Finite Group Databasebeta

← #15671708

Subgroups — #15671708

Order 2944.

264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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
2#13092467C212yesmaximal, complemented
3#13092142C212yesmaximal, complemented
4#13092141C211yesmaximal, characteristic
5C23×#323C211yesmaximal, characteristic
6C23×Dic23C411yescharacteristic
7C2×C22⋊C4×C23C2211yescharacteristic
8C2×C22⋊Dic23C411yescharacteristic
9C2×Dic23⋊C4C411yescharacteristic
10C2×Dic23⋊C4C2211yescharacteristic
11C2×C4×Dic23C411yescharacteristic
12C2×C4×Dic23C2211yescharacteristic
13#10625048—22no—
14#10625048—22no—
15C23×C22⋊C8C2212yes—
16C22⋊(C23⋊C8)C2212yes—
17Dic23⋊C8—22no—
18C8×Dic23—22no—
19C24×C23C2×C411yescharacteristic
20C22×C4×C23C2×C411yescharacteristic
21C22×C4×C23C2311yescharacteristic
22C22×Dic23—21no—
23C22×Dic23—21no—
24C22×Dic23—22no—
25C22×Dic23C814yescomplemented
26C22×Dic23C2×C411yescharacteristic
27C22×Dic23C2×C411yescharacteristic
28C22×Dic23C2×C411yescharacteristic
29C22×Dic23C2×C411yescharacteristic
30C2×C8×C23—22no—
31C22⋊C4×C23—22no—
32C22⋊Dic23—22no—
33Dic23⋊C4—22no—
34Dic23⋊C4—22no—
35C4×Dic23—21no—
36C4×Dic23—21no—
37C4×Dic23D412yes—
38C4×Dic23D412yes—
39C2×C23⋊C8—22no—
40C23×C23—21no—
41C23×C23—21no—
42C23×C23—41no—
43C23×C23—41no—
44C23×C23C2×C812yes—
45C23×C23C22×C411yescharacteristic
46C2×C4×C23—21no—
47C2×C4×C23—41no—
48C2×C4×C23—41no—
49C2×C4×C23C2×D412yes—
50C2×Dic23—21no—
51C2×Dic23—21no—
52C2×Dic23—24no—
53C2×Dic23—24no—
54C2×Dic23—21no—
55C2×Dic23—41no—
56C2×Dic23—41no—
57C2×Dic23C22⋊C412yes—
58C2×Dic23C22⋊C411yescharacteristic
59C2×Dic23C22⋊C411yescharacteristic
60C2×Dic23C2×C812yes—
61C2×Dic23C2×C812yes—
62C2×Dic23M1612yes—
63C8×C23—42no—
64C23⋊C8—42no—
65#1458—231nomaximal, Sylow
66C22×C23—21no—
67C22×C23—21no—
68C22×C23—22no—
69C22×C23—42no—
70C22×C23—42no—
71C22×C23—41no—
72C22×C23—41no—
73C22×C23C2×C22⋊C411yescharacteristic
74C22×C23C22×C811yescharacteristic
75C22×C23C2×M1611yescharacteristic
76C4×C23—22no—
77C4×C23—41no—
78Dic23—22no—
79Dic23—22no—
80Dic23—41no—
81Dic23C22⋊C812yes—
82Dic23C22⋊C812yes—
83C2×#117—231no—
84#431—232no—
85#324—232no—
86#323—231no—
87#323D2311yescharacteristic
88C2×C23—21no—
89C2×C23—21no—
90C2×C23—42no—
91C2×C23C2×C22⋊C811yescharacteristic
92C2×C23#41011yescharacteristic
93C2×C23#41311yescharacteristic
94C23×C4—231no—
95#117—462no—
96#117—462no—
97C2×C4⋊C4—231no—
98C2×C4⋊C4—231no—
99C2×C22⋊C4—231no—
100C2×C22⋊C4C2×D2311yescharacteristic
101C2×C42—231no—
102C2×C42—231no—
103C4⋊C8—462no—
104C22⋊C8—232no—
105C22⋊C8C2×D2312yes—
106C4×C8—462no—
107C23#145811yescharacteristic, complemented, Sylow
108C24C4×D2311yescharacteristic
109C22×C4—231no—
110C22×C4—234no—
111C22×C4—231no—
112C22×C4—231no—
113C22×C4—231no—
114C22×C4—461no—
115C22×C4—461no—
116C22×C4—462no—
117C22×C4C4×D2311yescharacteristic
118C22×C4C22×D2311yescharacteristic
119C2×C8—22no—
120C2×C8—462no—
121C4⋊C4—462no—
122C4⋊C4—462no—
123C22⋊C4—22no—
124C22⋊C4—462no—
125C42—232no—
126C42—232no—
127C42—461no—
128C42—461no—
129C23—21no—
130C23—21no—
131C23—41no—
132C23—41no—
133C23C8×D2312yes—
134C23C2×C4×D2311yescharacteristic
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—231no—
139C2×C4—231no—
140C2×C4—232no—
141C2×C4—232no—
142C2×C4—232no—
143C2×C4—232no—
144C2×C4—464no—
145C2×C4—464no—
146C2×C4—461no—
147C2×C4—461no—
148C2×C4—461no—
149C2×C4—921no—
150C2×C4—921no—
151C2×C4D4×D2312yes—
152C8—42no—
153C8—922no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22C22⋊C4×D2311yescharacteristic
162C22C2×C8×D2311yescharacteristic
163C22M16×D2311yescharacteristic
164C4—22no—
165C4—41no—
166C4—232no—
167C4—232no—
168C4—462no—
169C4—462no—
170C4—921no—
171C2—21no—
172C2—21no—
173C2—42no—
174C2C22⋊C8×D2311yescharacteristic
175C2#1309238911yescharacteristic
176C2#1309239811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC22×C23C22×C8
FrattiniC22×C4C22×D23
FittingC23×#323C2
socleC22×C23C2×C22⋊C4
prime radicalC24×C23C2×C4
cosocleC22×C4×C23C23
hypercenter#323D23
hypocenterC23#1458
LCSG ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #13092467C2semidirect
3. #13092142C2semidirect
25. C22×Dic23C8semidirect
107. C23#1458semidirect

Maximal subgroups

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

subgroupindex
C2×#106250482
#130924672
#130921422
#130921412
C23×#3232
#145823