Finite Group Databasebeta

← #44543682

Subgroups — #44543682

Order 31936.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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#30630345C211yesmaximal, characteristic, complemented
2#30630344C211yesmaximal, characteristic, complemented
3#30630340C211yesmaximal, characteristic, complemented
4#30630335C211yesmaximal, characteristic, complemented
5#30630333C211yesmaximal, characteristic, complemented
6#30630327C211yesmaximal, characteristic, complemented
7#30630324C211yesmaximal, characteristic, complemented
8#30630324C211yesmaximal, characteristic, complemented
9#30630323C211yesmaximal, characteristic, complemented
10#30630321C211yesmaximal, characteristic, complemented
11#30630319C211yesmaximal, characteristic, complemented
12C4×D1996C211yesmaximal, characteristic, complemented
13(C22⋊D499)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D499C211yesmaximal, characteristic, complemented
15#124×C499C211yesmaximal, characteristic, complemented
16C23×D499C2211yescharacteristic
17C2×D1996C2211yescharacteristic
18C2×D1996C2211yescharacteristic
19C2×C22⋊D499C2211yescharacteristic
20C2×C22⋊D499C2211yescharacteristic
21C2×C22⋊D499C2211yescharacteristic
22C2×C22⋊D499C2211yescharacteristic, complemented
23C22×Dic499C2211yescharacteristic, complemented
24C2×C4×D499C2211yescharacteristic
25C2×C4×D499C2211yescharacteristic
26C2×C4×D499C2211yescharacteristic, complemented
27C4⋊Dic499C2211yescharacteristic, complemented
28C4⋊Dic499C2211yescharacteristic, complemented
29Dic499⋊C4C2211yescharacteristic, complemented
30Dic499⋊C4C2211yescharacteristic, complemented
31Dic499⋊C4C2211yescharacteristic, complemented
32Dic499⋊C4C2211yescharacteristic, complemented
33C22⋊Dic499C2211yescharacteristic
34C22⋊Dic499C2211yescharacteristic
35(C2×D499)⋊C4C2211yescharacteristic
36(C2×D499)⋊C4C2211yescharacteristic
37(C2×D499)⋊C4C2211yescharacteristic
38(C2×D499)⋊C4C2211yescharacteristic
39(C2×D499)⋊C4C2211yescharacteristic
40(C2×D499)⋊C4C2211yescharacteristic
41(C2×D499)⋊C4C2211yescharacteristic, complemented
42(C2×D499)⋊C4C2211yescharacteristic, complemented
43C4×Dic499C2211yescharacteristic, complemented
44C2×Q8×C499C2211yescharacteristic, complemented
45C2×D4×C499C2211yescharacteristic
46C22⋊C4×C499C2211yescharacteristic
47C22⋊C4×C499C2211yescharacteristic
48C22⋊C4×C499C2211yescharacteristic, complemented
49C22⋊C4×C499C2211yescharacteristic, complemented
50C42×C499C2211yescharacteristic, complemented
51C22×D499—22no—
52C22×D499—41no—
53C22×D499—41no—
54C22×D499C2311yescharacteristic
55C22×D499C2311yescharacteristic
56C22×D499C2311yescharacteristic
57D1996—22no—
58D1996—41no—
59C22⋊D499—22no—
60C22⋊D499—41no—
61C22⋊D499—41no—
62C22⋊D499—41no—
63C2×Dic499—41no—
64C2×Dic499C2311yescharacteristic
65C2×Dic499C2311yescharacteristic
66C2×Dic499C2311yescharacteristic
67C2×Dic499C2311yescharacteristic
68C2×Dic499C2311yescharacteristic
69C4×D499—41no—
70C4×D499—41no—
71C4×D499—41no—
72C23×C499C2311yescharacteristic
73C23×C499C2311yescharacteristic
74Q8×C499—41no—
75D4×C499—41no—
76C2×C4×C499C2311yescharacteristic
77C2×C4×C499C2311yescharacteristic
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×C499C2411yescharacteristic
88C2×D499—21no—
89C2×D499—21no—
90C2×D499—21no—
91C2×D499—21no—
92C2×D499—21no—
93C2×D499—21no—
94C2×D499—21no—
95C2×D499—21no—
96C2×D499—44no—
97C2×D499#4112yes—
98C4×C499—21no—
99C4×C499—21no—
100C4×C499—21no—
101C4×C499—21no—
102C4×C499—21no—
103Dic499—21no—
104Dic499—21no—
