Finite Group Databasebeta

← #15689861

Subgroups — #15689861

Order 3008.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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#13094020C211yesmaximal, characteristic, complemented
2#13094019C211yesmaximal, characteristic, complemented
3#13094017C211yesmaximal, characteristic, complemented
4#13094009C211yesmaximal, characteristic, complemented
5#13094008C211yesmaximal, characteristic, complemented
6#13094007C211yesmaximal, characteristic, complemented
7#13093998C211yesmaximal, characteristic, complemented
8#13093997C211yesmaximal, characteristic, complemented
9#13093996C211yesmaximal, characteristic, complemented
10#13093996C211yesmaximal, characteristic, complemented
11#13093995C211yesmaximal, characteristic, complemented
12#13093994C211yesmaximal, characteristic, complemented
13#13093992C211yesmaximal, characteristic, complemented
14#13093992C211yesmaximal, characteristic, complemented
15#121×C47C211yesmaximal, characteristic, complemented
16C23×D47C2211yescharacteristic
17C2×D4×C47C2211yescharacteristic
18C2×D4×C47C2211yescharacteristic
19C2×D4×C47C2211yescharacteristic, complemented
20C22×C4×C47C2211yescharacteristic, complemented
21C2×C22⋊D47C2211yescharacteristic
22C2×C22⋊D47C2211yescharacteristic
23C2×C22⋊D47C2211yescharacteristic
24C2×C22⋊D47C2211yescharacteristic
25C2×C22⋊D47C2211yescharacteristic
26C2×C22⋊D47C2211yescharacteristic, complemented
27C2×C22⋊D47C2211yescharacteristic, complemented
28C22×Dic47C2211yescharacteristic, complemented
29C2×D188C2211yescharacteristic
30C2×D188C2211yescharacteristic
31C2×C4×D47C2211yescharacteristic, complemented
32C4⋊C4×C47C2211yescharacteristic, complemented
33C22⋊C4×C47C2211yescharacteristic
34C22⋊C4×C47C2211yescharacteristic, complemented
35C22⋊Dic47C2211yescharacteristic
36C22⋊Dic47C2211yescharacteristic
37C22⋊Dic47C2211yescharacteristic, complemented
38(C2×D47)⋊C4C2211yescharacteristic
39(C2×D47)⋊C4C2211yescharacteristic
40(C2×D47)⋊C4C2211yescharacteristic
41(C2×D47)⋊C4C2211yescharacteristic
42(C2×D47)⋊C4C2211yescharacteristic
43(C2×D47)⋊C4C2211yescharacteristic
44(C2×D47)⋊C4C2211yescharacteristic, complemented
45C4⋊Dic47C2211yescharacteristic, complemented
46C4⋊Dic47C2211yescharacteristic, complemented
47Dic47⋊C4C2211yescharacteristic, complemented
48Dic47⋊C4C2211yescharacteristic, complemented
49Dic47⋊C4C2211yescharacteristic, complemented
50C4×Dic47C2211yescharacteristic, complemented
51C23×C47C2311yescharacteristic
52C23×C47C2311yescharacteristic
53C23×C47C2311yescharacteristic
54C22×D47—41no—
55C22×D47—41no—
56C22×D47—41no—
57C22×D47C2311yescharacteristic
58C22×D47C2311yescharacteristic
59C22×D47C2311yescharacteristic
60D4×C47—41no—
61D4×C47—41no—
62D4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C2311yescharacteristic
65C2×C4×C47C2311yescharacteristic
66C2×C4×C47C2311yescharacteristic
67C2×C4×C47C2311yescharacteristic
68C22⋊D47—41no—
69C22⋊D47—41no—
70C22⋊D47—41no—
71C22⋊D47—41no—
72C22⋊D47—41no—
73C22⋊D47—41no—
74C22⋊D47—41no—
75C2×Dic47—41no—
76C2×Dic47C2311yescharacteristic
77C2×Dic47C2311yescharacteristic
78C2×Dic47C2311yescharacteristic
79C2×Dic47C2311yescharacteristic
80C2×Dic47C2311yescharacteristic
81D188—41no—
82D188—41no—
83C4×D47—41no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47C2411yescharacteristic
94C2×D47—21no—
95C2×D47—21no—
96C2×D47—21no—
97C2×D47—21no—
98C2×D47—21no—
99C2×D47—21no—
100C2×D47—21no—
101C2×D47—21no—
102C2×D47—21no—
103C2×D47—44no—
104C4×C47—21no—
105C4×C47—21no—
106C4×C47—21no—
107C4×C47—21no—
108Dic47—21no—
109Dic47—21no—
110Dic47—21no—
111Dic47—21no—
112Dic47—21no—
113C2×C47—41no—
114C2×C47—41no—
115C2×C47—41no—
116C2×C47H(5,𝔽2)11yescharacteristic
