Finite Group Databasebeta

← #15671730

Subgroups — #15671730

Order 2944.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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×#10625063C211yesmaximal, characteristic
2#13092471C212yesmaximal, complemented
3#13092143C211yesmaximal, characteristic, complemented
4#13092140C212yesmaximal
5C23×#324C211yesmaximal, characteristic, complemented
6C22×C4×D23C411yescharacteristic
7C2×C4⋊C4×C23C2211yescharacteristic
8C2×(C2×D23)⋊C4C411yescharacteristic
9C2×(C2×D23)⋊C4C2211yescharacteristic
10C2×C4⋊Dic23C411yescharacteristic
11C2×C4×Dic23C411yescharacteristic
12C2×C4×Dic23C2211yescharacteristic
13#10625063—22no—
14#10625063—22no—
15C23×C22⋊C8C2212yes—
16C22⋊(C23⋊C8)C2212yes—
17#10624997—22no—
18Dic23⋊C8—22no—
19C23×D23C2×C411yescharacteristic
20C22×C4×C23C2×C411yescharacteristic
21C22×C4×C23C2×C411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C22×Dic23C2×C411yescharacteristic
24C22×Dic23C2×C411yescharacteristic
25C22×Dic23C2×C411yescharacteristic
26C2×C4×D23—22no—
27C2×C4×D23—22no—
28C2×C4×D23—21no—
29C2×C4×D23—21no—
30C2×C8×C23—22no—
31C4⋊C4×C23—22no—
32(C2×D23)⋊C4—22no—
33(C2×D23)⋊C4—22no—
34C4⋊Dic23—22no—
35C4×Dic23—21no—
36C4×Dic23—21no—
37C4×Dic23D412yes—
38C4×Dic23D412yes—
39C2×C23⋊C8—22no—
40C23×C23C22×C411yescharacteristic
41C22×D23—21no—
42C22×D23—21no—
43C22×D23—41no—
44C22×D23—41no—
45C22×D23M1612yes—
46C2×C4×C23—21no—
47C2×C4×C23—21no—
48C2×C4×C23—21no—
49C2×C4×C23—41no—
50C2×C4×C23—41no—
51C2×C4×C23M1612yes—
52C2×C4×C23C2×D412yes—
53C2×Dic23—21no—
54C2×Dic23—21no—
55C2×Dic23—21no—
56C2×Dic23—41no—
57C2×Dic23—41no—
58C2×Dic23C22⋊C411yescharacteristic
59C2×Dic23C22⋊C411yescharacteristic
60C2×Dic23C22⋊C412yes—
61C4×D23—24no—
62C4×D23—24no—
63C8×C23—42no—
64C23⋊C8—42no—
65#1464—231nomaximal, Sylow
66C22×C23—21no—
67C22×C23—21no—
68C22×C23C2×C22⋊C411yescharacteristic
69C22×C23C2×M1611yescharacteristic
70C22×C23C2×M1611yescharacteristic
71C2×D23—22no—
72C2×D23—42no—
73C2×D23—41no—
74C2×D23—41no—
75C2×D23—42no—
76C4×C23—22no—
77C4×C23—22no—
78C4×C23—41no—
79Dic23—21no—
80Dic23—21no—
81Dic23—22no—
82Dic23—41no—
83C2×#117—231no—
84#432—232no—
85#324—231no—
86#324D2311yescharacteristic, complemented
87#323—232no—
88C2×C23—21no—
89C2×C23—21no—
90C2×C23#40711yescharacteristic
91C2×C23#41011yescharacteristic
92C2×C23#41311yescharacteristic
93D23—42no—
94C23×C4—231no—
95#117—462no—
96#117—462no—
97C2×C4⋊C4—231no—
98C2×C4⋊C4C2×D2311yescharacteristic
99C2×C22⋊C4—231no—
100C2×C22⋊C4—231no—
101C2×C42—231no—
102C2×C42—231no—
103C4⋊C8—462no—
104C22⋊C8—232no—
105C22⋊C8C2×D2312yes—
106#97—462no—
107C23#146411yescharacteristic, complemented, Sylow
108C24—231no—
109C22×C4—231no—
110C22×C4—231no—
111C22×C4—231no—
112C22×C4—461no—
113C22×C4—461no—
114C22×C4—462no—
115C22×C4—462no—
116C22×C4C4×D2311yescharacteristic
117C22×C4C4×D2311yescharacteristic
118C22×C4C22×D2311yescharacteristic
119C2×C8—22no—
120C2×C8—462no—
121C4⋊C4—22no—
122C4⋊C4—462no—
123C22⋊C4—462no—
124C22⋊C4—462no—
125C42—232no—
126C42—232no—
127C42—461no—
128C42—461no—
129C23—232no—
130C23—461no—
131C23—461no—
132C23—921no—
133C23—921no—
134C23C2×C4×D2311yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—231no—
141C2×C4—231no—
142C2×C4—232no—
143C2×C4—464no—
144C2×C4—464no—
145C2×C4—461no—
146C2×C4—461no—
147C2×C4—461no—
148C2×C4—921no—
149C2×C4—921no—
150C2×C4#6726212yes—
151C2×C4D4×D2312yes—
152C8—42no—
153C8—922no—
154C22—21no—
155C22—21no—
156C22—462no—
157C22—922no—
158C22—922no—
159C22—921no—
160C22—921no—
161C22C22⋊C4×D2311yescharacteristic
162C22C2×#6726211yescharacteristic
163C22M16×D2311yescharacteristic
164C4—22no—
165C4—22no—
166C4—41no—
167C4—461no—
168C4—461no—
169C4—462no—
170C4—921no—
171C2—21no—
172C2—21no—
173C2—922no—
174C2#1309237911yescharacteristic
175C2#1309238911yescharacteristic
176C2#1309240011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23C2×C22⋊C4
prime radicalC23×D23C2×C4
cosocleC22×C4×C23C23
hypercenter#324D23
hypocenterC23#1464
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #13092471C2semidirect
3. #13092143C2semidirect
5. C23×#324C2semidirect
86. #324D23semidirect
107. C23#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#106250632
#130924712
#130921432
#130921402
C23×#3242
#146423