Finite Group Databasebeta

← #15671342

Subgroups — #15671342

Order 2944.

134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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
1#13092286C211yesmaximal, characteristic
2#13092143C211yesmaximal, characteristic
3C23×#324C211yesmaximal, characteristic
4C2×C4⋊C4×C23C2211yescharacteristic
5C2×C4⋊Dic23C411yescharacteristic
6C2×Dic23⋊C4—21no—
7C2×Dic23⋊C4—21no—
8C2×C4×Dic23C411yescharacteristic
9C23×C22⋊C8—21no—
10C22⋊(C23⋊C8)—21no—
11C22×C4×C23C2×C411yescharacteristic
12C22×C4×C23D411yescharacteristic
13C22×C4×C23D411yescharacteristic
14C22×Dic23—21no—
15C22×Dic23—21no—
16C2×C8×C23—41no—
17C4⋊C4×C23—41no—
18C4⋊Dic23—41no—
19Dic23⋊C4—42no—
20Dic23⋊C4—42no—
21C4×Dic23—21no—
22C4×Dic23C812yescomplemented
23C2×C23⋊C8—41no—
24C23×C23C22⋊C411yescharacteristic
25C2×C4×C23—21no—
26C2×C4×C23—21no—
27C2×C4×C23—21no—
28C2×C4×C23—21no—
29C2×C4×C23—41no—
30C2×C4×C23—41no—
31C2×C4×C23C2×C811yescharacteristic
32C2×C4×C23M1611yescharacteristic
33C2×Dic23—22no—
34C2×Dic23—22no—
35C2×Dic23—22no—
36C2×Dic23—41no—
37C2×Dic23—41no—
38C2×Dic23—41no—
39C8×C23—81no—
40C23⋊C8—81no—
41#1325—231nomaximal, Sylow
42C22×C23—21no—
43C22×C23—21no—
44C22×C23C22⋊C811yescharacteristic
45C22×C23#9911yescharacteristic
46C22×C23#10111yescharacteristic
47C4×C23—21no—
48C4×C23—21no—
49C4×C23—41no—
50C4×C23—41no—
51Dic23—24no—
52Dic23—81no—
53#384—231no—
54#324—231no—
55#324D2311yescharacteristic
56C2×C23—21no—
57C2×C23—21no—
58C2×C23#32411yescharacteristic
59C2×C23#35311yescharacteristic
60C2×C23#35611yescharacteristic
61C2×C4⋊C4—231no—
62C2×C4⋊C4—461no—
63C2×C4⋊C4—461no—
64C2×C4⋊C4C2×D2311yescharacteristic
65C2×C42—231no—
66C22⋊C8—21no—
67C22⋊C8—461no—
68C23#132511yescharacteristic, complemented, Sylow
69C22×C4—461no—
70C22×C4—461no—
71C22×C4C4×D2311yescharacteristic
72C22×C4D9211yescharacteristic
73C22×C4C22⋊D2311yescharacteristic
74C2×C8—41no—
75C2×C8—921no—
76C4⋊C4—41no—
77C4⋊C4—921no—
78C4⋊C4—922no—
79C4⋊C4—922no—
80C42—232no—
81C42—461no—
82C23(C2×D23)⋊C411yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—462no—
90C2×C4—462no—
91C2×C4—462no—
92C2×C4—921no—
93C2×C4—921no—
94C2×C4—921no—
95C2×C4C8×D2311yescharacteristic
96C2×C4#6726211yescharacteristic
97C8—81no—
98C8—1841no—
99C22—21no—
100C22—21no—
101C22#1062498811yescharacteristic
102C22(C2×D23)⋊C811yescharacteristic
103C22#1062500611yescharacteristic
104C4—21no—
105C4—21no—
106C4—41no—
107C4—41no—
108C4—464no—
109C4—1841no—
110C2—21no—
111C2—21no—
112C2#1309214211yescharacteristic
113C2#1309220911yescharacteristic
114C2#1309221511yescharacteristic
subgroupG/H
centerC22#10624988
commutatorC2×C4×C23C2×C8
FrattiniC2×C4⋊C4C2×D23
FittingC23×#324C2
socleC22×C23#99
prime radicalC23×C23C22⋊C4
cosocleC2×C4⋊C4×C23C22
hypercenter#324D23
hypocenterC23#1325
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
22. C4×Dic23C8semidirect
68. C23#1325semidirect

Maximal subgroups

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

subgroupindex
#130922862
#130921432
C23×#3242
#132523