Finite Group Databasebeta

← #15675448

Subgroups — #15675448

Order 2944.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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×Dic184C212yesmaximal
2#13092797C211yesmaximal, characteristic
3C4×Dic92C211yesmaximal, characteristic
4#13092222C212yesmaximal
5C23×C4⋊C16C211yesmaximal, characteristic
6C2×Dic92—21no—
7C2×Dic92C2212yes—
8C2×Dic92C2211yescharacteristic
9#10625040—21no—
10C4×Dic46—21no—
11C2×C16×C23C2212yes—
12C4×C8×C23C2211yescharacteristic
13#10625000C2211yescharacteristic
14#10624998—21no—
15Dic184—24no—
16C2×Dic46—21no—
17C2×Dic46—22no—
18C2×C8×C23D411yescharacteristic
19C2×C8×C23C2311yescharacteristic
20C42×C23D411yescharacteristic
21C4⋊Dic23—21no—
22C4⋊Dic23—41no—
23C4⋊Dic23—41no—
24Dic23⋊C4—41no—
25C4×Dic23—41no—
26Dic92—22no—
27Dic92—21no—
28Dic92—22no—
29Dic92—42no—
30Dic92D412yes—
31C16×C23—22no—
32C2×C4×C23D811yescharacteristic
33C2×C4×C23D811yescharacteristic
34C2×C4×C23C2×D411yescharacteristic
35C2×Dic23—41no—
36C2×Dic23—41no—
37C2×Dic23—42no—
38Dic46—22no—
39Dic46—41no—
40Dic46—42no—
41Dic46—42no—
42C8×C23—21no—
43C8×C23C2×D411yescharacteristic
44C8×C23#4111yescharacteristic
45#2209—231nomaximal, Sylow
46C22×C23C2×D811yescharacteristic
47C4×C23—21no—
48C4×C23Q3212yescomplemented
49C4×C23#12111yescharacteristic
50C4×C23AGL(1,ℤ/8)11yescharacteristic
51Dic23—42no—
52Dic23—82no—
53Dic23—81no—
54C2×Q32—232no—
55#494—231no—
56C4×Q16—231no—
57C4⋊C16D2311yescharacteristic
58#358—232no—
59C2×C23#45911yescharacteristic
60C2×C23C2×Q3211yescharacteristic
61C2×C23#51011yescharacteristic
62C2×Q16—231no—
63C2×Q16—232no—
64C2×Q16—461no—
65C4⋊Q8—461no—
66C4×Q8—461no—
67Q32—464no—
68C2×C16C2×D2312yes—
69#107—231no—
70#103—461no—
71C4×C8C2×D2311yescharacteristic
72C23#220911yescharacteristic, complemented, Sylow
73C2×Q8—461no—
74C2×Q8—462no—
75Q16—232no—
76Q16—462no—
77Q16—461no—
78Q16—462no—
79Q16—922no—
80C2×C8D9211yescharacteristic
81C2×C8C22×D2311yescharacteristic
82C4⋊C4—461no—
83C4⋊C4—921no—
84C4⋊C4—921no—
85C4⋊C4—921no—
86C42—921no—
87C42D9211yescharacteristic
88C16—22no—
89Q8—462no—
90Q8—921no—
91Q8—922no—
92Q8—922no—
93C2×C4—921no—
94C2×C4—921no—
95C2×C4—922no—
96C2×C4D18411yescharacteristic
97C2×C4D18411yescharacteristic
98C2×C4C2×D9211yescharacteristic
99C8—21no—
100C8D4×D2311yescharacteristic
101C8#6729211yescharacteristic
102C22C2×D18411yescharacteristic
103C4—21no—
104C4—922no—
105C4—1842no—
106C4—1841no—
107C4Dic18412yescomplemented
108C4#1062506611yescharacteristic
109C4#1062507911yescharacteristic
110C2#1309261311yescharacteristic
111C2C2×Dic18411yescharacteristic
112C2#1309286011yescharacteristic
subgroupG/H
centerC22C2×D184
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×C4⋊C16C2
socle, prime radicalC22×C23C2×D8
hypercenterC4⋊C16D23
hypocenterC23#2209
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
48. C4×C23Q32semidirect
72. C23#2209semidirect
107. C4Dic184semidirect

Maximal subgroups

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

subgroupindex
C2×Dic1842
#130927972
C4×Dic922
#130922222
C23×C4⋊C162
#220923