Finite Group Databasebeta

← #15671740

Subgroups — #15671740

Order 2944.

236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×Dic46C211yesmaximal, characteristic
2#13092474C211yesmaximal, characteristic
3#13092142C214yesmaximal
4C23×#432C211yesmaximal, characteristic
5C22×Dic46C411yescharacteristic
6C2×C42×C23C2211yescharacteristic
7C2×C4⋊Dic23C411yescharacteristic
8C2×Dic23⋊C4C2212yes—
9C2×C4×Dic23C412yes—
10C4×Dic46—21no—
11C4×Dic46—21no—
12C4×Dic46—21no—
13C4×Dic46—21no—
14C23×C4⋊C8—21no—
15C23×C22⋊C8C2212yes—
16C23×#97—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×Dic46—21no—
26C2×Dic46—21no—
27C2×Dic46—24no—
28C2×C8×C23—22no—
29C42×C23D411yescharacteristic
30C42×C23D411yescharacteristic
31C42×C23D411yescharacteristic
32C42×C23D411yescharacteristic
33C4⋊Dic23—21no—
34C4⋊Dic23—21no—
35Dic23⋊C4—22no—
36Dic23⋊C4—22no—
37C4×Dic23—22no—
38C4×Dic23—22no—
39C2×C23⋊C8—22no—
40C23×C23C22×C411yescharacteristic
41C2×C4×C23—22no—
42C2×C4×C23—22no—
43C2×C4×C23—41no—
44C2×C4×C23C22⋊C411yescharacteristic
45C2×C4×C23C22⋊C411yescharacteristic
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23C22⋊C411yescharacteristic
48C2×C4×C23C2×D411yescharacteristic
49C2×C4×C23C2×D411yescharacteristic
50C2×Dic23—22no—
51C2×Dic23—22no—
52C2×Dic23—22no—
53C2×Dic23—42no—
54C2×Dic23M1614yes—
55Dic46—24no—
56Dic46—24no—
57C8×C23—42no—
58C23⋊C8—42no—
59#1467—231nomaximal, Sylow
60C22×C23—21no—
61C22×C23—21no—
62C22×C23C2×C22⋊C411yescharacteristic
63C22×C23C2×M1612yes—
64C4×C23—21no—
65C4×C23—21no—
66C4×C23—21no—
67C4×C23—21no—
68C4×C23—21no—
69C4×C23#10112yes—
70Dic23—24no—
71Dic23—42no—
72C2×C4×Q8—231no—
73#432—231no—
74#432D2311yescharacteristic
75#324—234no—
76C2×C23—22no—
77C2×C23#40711yescharacteristic
78C2×C23#41011yescharacteristic
79C2×C23C2×#10111yescharacteristic
80C22×Q8—231no—
81C4×Q8—461no—
82C4×Q8—461no—
83C4×Q8—461no—
84C4×Q8—461no—
85C2×C4⋊C4—231no—
86C2×C4⋊C4—232no—
87C2×C42—232no—
88C2×C42C2×D2311yescharacteristic
89C4⋊C8—21no—
90C4⋊C8—461no—
91C22⋊C8—232no—
92C22⋊C8C2×D2312yes—
93#97—21no—
94#97—461no—
95C23#146711yescharacteristic, complemented, Sylow
96C2×Q8—464no—
97C2×Q8—461no—
98C2×Q8—461no—
99C22×C4—232no—
100C22×C4—232no—
101C22×C4C4×D2311yescharacteristic
102C22×C4C4×D2311yescharacteristic
103C22×C4C22×D2311yescharacteristic
104C2×C8—22no—
105C2×C8—462no—
106C4⋊C4—461no—
107C4⋊C4—461no—
108C4⋊C4—462no—
109C4⋊C4—462no—
110C42—462no—
111C42—462no—
112C42D9211yescharacteristic
113C42D9211yescharacteristic
114C42C22⋊D2311yescharacteristic
115C42C22⋊D2311yescharacteristic
116C23C2×C4×D2311yescharacteristic
117Q8—464no—
118Q8—464no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4—234no—
123C2×C4—462no—
124C2×C4—462no—
125C2×C4—462no—
126C2×C4—922no—
127C2×C4(C2×D23)⋊C411yescharacteristic
128C2×C4(C2×D23)⋊C411yescharacteristic
129C2×C4(C2×D23)⋊C411yescharacteristic
130C2×C4(C2×D23)⋊C411yescharacteristic
131C2×C4C2×D9211yescharacteristic
132C2×C4C2×C22⋊D2311yescharacteristic
133C8—42no—
134C8—922no—
135C22—21no—
136C22—21no—
137C22M16×D2312yes—
138C22C2×(C2×D23)⋊C411yescharacteristic
139C4—21no—
140C4—21no—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—464no—
145C4—922no—
146C4#1062500612yes—
147C2—22no—
148C2#1309238011yescharacteristic
149C2#1309239011yescharacteristic
150C2C2×#1062500611yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutator, prime radicalC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#432C2
socleC22×C23C2×C22⋊C4
cosocleC22×C4×C23C23
hypercenter#432D23
hypocenterC23#1467
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
95. C23#1467semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic462
#130924742
#130921422
C23×#4322
#146723