Finite Group Databasebeta

← #20246099

Subgroups — #20246099

Order 6016.

612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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
1C2×#13094012C211yesmaximal, characteristic
2C2×C4×Dic94C211yesmaximal, characteristic, complemented
3C2×C4×D188C211yesmaximal, characteristic
4#15689029C211yesmaximal, characteristic, complemented
5#15689025C211yesmaximal, characteristic
6#15689015C214yesmaximal, complemented
7#15688997C214yesmaximal, complemented
8#15688993C211yesmaximal, characteristic, complemented
9C47×#376C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C22×C4×D47C2212yes—
13#13094012C418yescomplemented
14C4×Dic94—24no—
15C4×D188—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×C4⋊Dic47C2214yes—
19C2×Dic47⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2214yes—
22C2×(C2×D47)⋊C4C2214yes—
23C2×C4×Dic47C2212yes—
24C47⋊#95C2214yes—
25C2×C42×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28#95×C47C2212yes—
29#95×C47C2212yes—
30C23×D47C2312yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C2×D188—22no—
40C2×D188—22no—
41C2×D188C2×C414yes—
42C2×C4×D47—24no—
43C2×C4×D47—44no—
44C2×Dic94—22no—
45C2×Dic94—22no—
46C2×Dic94C2×C414yescomplemented
47C42×C47—22no—
48C42×C47C2×C414yescomplemented
49C42×C47D414yes—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—44no—
52(C2×D47)⋊C4C2×C4116yescomplemented
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47—44no—
56Dic47⋊C4—24no—
57C4×Dic47—24no—
58C23×C47C2411yescharacteristic
59C22×D47—22no—
60C22×D47—22no—
61C22×D47—24no—
62C22×D47—24no—
63C22×D47C22×C414yes—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47C22×C414yes—
72C2×C4×C47C22×C412yes—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D412yes—
76C2×C4×C47#4112yes—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—24no—
82C2×Dic47—24no—
83C2×Dic47C22×C414yes—
84D188—28no—
85C4×D47—48no—
86Dic94—28no—
87C22×C47C23×C411yescharacteristic
88C22×C47C22×D411yescharacteristic
89C22×C47C2×#4111yescharacteristic
90C22×C47H(5,𝔽2)12yes—
91C22×C472−1+412yes—
92C2×D47—24no—
93C2×D47—28no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—44no—
97C4×C47—24no—
98C4×C47—22no—
99C4×C47—22no—
100C4×C47—42no—
101C4×C47C4×D414yes—
102Dic47—24no—
103Dic47—42no—
104Dic47—42no—
105#2326—471nomaximal, Sylow
106C2×C47C2×C4×D411yescharacteristic
107C2×C47#52012yes—
108C2×C47#53511yescharacteristic
109C2×C47#53611yescharacteristic
110C2×C47#54212yes—
111D47—44no—
112C2×#124—471no—
113C2×C4×Q8—471no—
114C2×C4×D4—471no—
115#391—471no—
116#390—471no—
117#388—474no—
118#385—474no—
119#384—471no—
120#376D4711yescharacteristic, complemented
121C47#232611yescharacteristic, complemented, Sylow
122C22×Q8—471no—
123C22×D4—471no—
124C23×C4—472no—
125#124—478no—
126C4×Q8—944no—
127C4×D4—944no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4—471no—
131C2×C4⋊C4—474no—
132C2×C22⋊C4—474no—
133C2×C22⋊C4—472no—
134C2×C22⋊C4—474no—
135C2×C42—472no—
136C2×C42C2×D4711yescharacteristic
137C2×C42C2×D4711yescharacteristic
138C2×C42C2×D4711yescharacteristic
139#95—474no—
140#95C2×D4712yes—
141#95C2×D4712yes—
142C24—472no—
143C2×Q8—474no—
144C2×Q8—942no—
145C2×Q8—942no—
146C2×D4—474no—
147C2×D4—942no—
148C2×D4—942no—
149C22×C4—472no—
150C22×C4—472no—
151C22×C4—472no—
152C22×C4—944no—
153C22×C4—1884no—
154C22×C4C22×D4712yes—
155C22×C4C22×D4712yes—
156C22×C4C22×D4711yescharacteristic
157C22×C4C22×D4711yescharacteristic
158C22×C4C22×D4711yescharacteristic
159C4⋊C4—944no—
160C4⋊C4—942no—
161C4⋊C4—942no—
162C4⋊C4—1884no—
163C22⋊C4—4716no—
164C22⋊C4—944no—
165C22⋊C4—1884no—
166C42—22no—
167C42—944no—
168C42C4×D4714yescomplemented
169C42D18814yes—
170C23—474no—
171C23—942no—
172C23—942no—
173C23—944no—
174C23—944no—
175C23C23×D4711yescharacteristic
176Q8—948no—
177D4—948no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—474no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—944no—
191C2×C4—944no—
192C2×C4—1888no—
193C2×C4C2×C4×D4714yes—
194C2×C4C2×C4×D4712yes—
195C2×C4C2×D18812yes—
196C2×C4C2×D18812yes—
197C2×C4C2×D18812yes—
198C2×C4#1062535012yes—
199C22—944no—
200C22—948no—
201C22—1884no—
202C22—1882no—
203C22—1882no—
204C22C22×C4×D4711yescharacteristic
205C22C22×D18811yescharacteristic
206C22C2×#1062535011yescharacteristic
207C22#1309407012yes—
208C22#1309407112yes—
209C4—24no—
210C4—22no—
211C4—22no—
212C4—42no—
213C4—944no—
214C4—1882no—
215C4—1882no—
216C4C4×D18814yes—
217C2—1884no—
218C2C2×C4×D18811yescharacteristic
219C2#1568960312yes—
220C2#1568969211yescharacteristic
221C2#1568969911yescharacteristic
222C2#1568974412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#376C2
socleC23×C47C24
hypercenter#376D47
hypocenterC47#2326
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic94C2semidirect
4. #15689029C2semidirect
6. #15689015C2semidirect
7. #15688997C2semidirect
8. #15688993C2semidirect
9. C47×#376C2semidirect
13. #13094012C4semidirect
46. C2×Dic94C2×C4semidirect
48. C42×C47C2×C4semidirect
52. (C2×D47)⋊C4C2×C4semidirect
120. #376D47semidirect
121. C47#2326semidirect
168. C42C4×D47semidirect