Finite Group Databasebeta

← #15683939

Subgroups — #15683939

Order 2944.

380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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#13092974C211yesmaximal, characteristic
2#13092823C214yesmaximal, complemented
3#13092820C212yesmaximal, complemented
4#13092813C212yesmaximal, complemented
5#13092457C214yesmaximal
6C4×#67267C211yesmaximal, characteristic
7C2×C23×C4⋊Q8C211yesmaximal, characteristic
8C22×Q8×C23—21no—
9C23×C4⋊Q8—21no—
10C23×C4⋊Q8—21no—
11C23×C4⋊Q8C2212yes—
12C23×C4⋊Q8C2212yes—
13C2×C4⋊C4×C23—21no—
14C2×C4⋊C4×C23C2212yes—
15C2×C42×C23C2211yescharacteristic
16#10625097C2212yes—
17#10625095—21no—
18#10625095—21no—
19C2×#67267C2212yes—
20#10625041C2212yes—
21#10625040C2211yescharacteristic
22#10625040C2211yescharacteristic
23C4×Dic46—21no—
24C4×Dic46—21no—
25#10624990C2218yes—
26#10624989C2218yes—
27#10624985C2212yes—
28C4×C23⋊C8C2212yes—
29C2×Q8×C23—22no—
30C2×Q8×C23—22no—
31C2×Q8×C23—44no—
32C22×C4×C23—22no—
33C22×C4×C23D411yescharacteristic
34C22×C4×C23D411yescharacteristic
35C22×C4×C23C2311yescharacteristic
36C2×Dic46—21no—
37C2×Dic46—21no—
38C4⋊C4×C23—22no—
39C4⋊C4×C23—22no—
40C4⋊C4×C23—22no—
41C4⋊C4×C23C2314yes—
42C42×C23D411yescharacteristic
43C42×C23D411yescharacteristic
44C42×C23C2311yescharacteristic
45C42×C23C2311yescharacteristic
46C22⋊Dic23—22no—
47C4⋊Dic23—21no—
48C4⋊Dic23—21no—
49C4⋊Dic23C2312yes—
50C4⋊Dic23C2312yes—
51Dic23⋊C4—22no—
52Dic23⋊C4—22no—
53C4×Dic23—22no—
54#67267Q818yescomplemented
55C2×C23⋊C8C2314yes—
56C23×C23C2×D411yescharacteristic
57Q8×C23—44no—
58Q8×C23—44no—
59C2×C4×C23—22no—
60C2×C4×C23—22no—
61C2×C4×C23—24no—
62C2×C4×C23—44no—
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×Q814yes—
69C2×C4×C23C2411yescharacteristic
70C2×Dic23—22no—
71C2×Dic23—22no—
72Dic46—42no—
73Dic46—42no—
74C23⋊C8C2×Q818yescomplemented
75#3165—231nomaximal, Sylow
76C22×C23—21no—
77C22×C23—21no—
78C22×C23C4⋊Q812yes—
79C22×C23C22×D411yescharacteristic
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—44no—
83C4×C23C4⋊Q812yes—
84C4×C23AGL(1,ℤ/8)12yes—
85C4×C23#13712yes—
86C4×C23C22×Q812yes—
87Dic23—42no—
88Dic23—42no—
89#533—231no—
90C2×C4⋊Q8D2311yescharacteristic
91#501—234no—
92#500—232no—
93#498—232no—
94#428—234no—
95C4×M16—231no—
96C2×C23—22no—
97C2×C23C2×C4⋊Q811yescharacteristic
98C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
99C2×C23C2×#13711yescharacteristic
100C22×Q8—21no—
101C2×M16—232no—
102C4⋊Q8—21no—
103C4⋊Q8—21no—
104C4⋊Q8—231no—
105C4⋊Q8—231no—
106C4⋊Q8C2×D2312yes—
107C4⋊Q8C2×D2312yes—
108#125—232no—
109C22⋊Q8—461no—
110C22⋊Q8—461no—
111C4×Q8—461no—
112C4×Q8—461no—
113#117—232no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4C2×D2312yes—
116C2×C42C2×D2311yescharacteristic
117#107—238no—
118#106—238no—
119#97—232no—
120C4×C8—232no—
121C23#316511yescharacteristic, complemented, Sylow
122C2×Q8—22no—
123C2×Q8—22no—
124C2×Q8—44no—
125C2×Q8—461no—
126C2×Q8—461no—
127C22×C4—22no—
128C22×C4C22⋊D2311yescharacteristic
129C22×C4C22⋊D2311yescharacteristic
130C22×C4C22×D2311yescharacteristic
131M16—238no—
132C2×C8—234no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—232no—
137C4⋊C4—232no—
138C4⋊C4—462no—
139C4⋊C4—462no—
140C4⋊C4—461no—
141C4⋊C4—461no—
142C4⋊C4C22×D2314yes—
143C22⋊C4—462no—
144C42—462no—
145C42C22⋊D2311yescharacteristic
146C42C22⋊D2311yescharacteristic
147C42C22×D2311yescharacteristic
148C42C22×D2311yescharacteristic
149C23C2×C22⋊D2311yescharacteristic
150Q8—44no—
151Q8—44no—
152Q8—922no—
153Q8—922no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—44no—
158C2×C4—462no—
159C2×C4—462no—
160C2×C4Q8×D2314yes—
161C2×C4C2×C22⋊D2311yescharacteristic
162C2×C4C2×C22⋊D2311yescharacteristic
163C2×C4C2×C22⋊D2311yescharacteristic
164C2×C4C2×C22⋊D2311yescharacteristic
165C2×C4C2×C22⋊D2311yescharacteristic
166C2×C4C23×D2311yescharacteristic
167C8—238no—
168C22—21no—
169C22—21no—
170C22#1062511512yes—
171C22C22×C22⋊D2311yescharacteristic
172C4—21no—
173C4—21no—
174C4—44no—
175C4—922no—
176C4—922no—
177C4#1062510312yes—
178C4#1062511312yes—
179C4#1062511512yes—
180C4C2×Q8×D2312yes—
181C2—22no—
182C2C2×#1062511511yescharacteristic
183C2C2×#1062510311yescharacteristic
184C2C2×#1062511311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×C4⋊Q8C2
socleC22×C23C22×D4
prime radicalC23×C23C2×D4
hypercenterC2×C4⋊Q8D23
hypocenterC23#3165
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13092823C2semidirect
3. #13092820C2semidirect
4. #13092813C2semidirect
54. #67267Q8semidirect
74. C23⋊C8C2×Q8semidirect
121. C23#3165semidirect

Maximal subgroups

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

subgroupindex
#130929742
#130928232
#130928202
#130928132
#130924572
C4×#672672
C2×C23×C4⋊Q82
#316523