Finite Group Databasebeta

← #15671752

Subgroups — #15671752

Order 2944.

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

normal subgroups only

This group has 204 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×#10625041C211yesmaximal, characteristic
2#13092474C211yesmaximal, characteristic
3#13092142C214yesmaximal
4C23×#431C211yesmaximal, characteristic
5C2×C42×C23C2211yescharacteristic
6C2×C4⋊Dic23C411yescharacteristic
7C2×C4⋊Dic23C411yescharacteristic
8C2×Dic23⋊C4C412yes—
9C2×Dic23⋊C4C2212yes—
10#10625041—21no—
11#10625041—21no—
12#10625041—21no—
13#10625041—21no—
14C23×C4⋊C8—21no—
15C23×C22⋊C8C2212yes—
16C4×C8×C23—21no—
17C22⋊(C23⋊C8)C2212yes—
18C4⋊(C23⋊C8)—21no—
19#10624985—21no—
20C22×C4×C23C2×C411yescharacteristic
21C22×C4×C23C2×C411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C22×Dic23C2×C412yes—
24C22×Dic23C2×C412yes—
25C2×C8×C23—22no—
26C42×C23D411yescharacteristic
27C42×C23D411yescharacteristic
28C42×C23D411yescharacteristic
29C42×C23D411yescharacteristic
30C4⋊Dic23—21no—
31C4⋊Dic23—21no—
32C4⋊Dic23—21no—
33C4⋊Dic23—21no—
34Dic23⋊C4—22no—
35Dic23⋊C4—22no—
36Dic23⋊C4—22no—
37Dic23⋊C4—22no—
38C2×C23⋊C8—22no—
39C23×C23C22×C411yescharacteristic
40C2×C4×C23—22no—
41C2×C4×C23—22no—
42C2×C4×C23—41no—
43C2×C4×C23C22⋊C411yescharacteristic
44C2×C4×C23C22⋊C411yescharacteristic
45C2×C4×C23C22⋊C411yescharacteristic
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23C2×D411yescharacteristic
48C2×C4×C23C2×D411yescharacteristic
49C2×Dic23—22no—
50C2×Dic23—22no—
51C2×Dic23—24no—
52C2×Dic23—42no—
53C8×C23—42no—
54C23⋊C8—42no—
55#1470—231nomaximal, Sylow
56C22×C23—21no—
57C22×C23—21no—
58C22×C23C2×C22⋊C411yescharacteristic
59C22×C23#13112yes—
60C4×C23—21no—
61C4×C23—21no—
62C4×C23—21no—
63C4×C23—21no—
64C4×C23—21no—
65C4×C23#10112yes—
66Dic23—42no—
67Dic23—42no—
68C2×#125—231no—
69#432—231no—
70#431D2311yescharacteristic
71#324—234no—
72C2×C23—22no—
73C2×C23#40811yescharacteristic
74C2×C23#41011yescharacteristic
75C2×C23C2×#10111yescharacteristic
76#125—461no—
77#125—461no—
78#125—461no—
79#125—461no—
80C2×C4⋊C4—232no—
81C2×C4⋊C4—231no—
82C2×C4⋊C4—231no—
83C2×C4⋊C4—232no—
84C2×C42C2×D2311yescharacteristic
85C4⋊C8—21no—
86C4⋊C8—461no—
87C22⋊C8—232no—
88C22⋊C8C2×D2312yes—
89#97—461no—
90C4×C8—21no—
91C23#147011yescharacteristic, complemented, Sylow
92C22×C4—232no—
93C22×C4—232no—
94C22×C4C4×D2311yescharacteristic
95C22×C4C4×D2311yescharacteristic
96C22×C4C22×D2311yescharacteristic
97C2×C8—22no—
98C2×C8—462no—
99C4⋊C4—462no—
100C4⋊C4—462no—
101C4⋊C4—461no—
102C4⋊C4—461no—
103C4⋊C4—461no—
104C4⋊C4—461no—
105C4⋊C4—462no—
106C4⋊C4—462no—
107C42D9211yescharacteristic
108C42D9211yescharacteristic
109C42C22⋊D2311yescharacteristic
110C42C22⋊D2311yescharacteristic
111C23C2×C4×D2311yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—41no—
115C2×C4—464no—
116C2×C4—462no—
117C2×C4—462no—
118C2×C4—922no—
119C2×C4(C2×D23)⋊C411yescharacteristic
120C2×C4(C2×D23)⋊C411yescharacteristic
121C2×C4(C2×D23)⋊C411yescharacteristic
122C2×C4(C2×D23)⋊C411yescharacteristic
123C2×C4C2×D9211yescharacteristic
124C2×C4C2×C22⋊D2311yescharacteristic
125C8—42no—
126C8—922no—
127C22—21no—
128C22—21no—
129C22#1062507212yes—
130C22C2×(C2×D23)⋊C411yescharacteristic
131C4—21no—
132C4—21no—
133C4—21no—
134C4—21no—
135C4—21no—
136C4—922no—
137C4—922no—
138C4#1062500612yes—
139C2—22no—
140C2#1309238311yescharacteristic
141C2#1309239011yescharacteristic
142C2C2×#1062500611yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutator, prime radicalC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#431C2
socleC22×C23C2×C22⋊C4
cosocleC22×C4×C23C23
hypercenter#431D23
hypocenterC23#1470
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
91. C23#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#106250412
#130924742
#130921422
C23×#4312
#147023