Finite Group Databasebeta

← #15672371

Subgroups — #15672371

Order 2944.

238 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 57 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#13092572C212yesmaximal
2#13092337C211yesmaximal, characteristic
3#13092154C212yesmaximal
4#13092143C211yesmaximal, characteristic
5C23×#544C211yesmaximal, characteristic
6C22×Dic46C2211yescharacteristic
7C23×C4⋊Q8—22no—
8C23×#125—22no—
9C23×C22⋊Q8—21no—
10C23×C22⋊Q8C2212yes—
11C23×#117—21no—
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×#67275—22no—
14C2×Dic23⋊C4—21no—
15C23⋊#95—21no—
16C23⋊#95C2211yescharacteristic
17C22⋊(C23⋊C8)C2212yes—
18#10624992—22no—
19C2×Q8×C23—21no—
20C2×Q8×C23D412yes—
21C22×C4×C23D411yescharacteristic
22C22×C4×C23D411yescharacteristic
23C22×C4×C23C2311yescharacteristic
24C22×Dic23—21no—
25C22×Dic23—21no—
26C2×Dic46—22no—
27C2×Dic46—42no—
28C4⋊C4×C23—21no—
29C4⋊C4×C23—21no—
30C4⋊C4×C23—21no—
31C4⋊C4×C23—22no—
32C4⋊C4×C23—22no—
33C4⋊C4×C23—22no—
34C4⋊C4×C23D412yes—
35C22⋊C4×C23—22no—
36C42×C23—22no—
37#67275—44no—
38Dic23⋊C4—42no—
39C2×C23⋊C8—22no—
40C23×C23C2×D411yescharacteristic
41Q8×C23—42no—
42Q8×C23—81no—
43C2×C4×C23—21no—
44C2×C4×C23—21no—
45C2×C4×C23—22no—
46C2×C4×C23—22no—
47C2×C4×C23—21no—
48C2×C4×C23—41no—
49C2×C4×C23—41no—
50C2×C4×C23Q1612yescomplemented
51C2×C4×C23C2×D412yes—
52C2×Dic23—22no—
53C2×Dic23—22no—
54C2×Dic23—41no—
55C2×Dic23—41no—
56C2×Dic23—41no—
57C2×Dic23—41no—
58Dic46—24no—
59Dic46—42no—
60C23⋊C8—42no—
61#1605—231nomaximal, Sylow
62C22×C23—21no—
63C22×C23—21no—
64C22×C23#12011yescharacteristic
65C22×C23C2×Q1611yescharacteristic
66C22×C23#13711yescharacteristic
67C4×C23—22no—
68C4×C23—22no—
69C4×C23—42no—
70C4×C23—41no—
71C4×C23—42no—
72Dic23—42no—
73Dic23—42no—
74#544D2311yescharacteristic
75#451—232no—
76#395—231no—
77#328—232no—
78#324—231no—
79C2×C23—21no—
80C2×C23—21no—
81C2×C23#45111yescharacteristic
82C2×C23#45611yescharacteristic
83C2×C23B(4,𝔽2)11yescharacteristic
84C22×Q8—231no—
85C2×Q16—462no—
86C4⋊Q8—22no—
87#125—22no—
88C22⋊Q8—21no—
89C22⋊Q8C2×D2312yes—
90#117—21no—
91C2×C4⋊C4—461no—
92C2×C4⋊C4C2×D2311yescharacteristic
93#103—462no—
94C22⋊C8—232no—
95#95—231no—
96#95—461no—
97C23#160511yescharacteristic, complemented, Sylow
98C2×Q8—21no—
99C2×Q8—462no—
100C2×Q8—922no—
101C2×Q8C22⋊D2312yes—
102C22×C4—461no—
103C22×C4—461no—
104C22×C4C22⋊D2311yescharacteristic
105C22×C4C22⋊D2311yescharacteristic
106C22×C4C22×D2311yescharacteristic
107Q16—924no—
108C2×C8—462no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—22no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C4⋊C4—922no—
116C4⋊C4C22⋊D2312yes—
117C22⋊C4—22no—
118C42—22no—
119C23C2×C22⋊D2311yescharacteristic
120Q8—42no—
121Q8—81no—
122Q8—464no—
123Q8—922no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—462no—
132C2×C4—462no—
133C2×C4—921no—
134C2×C4—921no—
135C2×C4—921no—
136C2×C4—921no—
137C2×C4#6727512yescomplemented
138C2×C4C2×C22⋊D2312yes—
139C8—922no—
140C22—21no—
141C22—21no—
142C22#1062511311yescharacteristic
143C22C2×#6727511yescharacteristic
144C22#1062512411yescharacteristic
145C4—22no—
146C4—22no—
147C4—42no—
148C4—41no—
149C4—42no—
150C4—922no—
151C4—922no—
152C2—21no—
153C2—21no—
154C2#1309257311yescharacteristic
155C2#1309260011yescharacteristic
156C2#1309260411yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#544C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#544D23
hypocenterC23#1605
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
50. C2×C4×C23Q16semidirect
97. C23#1605semidirect
137. C2×C4#67275semidirect

Maximal subgroups

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

subgroupindex
#130925722
#130923372
#130921542
#130921432
C23×#5442
#160523