Finite Group Databasebeta

← #15671504

Subgroups — #15671504

Order 2944.

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

normal subgroups only

This group has 140 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×#10624994C211yesmaximal, characteristic
2#13092455C211yesmaximal, characteristic
3C2×C23×#106C211yesmaximal, characteristic
4C22×C8×C23C2211yescharacteristic
5C2×C4⋊C4×C23—21no—
6#10625097—21no—
7C23×#106—21no—
8C23×#106C412yescomplemented
9#10625000C412yescomplemented
10#10624999—21no—
11#10624994—21no—
12#10624994C412yescomplemented
13C2×C23⋊C16—21no—
14C22×C4×C23—41no—
15C22×C4×C23D411yescharacteristic
16C2×C8×C23C2×C411yescharacteristic
17C2×C8×C23C2×C411yescharacteristic
18C2×C8×C23C2×C411yescharacteristic
19C2×C8×C23D411yescharacteristic
20C2×C8×C23D411yescharacteristic
21C2×C8×C23Q811yescharacteristic
22C4⋊C4×C23—22no—
23C4⋊C4×C23—41no—
24C22⋊Dic23—41no—
25C4⋊Dic23—22no—
26C4×Dic23—41no—
27C23⋊C16—22no—
28C23×C23D811yescharacteristic
29C2×C4×C23—42no—
30C2×C4×C23—82no—
31C2×C4×C23C22⋊C411yescharacteristic
32C2×C4×C23C22⋊C411yescharacteristic
33C2×C4×C23C4⋊C411yescharacteristic
34C2×C4×C23SD1611yescharacteristic
35C2×C4×C23SD1611yescharacteristic
36C2×C4×C23Q1611yescharacteristic
37C2×Dic23—42no—
38C8×C23C4211yescharacteristic
39C8×C23C22⋊C411yescharacteristic
40C8×C23C4⋊C411yescharacteristic
41C8×C23C4⋊C411yescharacteristic
42#1386—231nomaximal, Sylow
43C22×C23—22no—
44C22×C23#10211yescharacteristic
45C22×C23#10211yescharacteristic
46C22×C23#10711yescharacteristic
47C4×C23—82no—
48C4×C23#9511yescharacteristic
49C4×C23#10311yescharacteristic
50C4×C23#10311yescharacteristic
51C4×C23#10611yescharacteristic
52Dic23—82no—
53C2×M32—231no—
54#427—231no—
55C2×#106D2311yescharacteristic
56C2×C23—21no—
57C2×C23—21no—
58C2×C23#34011yescharacteristic
59C2×C23#36012yes—
60C22×C8C2×D2311yescharacteristic
61#117—461no—
62C2×C4⋊C4—21no—
63M32—232no—
64M32—461no—
65C2×C16—461no—
66#107—232no—
67#106—21no—
68#106—461no—
69#106Dic2312yescomplemented
70C23#138611yescharacteristic, complemented, Sylow
71C22×C4—41no—
72C22×C4C22⋊D2311yescharacteristic
73C2×C8Dic4611yescharacteristic
74C2×C8C4×D2311yescharacteristic
75C2×C8C4×D2311yescharacteristic
76C2×C8D9211yescharacteristic
77C2×C8C2×Dic2311yescharacteristic
78C2×C8C22⋊D2311yescharacteristic
79C4⋊C4—22no—
80C4⋊C4—41no—
81C4⋊C4—462no—
82C22⋊C4—921no—
83C42—921no—
84C16—462no—
85C23#6727211yescharacteristic
86C2×C4—42no—
87C2×C4—82no—
88C2×C4—922no—
89C2×C4Dic23⋊C411yescharacteristic
90C2×C4(C2×D23)⋊C411yescharacteristic
91C2×C4#6727311yescharacteristic
92C2×C4#6727411yescharacteristic
93C2×C4#6727511yescharacteristic
94C2×C4C22⋊Dic2311yescharacteristic
95C8C4×Dic2311yescharacteristic
96C8Dic23⋊C411yescharacteristic
97C8C4⋊Dic2311yescharacteristic
98C8(C2×D23)⋊C411yescharacteristic
99C22—22no—
100C22#1062498911yescharacteristic
101C22#1062499111yescharacteristic
102C22#1062501411yescharacteristic
103C4—82no—
104C4—1842no—
105C4#1062499011yescharacteristic
106C4#1062499211yescharacteristic
107C4C23⋊#9511yescharacteristic
108C4#1062501711yescharacteristic
109C2—21no—
110C2—21no—
111C2#1309217911yescharacteristic
112C2#1309222612yes—
subgroupG/H
centerC22#10624991
commutatorC8×C23C42
FrattiniC22×C8C2×D23
FittingC2×C23×#106C2
socleC22×C23#102
prime radicalC23×C23D8
cosocleC22×C8×C23C22
hypercenterC2×#106D23
hypocenterC23#1386
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
8. C23×#106C4semidirect
9. #10625000C4semidirect
12. #10624994C4semidirect
69. #106Dic23semidirect
70. C23#1386semidirect

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×#1062
#138623