Finite Group Databasebeta

← #15689712

Subgroups — #15689712

Order 3008.

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#13094019C211yesmaximal, characteristic, complemented
2#13094012C211yesmaximal, characteristic, complemented
3#13094010C211yesmaximal, characteristic, complemented
4#13094009C211yesmaximal, characteristic, complemented
5#13094006C211yesmaximal, characteristic, complemented
6#13094002C211yesmaximal, characteristic, complemented
7#13093999C211yesmaximal, characteristic, complemented
8#13093999C211yesmaximal, characteristic, complemented
9#13093997C211yesmaximal, characteristic, complemented
10#13093994C211yesmaximal, characteristic, complemented
11#13093994C211yesmaximal, characteristic, complemented
12C4×D188C211yesmaximal, characteristic, complemented
13#13093986C211yesmaximal, characteristic, complemented
14C22⋊C4×D47C211yesmaximal, characteristic, complemented
15#126×C47C211yesmaximal, characteristic, complemented
16C23×D47C2211yescharacteristic
17C2×C22⋊D47C2211yescharacteristic
18C2×C22⋊D47C2211yescharacteristic
19C2×D188C2211yescharacteristic
20C2×D188C2211yescharacteristic
21C2×D188C2211yescharacteristic
22C2×D188C2211yescharacteristic
23C2×D188C2211yescharacteristic, complemented
24C2×C4×D47C2211yescharacteristic
25C2×C4×D47C2211yescharacteristic
26C2×C4×D47C2211yescharacteristic, complemented
27C2×C4×D47C2211yescharacteristic, complemented
28C2×Dic94C2211yescharacteristic, complemented
29C4⋊C4×C47C2211yescharacteristic, complemented
30C4⋊C4×C47C2211yescharacteristic, complemented
31C4⋊C4×C47C2211yescharacteristic, complemented
32C22⋊C4×C47C2211yescharacteristic
33C22⋊C4×C47C2211yescharacteristic
34C22⋊C4×C47C2211yescharacteristic
35C42×C47C2211yescharacteristic, complemented
36C22⋊Dic47C2211yescharacteristic
37(C2×D47)⋊C4C2211yescharacteristic
38(C2×D47)⋊C4C2211yescharacteristic
39(C2×D47)⋊C4C2211yescharacteristic
40(C2×D47)⋊C4C2211yescharacteristic
41(C2×D47)⋊C4C2211yescharacteristic
42(C2×D47)⋊C4C2211yescharacteristic
43(C2×D47)⋊C4C2211yescharacteristic, complemented
44(C2×D47)⋊C4C2211yescharacteristic, complemented
45(C2×D47)⋊C4C2211yescharacteristic, complemented
46(C2×D47)⋊C4C2211yescharacteristic, complemented
47C4⋊Dic47C2211yescharacteristic, complemented
48Dic47⋊C4C2211yescharacteristic, complemented
49Dic47⋊C4C2211yescharacteristic, complemented
50C4×Dic47C2211yescharacteristic, complemented
51C23×C47C2311yescharacteristic
52C22×D47—22no—
53C22×D47—41no—
54C22×D47—41no—
55C22×D47C2311yescharacteristic
56C22×D47C2311yescharacteristic
57C22×D47C2311yescharacteristic
58C22×D47C2311yescharacteristic
59C2×C4×C47C2311yescharacteristic
60C2×C4×C47C2311yescharacteristic
61C2×C4×C47C2311yescharacteristic
62C2×C4×C47C2311yescharacteristic
63C2×C4×C47C2311yescharacteristic
64C2×C4×C47C2311yescharacteristic
65C22⋊D47—41no—
66C22⋊D47—41no—
67C2×Dic47C2311yescharacteristic
68C2×Dic47C2311yescharacteristic
69C2×Dic47C2311yescharacteristic
70C2×Dic47C2311yescharacteristic
71D188—22no—
72D188—22no—
73D188—41no—
74D188—41no—
75D188—41no—
76C4×D47—41no—
77C4×D47—41no—
78C4×D47—41no—
79C4×D47—41no—
80Dic94—41no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47C2411yescharacteristic
85C2×D47—21no—
86C2×D47—21no—
87C2×D47—21no—
88C2×D47—21no—
89C2×D47—21no—
90C2×D47—21no—
91C2×D47—21no—
92C2×D47—21no—
93C2×D47—21no—
94C2×D47—21no—
95C2×D47—21no—
96C2×D47—44no—
97C2×D47#4112yes—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—21no—
104Dic47—21no—
105Dic47—21no—
106Dic47—21no—
107Dic47—21no—
108C2×C47—41no—
109C2×C47C2×#4111yescharacteristic
110C2×C47H(5,𝔽2)11yescharacteristic
111C2×C47H(5,𝔽2)11yescharacteristic
