Finite Group Databasebeta

← #15689797

Subgroups — #15689797

Order 3008.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#13094019C211yesmaximal, characteristic, complemented
2#13094018C211yesmaximal, characteristic, complemented
3#13094012C211yesmaximal, characteristic, complemented
4#13094009C211yesmaximal, characteristic, complemented
5#13094009C211yesmaximal, characteristic, complemented
6#13094007C211yesmaximal, characteristic, complemented
7#13094002C211yesmaximal, characteristic, complemented
8#13094001C211yesmaximal, characteristic, complemented
9#13093994C211yesmaximal, characteristic
10C4×D188C211yesmaximal, characteristic, complemented
11(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
12#13093981C211yesmaximal, characteristic, complemented
13C2×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D47C211yesmaximal, characteristic, complemented
15#117×C47C211yesmaximal, characteristic, complemented
16C23×D47C2211yescharacteristic
17C22×C4×C47C2211yescharacteristic
18C2×C22⋊D47C2211yescharacteristic
19C22×Dic47C2211yescharacteristic
20C2×D188C2211yescharacteristic
21C2×D188C2211yescharacteristic
22C2×C4×D47C2211yescharacteristic
23C2×C4×D47C2211yescharacteristic
24C2×C4×D47C2211yescharacteristic, complemented
25C2×Dic94C2211yescharacteristic, complemented
26C4⋊C4×C47C2211yescharacteristic, complemented
27C4⋊C4×C47C2211yescharacteristic, complemented
28C22⋊C4×C47C2211yescharacteristic
29C22⋊C4×C47C2211yescharacteristic
30C42×C47C2211yescharacteristic, complemented
31C42×C47C2211yescharacteristic, complemented
32C22⋊Dic47C2211yescharacteristic
33(C2×D47)⋊C4C2211yescharacteristic
34(C2×D47)⋊C4C2211yescharacteristic
35(C2×D47)⋊C4C2211yescharacteristic
36(C2×D47)⋊C4C2211yescharacteristic
37(C2×D47)⋊C4C2211yescharacteristic
38(C2×D47)⋊C4C2211yescharacteristic
39(C2×D47)⋊C4C2211yescharacteristic
40(C2×D47)⋊C4C2211yescharacteristic
41(C2×D47)⋊C4C2211yescharacteristic, complemented
42(C2×D47)⋊C4C2211yescharacteristic, complemented
43(C2×D47)⋊C4C2211yescharacteristic, complemented
44C4⋊Dic47C2211yescharacteristic, complemented
45Dic47⋊C4C2211yescharacteristic, complemented
46Dic47⋊C4C2211yescharacteristic, complemented
47Dic47⋊C4C2211yescharacteristic, complemented
48Dic47⋊C4C2211yescharacteristic, complemented
49Dic47⋊C4C2211yescharacteristic, complemented
50C4×Dic47C2211yescharacteristic, complemented
51C23×C47C2311yescharacteristic
52C22×D47—22no—
53C22×D47—22no—
54C22×D47—41no—
55C22×D47C2311yescharacteristic
56C22×D47C2311yescharacteristic
57C22×D47C2311yescharacteristic
58C2×C4×C47—22no—
59C2×C4×C47C2311yescharacteristic
60C2×C4×C47C2311yescharacteristic
61C2×C4×C47C2311yescharacteristic
62C2×C4×C47C2311yescharacteristic
63C2×C4×C47C2311yescharacteristic
64C2×C4×C47C2311yescharacteristic
65C22⋊D47—22no—
66C2×Dic47—41no—
67C2×Dic47C2311yescharacteristic
68C2×Dic47C2311yescharacteristic
69C2×Dic47C2311yescharacteristic
70C2×Dic47C2311yescharacteristic
71C2×Dic47C2311yescharacteristic
72D188—22no—
73D188—41no—
74C4×D47—22no—
75C4×D47—41no—
76C4×D47—41no—
77Dic94—41no—
78C22×C47—21no—
79C22×C47—21no—
80C22×C47#4112yes—
81C22×C47C2411yescharacteristic
82C2×D47—21no—
83C2×D47—21no—
84C2×D47—21no—
85C2×D47—21no—
86C2×D47—21no—
87C2×D47—21no—
88C2×D47—21no—
89C2×D47—21no—
90C2×D47—44no—
91C2×D47#4112yes—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—21no—
95C4×C47—21no—
96C4×C47—21no—
97C4×C47—21no—
98Dic47—21no—
99Dic47—21no—
100Dic47—21no—
101Dic47—21no—
102Dic47—21no—
103C2×C47—22no—
104C2×C47C2×#4111yescharacteristic
105C2×C47C2×#4111yescharacteristic
