Finite Group Databasebeta

← #15672727

Subgroups — #15672727

Order 2944.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C23⋊#564C211yesmaximal, characteristic
2#13092827C211yesmaximal, characteristic
3#13092826C211yesmaximal, characteristic
4#13092786C211yesmaximal, characteristic
5#13092158C211yesmaximal, characteristic
6#13092158C211yesmaximal, characteristic
7C23×#330C211yesmaximal, characteristic
8C23×#125C2211yescharacteristic
9#10625061—21no—
10#10625061—21no—
11#10625060—21no—
12#10625060—21no—
13#10625060—21no—
14#10625060—21no—
15#10625041C2211yescharacteristic
16#10625041C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×#97C2211yescharacteristic
19C23×#97C2211yescharacteristic
20#10625000—21no—
21#10624999—21no—
22#10624998—21no—
23#10624998—21no—
24#10624990—21no—
25#10624989—21no—
26#10624985C2211yescharacteristic
27C2×Dic46—21no—
28C2×C8×C23—21no—
29C2×C8×C23—21no—
30C4⋊C4×C23—21no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23D411yescharacteristic
33C4⋊C4×C23D411yescharacteristic
34C42×C23C2311yescharacteristic
35C4⋊Dic23—21no—
36C4⋊Dic23—21no—
37C4⋊Dic23—21no—
38C4⋊Dic23—21no—
39C4⋊Dic23D411yescharacteristic
40C4⋊Dic23D411yescharacteristic
41C4⋊Dic23D411yescharacteristic
42C4⋊Dic23D411yescharacteristic
43Dic23⋊C4—21no—
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50Dic23⋊C4—21no—
51C4×Dic23—21no—
52C4×Dic23—21no—
53C2×C23⋊C8—21no—
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×Dic23—21no—
60C2×Dic23—21no—
61C2×Dic23—21no—
62C2×Dic23—21no—
63C2×Dic23—41no—
64Dic46—42no—
65C8×C23—22no—
66C8×C23—41no—
67C23⋊C8—22no—
68#1663—231nomaximal, Sylow
69C22×C23#12011yescharacteristic
70C4×C23—21no—
71C4×C23—21no—
72C4×C23—21no—
73C4×C23—41no—
74C4×C23—41no—
75Dic23—41no—
76Dic23—41no—
77Dic23—41no—
78Dic23—41no—
79Dic23—81no—
80#564—231no—
81#501—231no—
82#501—231no—
83#491—231no—
84#330—231no—
85#330—231no—
86#330D2311yescharacteristic
87C2×C23#45411yescharacteristic
88C2×C23#45611yescharacteristic
89C2×C23#45611yescharacteristic
90C4⋊Q8—231no—
91#125—231no—
92#125—231no—
93#125—461no—
94#125—461no—
95#125—461no—
96#125—461no—
97#125—461no—
98#125—461no—
99#125C2×D2311yescharacteristic
100#107—461no—
101#107—461no—
102#106—461no—
103#106—461no—
104#103—461no—
105#103—461no—
106#97—231no—
107#97C2×D2311yescharacteristic
108#97C2×D2311yescharacteristic
109C23#166311yescharacteristic, complemented, Sylow
110C2×Q8—461no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—461no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—231no—
117C4⋊C4—231no—
118C4⋊C4—231no—
119C4⋊C4—231no—
120C4⋊C4—461no—
121C4⋊C4—461no—
122C4⋊C4—461no—
123C4⋊C4—461no—
124C4⋊C4—461no—
125C4⋊C4—461no—
126C4⋊C4—461no—
127C4⋊C4—461no—
128C4⋊C4—461no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C4⋊C4—461no—
132C4⋊C4D9211yescharacteristic
133C4⋊C4D9211yescharacteristic
134C42—461no—
135C42—461no—
136C42C22×D2311yescharacteristic
137Q8—922no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—461no—
141C2×C4—461no—
142C2×C4—461no—
143C2×C4—461no—
144C2×C4—921no—
145C2×C4C2×D9211yescharacteristic
146C2×C4D4×D2311yescharacteristic
147C2×C4D4×D2311yescharacteristic
148C8—22no—
149C8—41no—
150C8—462no—
151C22#1062505311yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—921no—
158C4—921no—
159C4—921no—
160C4—921no—
161C4—1841no—
162C2#1309259111yescharacteristic
163C2#1309260111yescharacteristic
164C2#1309260211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#330C2
socle, prime radicalC22×C23#120
hypercenter#330D23
hypocenterC23#1663
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
109. C23#1663semidirect

Maximal subgroups

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

subgroupindex
C23⋊#5642
#130928272
#130928262
#130927862
#130921582
C23×#3302
#166323