2×C4×C499C2311yescharacteristic
81C22×C499—21no—
82C22×C499—21no—
83C22×C499—21no—
84C22×C499—21no—
85C22×C499—21no—
86C22×C499—21no—
87C22×C499—21no—
88C22×C499—21no—
89C22×C499—21no—
90C22×C499—21no—
91C22×C499—21no—
92C22×C499—44no—
93C22×C499#4112yes—
94C22×C499C2411yescharacteristic
95C2×D499—21no—
96C2×D499—21no—
97C2×D499—21no—
98C4×C499—21no—
99C4×C499—21no—
100C4×C499—21no—
101Dic499—21no—
102Dic499—21no—
103Dic499—21no—
104Dic499—21no—
105Dic499—21no—
106Dic499—21no—
107Dic499—21no—
108C2×C499—22no—
109C2×C499—41no—
110C2×C499—41no—
111C2×C499—41no—
112C2×C499C2×#4111yescharacteristic
113C2×C499H(5,𝔽2)11yescharacteristic
114C2×C499H(5,𝔽2)11yescharacteristic
115D499—41no—
116C499#53811yescharacteristic, complemented, Sylow
117#538—4991nomaximal, Sylow
118#126—4991no—
119#126—4991no—
120#124—4991no—
121#124—4991no—
122#123—4991no—
123#123—4991no—
124C22⋊Q8—4991no—
125#121—4991no—
126#121—4991no—
127#121—4991no—
128#120—4991no—
129#120D49911yescharacteristic, complemented
130C4×D4—4991no—
131C4×D4—4991no—
132C2×C22⋊C4—4991no—
133C24C2×D49911yescharacteristic
134C2×Q8—4991no—
135C2×D4—4991no—
136C2×D4—4991no—
137C2×D4—4991no—
138C2×D4—4991no—
139C2×D4C2×D49911yescharacteristic
140C2×D4C2×D49911yescharacteristic
141C2×D4C2×D49911yescharacteristic
142C22×C4—4991no—
143C22×C4—4991no—
144C22×C4—4991no—
145C22×C4—4991no—
146C4⋊C4—4991no—
147C4⋊C4—4991no—
148C4⋊C4—4991no—
149C4⋊C4—4991no—
150C4⋊C4—4991no—
151C4⋊C4—4991no—
152C22⋊C4—4991no—
153C22⋊C4—4991no—
154C22⋊C4—4991no—
155C22⋊C4—4991no—
156C22⋊C4—4991no—
157C22⋊C4—4991no—
158C22⋊C4—4991no—
159C22⋊C4—4991no—
160C22⋊C4—4991no—
161C22⋊C4—4991no—
162C22⋊C4—4991no—
163C22⋊C4C2×D49911yescharacteristic
164C22⋊C4C2×D49911yescharacteristic
165C22⋊C4C2×D49911yescharacteristic
166C42—4991no—
167C42—4991no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—4991no—
172C23C22×D49911yescharacteristic
173C23C22×D49911yescharacteristic
174C23C22×D49911yescharacteristic
175C23C22×D49911yescharacteristic
176Q8—19961no—
177D4—22no—
178D4—41no—
179D4—41no—
180D4—19961no—
181D4—19961no—
182D4—19961no—
183D4—9982no—
184C2×C4—19961no—
185C2×C4—19961no—
186C2×C4—19961no—
187C2×C4—19961no—
188C2×C4—4991no—
189C2×C4—4991no—
190C2×C4—4991no—
191C2×C4—4991no—
192C2×C4—4991no—
193C2×C4—4991no—
194C2×C4—4991no—
195C2×C4C22×D49911yescharacteristic
196C2×C4C22×D49911yescharacteristic
197C2×C4C22×D49911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22—9981no—
211C22—9981no—
212C22—9981no—
213C22#2254781012yes—
214C22C23×D49911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—9981no—
219C4—9981no—
220C4—9981no—
221C4—9981no—
222C4—9981no—
223C4—9981no—
224C4—9981no—
225C2—22no—
226C2—41no—
227C2—41no—
228C2—41no—
229C2—19961no—
230C2C2×#2254781011yescharacteristic
231C2#3063039611yescharacteristic
232C2#3063039611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#120×C499C2
hypercenter#120D499
hypocenterC499#538
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #30630344C2semidirect
2. #30630344C2semidirect
3. #30630338C2semidirect
4. #30630337C2semidirect
5. #30630333C2semidirect
6. #30630332C2semidirect
7. #30630328C2semidirect
8. #30630323C2semidirect
9. #30630323C2semidirect
10. #30630322C2semidirect
11. #30630320C2semidirect
12. D4×Dic499C2semidirect
13. (C22⋊D499)⋊C4C2semidirect
14. C2×C22⋊Dic499C2semidirect
15. #120×C499C2semidirect
16. C2×Dic998C22semidirect
20. C2×C22⋊D499C22semidirect
23. C22×Dic499C22semidirect
24. C2×C4×D499C22semidirect
25. C4⋊Dic499C22semidirect
26. C4⋊Dic499C22semidirect
27. Dic499⋊C4C22semidirect
28. Dic499⋊C4C22semidirect
29. Dic499⋊C4C22semidirect
30. Dic499⋊C4C22semidirect
38. C22⋊Dic499C22semidirect
39. C22⋊Dic499C22semidirect
40. (C2×D499)⋊C4C22semidirect
41. (C2×D499)⋊C4C22semidirect
42. C4×Dic499C22semidirect
43. C4×Dic499C22semidirect
116. C499#538semidirect
129. #120D499semidirect

Maximal subgroups

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

subgroupindex
#306303442
#306303382
#306303372
#306303332
#306303322
#306303282
#306303232
#306303222
#306303202
D4×Dic4992
(C22⋊D499)⋊C42
C2×C22⋊Dic4992
#120×C4992
#538499