Finite Group Databasebeta

← #15673128

Subgroups — #15673128

Order 2944.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10625048C211yesmaximal, characteristic
2C2×#10625048C212yesmaximal
3#13092184C211yesmaximal, characteristic
4#13092183C212yesmaximal
5C23×#342C211yesmaximal, characteristic
6C23×Dic23C2211yescharacteristic
7C2×C22⋊C4×C23C2211yescharacteristic
8C2×C22⋊C4×C23C2212yes—
9C2×C22⋊Dic23C2211yescharacteristic
10C2×C22⋊Dic23C2212yes—
11C2×Dic23⋊C4—22no—
12C2×Dic23⋊C4C412yescomplemented
13C2×C4×Dic23—22no—
14C2×C4×Dic23C412yescomplemented
15#10625048—22no—
16#10625048—22no—
17#10625048—24no—
18#10625048C418yescomplemented
19C24×C23C2311yescharacteristic
20C22×C4×C23—22no—
21C22×C4×C23C2×C412yes—
22C22×Dic23—22no—
23C22×Dic23C2×C412yes—
24C22×Dic23C2×C414yes—
25C22×Dic23C2×C411yescharacteristic
26C22×Dic23C2×C411yescharacteristic
27C22×Dic23D412yes—
28C22×Dic23D412yes—
29C22×Dic23D412yes—
30C22×Dic23Q812yes—
31C22⋊C4×C23—22no—
32C22⋊C4×C23—22no—
33C22⋊C4×C23C2×C414yes—
34C22⋊Dic23—22no—
35C22⋊Dic23—22no—
36C22⋊Dic23C2×C414yes—
37Dic23⋊C4—24no—
38Dic23⋊C4—28no—
39C4×Dic23—22no—
40C4×Dic23—22no—
41C4×Dic23—28no—
42C23×C23—42no—
43C23×C23C22×C411yescharacteristic
44C23×C23C22×C412yes—
45C23×C23C2×D412yes—
46C23×C23C2×D411yescharacteristic
47C23×C23C2×Q811yescharacteristic
48C2×C4×C23—22no—
49C2×C4×C23—24no—
50C2×C4×C23—44no—
51C2×C4×C23—42no—
52C2×Dic23—22no—
53C2×Dic23—24no—
54C2×Dic23—44no—
55C2×Dic23—42no—
56C2×Dic23C4212yes—
57C2×Dic23C4212yes—
58C2×Dic23C22⋊C414yes—
59C2×Dic23C22⋊C411yescharacteristic
60C2×Dic23C22⋊C411yescharacteristic
61C2×Dic23C22⋊C414yes—
62C2×Dic23C22⋊C412yes—
63C2×Dic23C4⋊C414yes—
64C2×Dic23C4⋊C414yes—
65C2×Dic23C4⋊C412yes—
66C2×Dic23C4⋊C412yes—
67#1740—231nomaximal, Sylow
68C22×C23—22no—
69C22×C23—24no—
70C22×C23—42no—
71C22×C23—41no—
72C22×C23—41no—
73C22×C23C2×C4211yescharacteristic
74C22×C23C2×C22⋊C412yes—
75C22×C23C2×C22⋊C411yescharacteristic
76C22×C23C2×C4⋊C411yescharacteristic
77C22×C23C2×C4⋊C412yes—
78C4×C23—44no—
79C4×C23—42no—
80Dic23—44no—
81Dic23—42no—
82Dic23#9512yes—
83Dic23#9514yes—
84Dic23#9512yes—
85C2×#117—231no—
86C2×#117—232no—
87#342—232no—
88#342—231no—
89#342D2311yescharacteristic
90C2×C23—22no—
91C2×C23—21no—
92C2×C23—21no—
93C2×C23—22no—
94C2×C23C2×#9511yescharacteristic
95C2×C23#41012yes—
96C23×C4—231no—
97#117—238no—
98#117—462no—
99#117—462no—
100#117—464no—
101C2×C4⋊C4—232no—
102C2×C4⋊C4—462no—
103C2×C22⋊C4—232no—
104C2×C22⋊C4—231no—
105C2×C22⋊C4C2×D2311yescharacteristic
106C2×C22⋊C4C2×D2312yes—
107C2×C42—232no—
108C2×C42—462no—
109C23#174011yescharacteristic, complemented, Sylow
110C24C22×D2311yescharacteristic
111C22×C4—22no—
112C22×C4—231no—
113C22×C4—231no—
114C22×C4—234no—
115C22×C4—232no—
116C22×C4—232no—
117C22×C4—232no—
118C22×C4—232no—
119C22×C4—232no—
120C22×C4—462no—
121C22×C4C4×D2312yes—
122C4⋊C4—464no—
123C4⋊C4—468no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—234no—
127C22⋊C4—462no—
128C22⋊C4—462no—
129C22⋊C4C4×D2314yes—
130C42—462no—
131C42—462no—
132C42—468no—
133C23—42no—
134C23C2×C4×D2311yescharacteristic
135C23C2×C4×D2312yes—
136C23D4×D2312yes—
137C23D4×D2311yescharacteristic
138C23Q8×D2311yescharacteristic
139C2×C4—24no—
140C2×C4—22no—
141C2×C4—44no—
142C2×C4—42no—
143C2×C4—232no—
144C2×C4—232no—
145C2×C4—234no—
146C2×C4—234no—
147C2×C4—231no—
148C2×C4—231no—
149C2×C4—232no—
150C2×C4—232no—
151C2×C4—232no—
152C2×C4—234no—
153C2×C4—234no—
154C2×C4—464no—
155C2×C4—462no—
156C2×C4—924no—
157C2×C4—922no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22C42×D2311yescharacteristic
164C22C22⋊C4×D2312yes—
165C22C22⋊C4×D2311yescharacteristic
166C22C4⋊C4×D2311yescharacteristic
167C22C4⋊C4×D2312yes—
168C4—44no—
169C4—42no—
170C4—232no—
171C4—234no—
172C4—232no—
173C4—924no—
174C4—922no—
175C2—22no—
176C2—21no—
177C2—21no—
178C2—22no—
179C2#95×D2311yescharacteristic
180C2#1309238912yes—
subgroupG/H
centerC22C22⋊C4×D23
commutatorC22×C23C2×C42
FrattiniC24C22×D23
FittingC23×#342C2
socleC22×C23C2×C22⋊C4
prime radical, cosocleC24×C23C23
hypercenter#342D23
hypocenterC23#1740
LCSG ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
12. C2×Dic23⋊C4C4semidirect
14. C2×C4×Dic23C4semidirect
18. #10625048C4semidirect
109. C23#1740semidirect

Maximal subgroups

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

subgroupindex
C2×#106250482
#130921842
#130921832
C23×#3422
#174023