Finite Group Databasebeta

← #20254336

Subgroups — #20254336

Order 6016.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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#15689680C211yesmaximal, characteristic
2#15689502C212yesmaximal, complemented
3#15689473C212yesmaximal, complemented
4#15689330C214yesmaximal, complemented
5#15689279C214yesmaximal
6#15689176C211yesmaximal, characteristic
7C2×C4⋊Q8×C47C211yesmaximal, characteristic
8C2×#10625337C2218yes—
9#13094024C2211yescharacteristic
10#13094024C2211yescharacteristic
11#13094016—21no—
12#13094003—21no—
13#13094003C2212yes—
14C4×Dic94—21no—
15C4×Dic94C2212yes—
16#13093983—21no—
17C4⋊(C47⋊C8)C2212yes—
18#13093948C2218yes—
19C22⋊(C47⋊C8)C2212yes—
20C4×C47⋊C8C2212yes—
21C22×Q8×C47C2212yes—
22C4⋊Q8×C47—21no—
23C4⋊Q8×C47—21no—
24C4⋊Q8×C47C2212yes—
25C4⋊Q8×C47C2212yes—
26C2×C4⋊C4×C47—21no—
27C2×C4⋊C4×C47—21no—
28C2×C42×C47C2211yescharacteristic
29C2×Q8×C47—22no—
30C2×Q8×C47—44no—
31C2×Q8×C47C2314yes—
32C22×C4×C47—22no—
33C22×C4×C47D411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C2×Dic94—21no—
37C2×Dic94C2312yes—
38C4⋊C4×C47—22no—
39C4⋊C4×C47—22no—
40C4⋊C4×C47—22no—
41C4⋊C4×C47—22no—
42C42×C47D411yescharacteristic
43C42×C47D411yescharacteristic
44C42×C47C2311yescharacteristic
45C42×C47C2311yescharacteristic
46C22⋊Dic47—22no—
47#10625337—48no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47C2312yes—
52Dic47⋊C4—22no—
53Dic47⋊C4—22no—
54C4×Dic47—22no—
55C2×C47⋊C8C2314yes—
56C23×C47C2×D411yescharacteristic
57Q8×C47—28no—
58Q8×C47—44no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47—24no—
62C2×C4×C47—44no—
63C2×C4×C47Q1614yescomplemented
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2411yescharacteristic
70C2×Dic47—22no—
71C2×Dic47—22no—
72Dic94—24no—
73Dic94—42no—
74C47⋊C8—24no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47C2×Q1612yes—
78C22×C47C22×D411yescharacteristic
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—44no—
82C4×C47C2×Q1612yes—
83C4×C47C2×Q1612yes—
84C4×C47#13712yes—
85C4×C47H(5,𝔽2)12yes—
86Dic47—42no—
87Dic47—42no—
88#3209—471nomaximal, Sylow
89C2×C47—22no—
90C2×C47#53511yescharacteristic
91C2×C47C22×Q1611yescharacteristic
92C2×C47C2×#13711yescharacteristic
93#533—471no—
94C2×C4⋊Q8D4711yescharacteristic
95#494—472no—
96#487—472no—
97#462—474no—
98#451—474no—
99#431—471no—
100C47#320911yescharacteristic, complemented, Sylow
101C22×Q8C2×D4712yes—
102C2×Q16—478no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—471no—
106C4⋊Q8—471no—
107C4⋊Q8C2×D4712yes—
108C4⋊Q8C2×D4712yes—
109#125—941no—
110C22⋊Q8—472no—
111C22⋊Q8—941no—
112C4×Q8—472no—
113C4×Q8—941no—
114#117—941no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C42C2×D4711yescharacteristic
118C4⋊C8—472no—
119#103—478no—
120C22⋊C8—472no—
121C4×C8—472no—
122C2×Q8—22no—
123C2×Q8—44no—
124C2×Q8—472no—
125C2×Q8—941no—
126C2×Q8C22×D4714yes—
127C22×C4—22no—
128C22×C4C22⋊D4711yescharacteristic
129C22×C4C22⋊D4711yescharacteristic
130C22×C4C22×D4711yescharacteristic
131Q16—1888no—
132C2×C8—474no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4—472no—
138C4⋊C4—942no—
139C4⋊C4—942no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C22⋊C4—942no—
144C42—942no—
145C42C22⋊D4711yescharacteristic
146C42C22⋊D4711yescharacteristic
147C42C22×D4711yescharacteristic
148C42C22×D4711yescharacteristic
149C23C2×C22⋊D4711yescharacteristic
150Q8—28no—
151Q8—44no—
152Q8—944no—
153Q8—1882no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—44no—
158C2×C4—942no—
159C2×C4—942no—
160C2×C4#1062533714yescomplemented
161C2×C4C2×C22⋊D4711yescharacteristic
162C2×C4C2×C22⋊D4711yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C2×C4C2×C22⋊D4711yescharacteristic
165C2×C4C2×C22⋊D4711yescharacteristic
166C2×C4C23×D4711yescharacteristic
167C8—944no—
168C22—21no—
169C22—21no—
170C22C2×#1062533712yes—
171C22C22×C22⋊D4711yescharacteristic
172C4—21no—
173C4—21no—
174C4—44no—
175C4—1882no—
176C4—1882no—
177C4C2×#1062533712yes—
178C4C2×#1062533712yes—
179C4#1309405512yes—
180C4#1309406912yes—
181C2—22no—
182C2#1568969011yescharacteristic
183C2C22×#1062533711yescharacteristic
184C2C2×#1309405511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C4⋊Q8×C47C2
socleC22×C47C22×D4
hypercenterC2×C4⋊Q8D47
hypocenterC47#3209
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689502C2semidirect
3. #15689473C2semidirect
4. #15689330C2semidirect
63. C2×C4×C47Q16semidirect
100. C47#3209semidirect
160. C2×C4#10625337semidirect