Finite Group Databasebeta

← #20241922

Subgroups — #20241922

Order 6016.

274 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13094003C211yesmaximal, characteristic
2#15688986C211yesmaximal, characteristic
3#15688861C214yesmaximal, complemented
4C47×#407C211yesmaximal, characteristic
5C22×Dic94C411yescharacteristic, complemented
6#13094003—21no—
7#13094003—21no—
8#13094003C412yescomplemented
9#13094003C2212yes—
10C2×C4⋊Dic47C411yescharacteristic, complemented
11C2×Dic47⋊C4—21no—
12C2×C22⋊Dic47—21no—
13C2×C22⋊Dic47—21no—
14C47⋊#95—21no—
15C47⋊#95C2212yes—
16C23×C4×C47C2211yescharacteristic
17C2×M16×C47—21no—
18C22⋊C8×C47—21no—
19C22⋊C8×C47C2212yes—
20C24×C47D411yescharacteristic
21C22×C4×C47—42no—
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—21no—
29C22×Dic47—21no—
30C22×Dic47—22no—
31C2×Dic94—21no—
32C2×Dic94—42no—
33C2×Dic94C2×C412yes—
34M16×C47—42no—
35C2×C8×C47—22no—
36C22⋊Dic47—22no—
37C22⋊Dic47—22no—
38C22⋊Dic47—42no—
39C4⋊Dic47—21no—
40C4⋊Dic47C2×C412yes—
41Dic47⋊C4—22no—
42Dic47⋊C4—22no—
43C23×C47—22no—
44C23×C47—22no—
45C23×C47—41no—
46C23×C47C22⋊C411yescharacteristic
47C23×C47C22⋊C411yescharacteristic
48C23×C47C2×D411yescharacteristic
49C2×C4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47C22⋊C411yescharacteristic
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22×C411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×Dic47—22no—
60C2×Dic47—22no—
61C2×Dic47—42no—
62C2×Dic47—42no—
63C2×Dic47—42no—
64C2×Dic47—42no—
65C2×Dic47—42no—
66Dic94—42no—
67Dic94—42no—
68C8×C47—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—
84Dic47—42no—
85Dic47—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⋊Q8—471no—
95#407D4711yescharacteristic
96#381—471no—
97#328—474no—
98C47#151111yescharacteristic, complemented, Sylow
99C22×Q8—471no—
100C23×C4C2×D4711yescharacteristic
101C2×M16—21no—
102C22⋊Q8—472no—
103C22⋊Q8—472no—
104C22⋊Q8—941no—
105C22⋊Q8—941no—
106C2×C4⋊C4—471no—
107C2×C4⋊C4—941no—
108C2×C22⋊C4—941no—
109C2×C22⋊C4—941no—
110C22⋊C8—21no—
111C22⋊C8C2×D4712yes—
112#95—472no—
113#95—941no—
114C24D18811yescharacteristic
115C2×Q8—472no—
116C2×Q8—941no—
117C2×Q8—1882no—
118C22×C4—42no—
119C22×C4—941no—
120C22×C4—941no—
121C22×C4—942no—
122C22×C4C4×D4711yescharacteristic
123C22×C4C4×D4711yescharacteristic
124C22×C4D18811yescharacteristic
125C22×C4C22⋊D4711yescharacteristic
126C22×C4C22⋊D4711yescharacteristic
127C22×C4C22×D4711yescharacteristic
128M16—42no—
129C2×C8—22no—
130C4⋊C4—472no—
131C4⋊C4—942no—
132C4⋊C4—941no—
133C4⋊C4—942no—
134C22⋊C4—942no—
135C22⋊C4—942no—
136C22⋊C4—1882no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23(C2×D47)⋊C411yescharacteristic
141C23(C2×D47)⋊C411yescharacteristic
142C23C2×D18811yescharacteristic
143Q8—1882no—
144Q8—1882no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—942no—
152C2×C4—942no—
153C2×C4—1882no—
154C2×C4—1882no—
155C2×C4—1882no—
156C2×C4—1882no—
157C2×C4—1882no—
158C2×C4(C2×D47)⋊C411yescharacteristic
159C2×C4(C2×D47)⋊C411yescharacteristic
160C2×C4C2×C4×D4711yescharacteristic
161C2×C4C2×C22⋊D4711yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1309393812yes—
172C22C2×(C2×D47)⋊C411yescharacteristic
173C22#1309405712yes—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—3762no—
179C4—1882no—
180C4—1882no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1309393811yescharacteristic
185C2#1568913311yescharacteristic
186C2#1568913911yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC22×C47C2×C22⋊C4
hypercenter#407D47
hypocenterC47#1511
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #15688861C2semidirect
5. C22×Dic94C4semidirect
8. #13094003C4semidirect
10. C2×C4⋊Dic47C4semidirect
98. C47#1511semidirect