105Dic499—21no—
106Dic499—21no—
107Dic499—21no—
108C2×C499—41no—
109C2×C499—41no—
110C2×C499C2×#4111yescharacteristic
111C2×C499H(5,𝔽2)11yescharacteristic
112C2×C499H(5,𝔽2)11yescharacteristic
113D499—22no—
114D499—41no—
115D499—41no—
116C499#53811yescharacteristic, complemented, Sylow
117#538—4991nomaximal, Sylow
118#126—4991no—
119#126—4991no—
120#124—4991no—
121#124D49911yescharacteristic, complemented
122#123—4991no—
123#123—4991no—
124C22⋊Q8—4991no—
125#121—4991no—
126#121—4991no—
127#121—4991no—
128#120—4991no—
129#120—4991no—
130C4×D4—4991no—
131C4×D4—4991no—
132C2×C22⋊C4—4991no—
133C24—4991no—
134C2×Q8C2×D49911yescharacteristic, complemented
135C2×D4—4991no—
136C2×D4—4991no—
137C2×D4—4991no—
138C2×D4—4991no—
139C2×D4—4991no—
140C2×D4—4991no—
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⋊C4C2×D49911yescharacteristic
163C22⋊C4C2×D49911yescharacteristic
164C22⋊C4C2×D49911yescharacteristic, complemented
165C22⋊C4C2×D49911yescharacteristic, complemented
166C42—4991no—
167C42C2×D49911yescharacteristic, complemented
168C23—19961no—
169C23—19961no—
170C23—9982no—
171C23—4991no—
172C23—4991no—
173C23—4991no—
174C23C22×D49911yescharacteristic
175C23C22×D49911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—19961no—
179D4—19961no—
180D4—19961no—
181D4—19961no—
182D4—9982no—
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×C4C22×D49911yescharacteristic
194C2×C4C22×D49911yescharacteristic
195C2×C4C22×D49911yescharacteristic
196C2×C4C22×D49911yescharacteristic
197C2×C4C22×D49911yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—19964no—
205C22—9981no—
206C22—9981no—
207C22—9981no—
208C22—9981no—
209C22—9981no—
210C22—9981no—
211C22—9981no—
212C22—9981no—
213C22—4992no—
214C22C23×D49911yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—9981no—
221C4—9981no—
222C4—9981no—
223C4—9981no—
224C4—9981no—
225C2—41no—
226C2—41no—
227C2—19961no—
228C2—19961no—
229C2—9982no—
230C2#41×D49911yescharacteristic
231C2#3063039611yescharacteristic
232C2#3063039711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D499
commutator, socle, cosocleC22×C499C24
Fitting#124×C499C2
hypercenter#124D499
hypocenterC499#538
LCSG ▷ C22×C499 ▷ C499
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #30630345C2semidirect
2. #30630344C2semidirect
3. #30630340C2semidirect
4. #30630335C2semidirect
5. #30630333C2semidirect
6. #30630327C2semidirect
7. #30630324C2semidirect
8. #30630324C2semidirect
9. #30630323C2semidirect
10. #30630321C2semidirect
11. #30630319C2semidirect
12. C4×D1996C2semidirect
13. (C22⋊D499)⋊C4C2semidirect
14. C22⋊C4×D499C2semidirect
15. #124×C499C2semidirect
22. C2×C22⋊D499C22semidirect
23. C22×Dic499C22semidirect
26. C2×C4×D499C22semidirect
27. C4⋊Dic499C22semidirect
28. C4⋊Dic499C22semidirect
29. Dic499⋊C4C22semidirect
30. Dic499⋊C4C22semidirect
31. Dic499⋊C4C22semidirect
32. Dic499⋊C4C22semidirect
41. (C2×D499)⋊C4C22semidirect
42. (C2×D499)⋊C4C22semidirect
43. C4×Dic499C22semidirect
44. C2×Q8×C499C22semidirect
48. C22⋊C4×C499C22semidirect
49. C22⋊C4×C499C22semidirect
50. C42×C499C22semidirect
116. C499#538semidirect
121. #124D499semidirect
134. C2×Q8C2×D499semidirect
164. C22⋊C4C2×D499semidirect
165. C22⋊C4C2×D499semidirect
167. C42C2×D499semidirect

Maximal subgroups

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

subgroupindex
#306303452
#306303442
#306303402
#306303352
#306303332
#306303272
#306303242
#306303232
#306303212
#306303192
C4×D19962
(C22⋊D499)⋊C42
C22⋊C4×D4992
#124×C4992
#538499