106C2×C47H(5,𝔽2)11yescharacteristic
107D47—22no—
108D47—41no—
109D47—41no—
110#551—471nomaximal, Sylow
111C47#55111yescharacteristic, complemented, Sylow
112#126—471no—
113#126—471no—
114#124—471no—
115#123—471no—
116#123—471no—
117#123—471no—
118C22⋊Q8—471no—
119C22⋊Q8—471no—
120#120—471no—
121C4×D4—471no—
122C4×D4—471no—
123#117—471no—
124#117D4711yescharacteristic, complemented
125C2×C22⋊C4—471no—
126C2×C22⋊C4—471no—
127C24—471no—
128C2×Q8—471no—
129C2×D4—471no—
130C2×D4—471no—
131C2×D4—471no—
132C22×C4—471no—
133C22×C4—471no—
134C22×C4—471no—
135C22×C4—471no—
136C22×C4C2×D4711yescharacteristic
137C4⋊C4—471no—
138C4⋊C4—471no—
139C4⋊C4—471no—
140C4⋊C4—471no—
141C4⋊C4—471no—
142C4⋊C4—471no—
143C4⋊C4C2×D4711yescharacteristic, complemented
144C4⋊C4C2×D4711yescharacteristic, complemented
145C22⋊C4—471no—
146C22⋊C4—471no—
147C22⋊C4—471no—
148C22⋊C4—471no—
149C22⋊C4—471no—
150C22⋊C4—471no—
151C22⋊C4—471no—
152C22⋊C4—471no—
153C22⋊C4—471no—
154C22⋊C4—471no—
155C22⋊C4—471no—
156C22⋊C4—471no—
157C22⋊C4C2×D4711yescharacteristic
158C22⋊C4C2×D4711yescharacteristic
159C42—471no—
160C42C2×D4711yescharacteristic, complemented
161C42C2×D4711yescharacteristic, complemented
162C23—471no—
163C23—471no—
164C23—471no—
165C23—942no—
166C23—942no—
167C23—1881no—
168C23C22×D4711yescharacteristic
169Q8—1881no—
170D4—942no—
171D4—942no—
172D4—1881no—
173C2×C4—22no—
174C2×C4—471no—
175C2×C4—471no—
176C2×C4—471no—
177C2×C4—471no—
178C2×C4—471no—
179C2×C4—942no—
180C2×C4—1881no—
181C2×C4—1881no—
182C2×C4—1881no—
183C2×C4C22×D4711yescharacteristic
184C2×C4C22×D4711yescharacteristic
185C2×C4C22×D4711yescharacteristic
186C2×C4C22×D4711yescharacteristic
187C2×C4C22×D4711yescharacteristic
188C2×C4C22×D4711yescharacteristic
189C22—21no—
190C22—21no—
191C22—472no—
192C22—941no—
193C22—941no—
194C22—941no—
195C22—941no—
196C22—941no—
197C22—941no—
198C22—941no—
199C22—941no—
200C22—1884no—
201C22#1062535012yes—
202C22C23×D4711yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—941no—
210C4—941no—
211C4—941no—
212C4—941no—
213C4—941no—
214C2—22no—
215C2—942no—
216C2—1881no—
217C2—1881no—
218C2#41×D4711yescharacteristic
219C2C2×#1062535011yescharacteristic
220C2#1309407011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
Fitting#117×C47C2
prime radical#13093994C2
hypercenter#117D47
hypocenterC47#551
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #13094019C2semidirect
2. #13094018C2semidirect
3. #13094012C2semidirect
4. #13094009C2semidirect
5. #13094009C2semidirect
6. #13094007C2semidirect
7. #13094002C2semidirect
8. #13094001C2semidirect
10. C4×D188C2semidirect
11. (C22⋊D47)⋊C4C2semidirect
12. #13093981C2semidirect
13. C2×(C2×D47)⋊C4C2semidirect
14. C22⋊C4×D47C2semidirect
15. #117×C47C2semidirect
24. C2×C4×D47C22semidirect
25. C2×Dic94C22semidirect
26. C4⋊C4×C47C22semidirect
27. C4⋊C4×C47C22semidirect
30. C42×C47C22semidirect
31. C42×C47C22semidirect
41. (C2×D47)⋊C4C22semidirect
42. (C2×D47)⋊C4C22semidirect
43. (C2×D47)⋊C4C22semidirect
44. C4⋊Dic47C22semidirect
45. Dic47⋊C4C22semidirect
46. Dic47⋊C4C22semidirect
47. Dic47⋊C4C22semidirect
48. Dic47⋊C4C22semidirect
49. Dic47⋊C4C22semidirect
50. C4×Dic47C22semidirect
111. C47#551semidirect
124. #117D47semidirect
143. C4⋊C4C2×D47semidirect
144. C4⋊C4C2×D47semidirect
160. C42C2×D47semidirect
161. C42C2×D47semidirect

Maximal subgroups

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

subgroupindex
#130940192
#130940182
#130940122
#130940092
#130940072
#130940022
#130940012
#130939942
C4×D1882
(C22⋊D47)⋊C42
#130939812
C2×(C2×D47)⋊C42
C22⋊C4×D472
#117×C472
#55147