117C2×C47H(5,𝔽2)11yescharacteristic
118C2×C47H(5,𝔽2)11yescharacteristic
119D47—41no—
120D47—41no—
121D47—41no—
122#560—471nomaximal, Sylow
123C47#56011yescharacteristic, complemented, Sylow
124#127—471no—
125#126—471no—
126#126—471no—
127#123—471no—
128#123—471no—
129#123—471no—
130#121—471no—
131#121—471no—
132#121—471no—
133#121—471no—
134#121—471no—
135#121D4711yescharacteristic, complemented
136#120—471no—
137#120—471no—
138#120—471no—
139C24—471no—
140C2×D4—471no—
141C2×D4—471no—
142C2×D4—471no—
143C2×D4—471no—
144C2×D4—471no—
145C2×D4—471no—
146C2×D4—471no—
147C2×D4—471no—
148C2×D4—471no—
149C2×D4C2×D4711yescharacteristic
150C2×D4C2×D4711yescharacteristic
151C2×D4C2×D4711yescharacteristic, complemented
152C22×C4—471no—
153C22×C4—471no—
154C22×C4C2×D4711yescharacteristic, complemented
155C4⋊C4—471no—
156C4⋊C4—471no—
157C4⋊C4—471no—
158C4⋊C4—471no—
159C4⋊C4—471no—
160C4⋊C4C2×D4711yescharacteristic, complemented
161C22⋊C4—471no—
162C22⋊C4—471no—
163C22⋊C4—471no—
164C22⋊C4—471no—
165C22⋊C4—471no—
166C22⋊C4—471no—
167C22⋊C4—471no—
168C22⋊C4—471no—
169C22⋊C4—471no—
170C22⋊C4—471no—
171C22⋊C4C2×D4711yescharacteristic
172C22⋊C4C2×D4711yescharacteristic, complemented
173C42—471no—
174C23—471no—
175C23—471no—
176C23—471no—
177C23—1881no—
178C23—1881no—
179C23—1881no—
180C23C22×D4711yescharacteristic
181C23C22×D4711yescharacteristic
182C23C22×D4711yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—1881no—
187D4—1881no—
188D4—1881no—
189D4—1881no—
190D4—1881no—
191D4—1881no—
192D4—1881no—
193D4—1881no—
194D4—1881no—
195C2×C4—41no—
196C2×C4—471no—
197C2×C4—471no—
198C2×C4—471no—
199C2×C4—471no—
200C2×C4—471no—
201C2×C4—1881no—
202C2×C4—1881no—
203C2×C4C22×D4711yescharacteristic
204C2×C4C22×D4711yescharacteristic
205C2×C4C22×D4711yescharacteristic
206C2×C4C22×D4711yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—941no—
217C22—941no—
218C22—941no—
219C22—941no—
220C22—941no—
221C22—941no—
222C22—941no—
223C22—941no—
224C22—941no—
225C22—1884no—
226C22C23×D4711yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—941no—
232C4—941no—
233C4—941no—
234C4—941no—
235C4—941no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—1881no—
240C2—1881no—
241C2—1881no—
242C2#1309406911yescharacteristic
243C2#1309406911yescharacteristic
244C2#1309407011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D47
commutator, socle, cosocleC22×C47C24
Fitting#121×C47C2
hypercenter#121D47
hypocenterC47#560
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #13094020C2semidirect
2. #13094019C2semidirect
3. #13094017C2semidirect
4. #13094009C2semidirect
5. #13094008C2semidirect
6. #13094007C2semidirect
7. #13093998C2semidirect
8. #13093997C2semidirect
9. #13093996C2semidirect
10. #13093996C2semidirect
11. #13093995C2semidirect
12. #13093994C2semidirect
13. #13093992C2semidirect
14. #13093992C2semidirect
15. #121×C47C2semidirect
19. C2×D4×C47C22semidirect
20. C22×C4×C47C22semidirect
26. C2×C22⋊D47C22semidirect
27. C2×C22⋊D47C22semidirect
28. C22×Dic47C22semidirect
31. C2×C4×D47C22semidirect
32. C4⋊C4×C47C22semidirect
34. C22⋊C4×C47C22semidirect
37. C22⋊Dic47C22semidirect
44. (C2×D47)⋊C4C22semidirect
45. C4⋊Dic47C22semidirect
46. C4⋊Dic47C22semidirect
47. Dic47⋊C4C22semidirect
48. Dic47⋊C4C22semidirect
49. Dic47⋊C4C22semidirect
50. C4×Dic47C22semidirect
123. C47#560semidirect
135. #121D47semidirect
151. C2×D4C2×D47semidirect
154. C22×C4C2×D47semidirect
160. C4⋊C4C2×D47semidirect
172. C22⋊C4C2×D47semidirect

Maximal subgroups

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

subgroupindex
#130940202
#130940192
#130940172
#130940092
#130940082
#130940072
#130939982
#130939972
#130939962
#130939952
#130939942
#130939922
#121×C472
#56047