Finite Group Databasebeta

← #15671511

Subgroups — #15671511

Order 2944.

128 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 69 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×#10624994C211yesmaximal, characteristic
2#13092455C211yesmaximal, characteristic
3C2×C23×#108C211yesmaximal, characteristic
4C2×M16×C23—21no—
5C22×C8×C23C2211yescharacteristic
6#10625097—21no—
7C23×#108—21no—
8C23×#108C412yescomplemented
9#10625000—21no—
10#10624999C412yes—
11#10624994—21no—
12#10624994C412yescomplemented
13C2×C23⋊C16—21no—
14C22×C4×C23D411yescharacteristic
15M16×C23—22no—
16M16×C23—41no—
17C2×C8×C23—41no—
18C2×C8×C23C2×C411yescharacteristic
19C2×C8×C23C2×C411yescharacteristic
20C2×C8×C23C2×C411yescharacteristic
21C2×C8×C23D411yescharacteristic
22C2×C8×C23D411yescharacteristic
23C2×C8×C23Q811yescharacteristic
24C22⋊Dic23—41no—
25C4⋊Dic23—22no—
26C4×Dic23—41no—
27C23⋊C16—22no—
28C23×C23SD1611yescharacteristic
29C2×C4×C23C22⋊C411yescharacteristic
30C2×C4×C23C22⋊C411yescharacteristic
31C2×C4×C23C4⋊C411yescharacteristic
32C2×C4×C23D811yescharacteristic
33C2×C4×C23SD1611yescharacteristic
34C2×C4×C23Q1611yescharacteristic
35C2×Dic23—42no—
36C8×C23—42no—
37C8×C23C4211yescharacteristic
38C8×C23C22⋊C411yescharacteristic
39C8×C23C4⋊C411yescharacteristic
40C8×C23C4⋊C411yescharacteristic
41#1389—231nomaximal, Sylow
42C22×C23—41no—
43C22×C23#10211yescharacteristic
44C22×C23#10311yescharacteristic
45C22×C23#10611yescharacteristic
46C4×C23#9511yescharacteristic
47C4×C23#10211yescharacteristic
48C4×C23#10311yescharacteristic
49C4×C23#10711yescharacteristic
50Dic23—82no—
51C2×M32—231no—
52C2×#108D2311yescharacteristic
53#427—231no—
54C2×C23—21no—
55C2×C23—21no—
56C2×C23—21no—
57C2×C23#34011yescharacteristic
58C2×M16—21no—
59C22×C8C2×D2311yescharacteristic
60#117—461no—
61M32—232no—
62M32—461no—
63C2×C16—461no—
64#108—21no—
65#108Dic2312yescomplemented
66#107—461no—
67#106—232no—
68C23#138911yescharacteristic, complemented, Sylow
69C22×C4C22⋊D2311yescharacteristic
70M16—22no—
71M16—41no—
72C2×C8—41no—
73C2×C8Dic4611yescharacteristic
74C2×C8C4×D2311yescharacteristic
75C2×C8C4×D2311yescharacteristic
76C2×C8D9211yescharacteristic
77C2×C8C2×Dic2311yescharacteristic
78C2×C8C22⋊D2311yescharacteristic
79C4⋊C4—462no—
80C22⋊C4—921no—
81C42—921no—
82C16—462no—
83C23#6727411yescharacteristic
84C2×C4—922no—
85C2×C4Dic23⋊C411yescharacteristic
86C2×C4(C2×D23)⋊C411yescharacteristic
87C2×C4#6727211yescharacteristic
88C2×C4#6727311yescharacteristic
89C2×C4#6727511yescharacteristic
90C2×C4C22⋊Dic2311yescharacteristic
91C8—42no—
92C8C4×Dic2311yescharacteristic
93C8Dic23⋊C411yescharacteristic
94C8C4⋊Dic2311yescharacteristic
95C8(C2×D23)⋊C411yescharacteristic
96C22—41no—
97C22#1062499011yescharacteristic
98C22#1062499111yescharacteristic
99C22#1062501711yescharacteristic
100C4—1842no—
101C4#1062498911yescharacteristic
102C4#1062499211yescharacteristic
103C4C23⋊#9511yescharacteristic
104C4#1062501411yescharacteristic
105C2—21no—
106C2—21no—
107C2—21no—
108C2#1309217911yescharacteristic
subgroupG/H
centerC4#10625014
commutatorC8×C23C42
FrattiniC22×C8C2×D23
FittingC2×C23×#108C2
socleC2×C23#340
prime radicalC23×C23SD16
cosocleC22×C8×C23C22
hypercenterC2×#108D23
hypocenterC23#1389
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
8. C23×#108C4semidirect
12. #10624994C4semidirect
65. #108Dic23semidirect
68. C23#1389semidirect

Maximal subgroups

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

subgroupindex
C2×#106249942
#130924552
C2×C23×#1082
#138923