112D47—22no—
113D47—41no—
114D47—41no—
115D47—41no—
116#538—471nomaximal, Sylow
117C47#53811yescharacteristic, complemented, Sylow
118#126—471no—
119#126D4711yescharacteristic, complemented
120#124—471no—
121#124—471no—
122#123—471no—
123#123—471no—
124C22⋊Q8—471no—
125#121—471no—
126#121—471no—
127#121—471no—
128#120—471no—
129#120—471no—
130C4×D4—471no—
131C4×D4—471no—
132C2×C22⋊C4—471no—
133C24—471no—
134C2×Q8—471no—
135C2×D4—471no—
136C2×D4—471no—
137C2×D4—471no—
138C2×D4—471no—
139C2×D4—471no—
140C2×D4—471no—
141C2×D4—471no—
142C22×C4—471no—
143C22×C4—471no—
144C22×C4—471no—
145C22×C4—471no—
146C4⋊C4—471no—
147C4⋊C4—471no—
148C4⋊C4—471no—
149C4⋊C4C2×D4711yescharacteristic, complemented
150C4⋊C4C2×D4711yescharacteristic, complemented
151C4⋊C4C2×D4711yescharacteristic, complemented
152C22⋊C4—471no—
153C22⋊C4—471no—
154C22⋊C4—471no—
155C22⋊C4—471no—
156C22⋊C4—471no—
157C22⋊C4—471no—
158C22⋊C4—471no—
159C22⋊C4—471no—
160C22⋊C4—471no—
161C22⋊C4—471no—
162C22⋊C4—471no—
163C22⋊C4C2×D4711yescharacteristic
164C22⋊C4C2×D4711yescharacteristic
165C22⋊C4C2×D4711yescharacteristic
166C42—471no—
167C42C2×D4711yescharacteristic, complemented
168C23—471no—
169C23—471no—
170C23—471no—
171C23—471no—
172C23—942no—
173C23—1881no—
174C23—1881no—
175C23C22×D4711yescharacteristic
176Q8—1881no—
177D4—942no—
178D4—942no—
179D4—1881no—
180D4—1881no—
181D4—1881no—
182D4—1881no—
183D4—1881no—
184C2×C4—471no—
185C2×C4—471no—
186C2×C4—471no—
187C2×C4—471no—
188C2×C4—1881no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4—1881no—
192C2×C4C22×D4711yescharacteristic
193C2×C4C22×D4711yescharacteristic
194C2×C4C22×D4711yescharacteristic
195C2×C4C22×D4711yescharacteristic
196C2×C4C22×D4711yescharacteristic
197C2×C4C22×D4711yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—472no—
202C22—941no—
203C22—941no—
204C22—941no—
205C22—941no—
206C22—941no—
207C22—941no—
208C22—941no—
209C22—941no—
210C22—941no—
211C22—941no—
212C22—941no—
213C22—1884no—
214C22C23×D4711yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—941no—
222C4—941no—
223C4—941no—
224C4—941no—
225C2—41no—
226C2—942no—
227C2—1881no—
228C2—1881no—
229C2—1881no—
230C2#41×D4711yescharacteristic
231C2#1309407011yescharacteristic
232C2#1309407011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
Fitting#126×C47C2
hypercenter#126D47
hypocenterC47#538
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #13094019C2semidirect
2. #13094012C2semidirect
3. #13094010C2semidirect
4. #13094009C2semidirect
5. #13094006C2semidirect
6. #13094002C2semidirect
7. #13093999C2semidirect
8. #13093999C2semidirect
9. #13093997C2semidirect
10. #13093994C2semidirect
11. #13093994C2semidirect
12. C4×D188C2semidirect
13. #13093986C2semidirect
14. C22⋊C4×D47C2semidirect
15. #126×C47C2semidirect
23. C2×D188C22semidirect
26. C2×C4×D47C22semidirect
27. C2×C4×D47C22semidirect
28. C2×Dic94C22semidirect
29. C4⋊C4×C47C22semidirect
30. C4⋊C4×C47C22semidirect
31. C4⋊C4×C47C22semidirect
35. C42×C47C22semidirect
43. (C2×D47)⋊C4C22semidirect
44. (C2×D47)⋊C4C22semidirect
45. (C2×D47)⋊C4C22semidirect
46. (C2×D47)⋊C4C22semidirect
47. C4⋊Dic47C22semidirect
48. Dic47⋊C4C22semidirect
49. Dic47⋊C4C22semidirect
50. C4×Dic47C22semidirect
117. C47#538semidirect
119. #126D47semidirect
149. C4⋊C4C2×D47semidirect
150. C4⋊C4C2×D47semidirect
151. C4⋊C4C2×D47semidirect
167. C42C2×D47semidirect

Maximal subgroups

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

subgroupindex
#130940192
#130940122
#130940102
#130940092
#130940062
#130940022
#130939992
#130939972
#130939942
C4×D1882
#130939862
C22⋊C4×D472
#126×C472
#53847