Finite Group Databasebeta

← #20241921

Subgroups — #20241921

Order 6016.

274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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#15689087C211yesmaximal, characteristic
2#15688986C211yesmaximal, characteristic
3#15688860C214yesmaximal, complemented
4C2×C22⋊Q8×C47C211yesmaximal, characteristic
5C2×#10625329—21no—
6C2×C22⋊Dic47—21no—
7C22⋊(C47⋊C8)—21no—
8C22⋊(C47⋊C8)C2212yes—
9C47⋊#95—21no—
10C47⋊#95C2212yes—
11C22×Q8×C47C411yescharacteristic, complemented
12C23×C4×C47C2211yescharacteristic
13C22⋊Q8×C47—21no—
14C22⋊Q8×C47—21no—
15C22⋊Q8×C47C412yescomplemented
16C22⋊Q8×C47C2212yes—
17C2×C4⋊C4×C47—21no—
18C2×C4⋊C4×C47C411yescharacteristic, complemented
19C2×C22⋊C4×C47—21no—
20C24×C47D411yescharacteristic
21C2×Q8×C47—21no—
22C2×Q8×C47—42no—
23C2×Q8×C47C2×C412yes—
24C22×C4×C47—21no—
25C22×C4×C47—21no—
26C22×C4×C47—42no—
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47C2×C411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—22no—
34C4⋊C4×C47—22no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—22no—
37C4⋊C4×C47C2×C412yes—
38C22⋊C4×C47—22no—
39C22⋊C4×C47—22no—
40C22⋊Dic47—42no—
41#10625329—42no—
42C2×C47⋊C8—22no—
43C23×C47—22no—
44C23×C47—22no—
45C23×C47—41no—
46C23×C47C22⋊C411yescharacteristic
47C23×C47C22⋊C411yescharacteristic
48C23×C47C2×D411yescharacteristic
49Q8×C47—42no—
50Q8×C47—42no—
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47—22no—
54C2×C4×C47—22no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—42no—
60C2×C4×C47—42no—
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47C22⋊C411yescharacteristic
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×Dic47—42no—
66C2×Dic47—42no—
67C2×Dic47—42no—
68C47⋊C8—42no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47—21no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—21no—
76C22×C47—44no—
77C22×C47#9912yes—
78C22×C47C2×C22⋊C411yescharacteristic
79C22×C47#13712yes—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—21no—
84C4×C47—42no—
85C4×C47—42no—
86Dic47—82no—
87#1511—471nomaximal, Sylow
88C2×C47—22no—
89C2×C47—22no—
90C2×C47—41no—
91C2×C47C2×#9911yescharacteristic
92C2×C47#41911yescharacteristic
93C2×C47#42111yescharacteristic
94C2×C22⋊Q8D4711yescharacteristic
95#407—471no—
96#381—471no—
97#328—474no—
98C47#151111yescharacteristic, complemented, Sylow
99C22×Q8Dic4711yescharacteristic, complemented
100C23×C4C2×D4711yescharacteristic
101C2×M16—941no—
102C22⋊Q8—21no—
103C22⋊Q8—21no—
104C22⋊Q8Dic4712yescomplemented
105C22⋊Q8C2×D4712yes—
106C2×C4⋊C4—21no—
107C2×C4⋊C4Dic4711yescharacteristic, complemented
108C2×C22⋊C4—21no—
109C2×C22⋊C4—941no—
110C22⋊C8—472no—
111C22⋊C8—941no—
112#95—472no—
113#95—941no—
114C24C22⋊D4711yescharacteristic
115C2×Q8—21no—
116C2×Q8—42no—
117C2×Q8C2×Dic4712yes—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—42no—
121C22×C4—942no—
122C22×C4C2×Dic4711yescharacteristic
123C22×C4C2×Dic4711yescharacteristic
124C22×C4C22⋊D4711yescharacteristic
125C22×C4C22⋊D4711yescharacteristic
126C22×C4C22⋊D4711yescharacteristic
127C22×C4C22×D4711yescharacteristic
128M16—1882no—
129C2×C8—942no—
130C4⋊C4—22no—
131C4⋊C4—21no—
132C4⋊C4—22no—
133C4⋊C4C2×Dic4712yes—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—1882no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23C22⋊Dic4711yescharacteristic
141C23C22⋊Dic4711yescharacteristic
142C23C2×C22⋊D4711yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—1882no—
156C2×C4—1882no—
157C2×C4—1882no—
158C2×C4C22⋊Dic4711yescharacteristic
159C2×C4C22⋊Dic4711yescharacteristic
160C2×C4C22×Dic4711yescharacteristic
161C2×C4C2×C22⋊D4711yescharacteristic
162C8—1882no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1309393912yes—
172C22C2×C22⋊Dic4711yescharacteristic
173C22#1309405512yes—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—42no—
179C4—42no—
180C4—3762no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1309393911yescharacteristic
185C2#1568913211yescharacteristic
186C2#1568914011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊Q8×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×C22⋊Q8D47
hypocenterC47#1511
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #15688860C2semidirect
11. C22×Q8×C47C4semidirect
15. C22⋊Q8×C47C4semidirect
18. C2×C4⋊C4×C47C4semidirect
98. C47#1511semidirect
99. C22×Q8Dic47semidirect
104. C22⋊Q8Dic47semidirect
107. C2×C4⋊C4Dic47semidirect