Finite Group Databasebeta

← #15671751

Subgroups — #15671751

Order 2944.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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×#10625060C211yesmaximal, characteristic
2#13092471C211yesmaximal, characteristic
3#13092467C211yesmaximal, characteristic
4#13092143C211yesmaximal, characteristic
5#13092142C211yesmaximal, characteristic
6#13092142C211yesmaximal, characteristic
7C23×#324C211yesmaximal, characteristic
8C2×C4⋊C4×C23C2211yescharacteristic
9C2×C4⋊Dic23C411yescharacteristic
10C2×Dic23⋊C4C411yescharacteristic
11C2×Dic23⋊C4C411yescharacteristic
12C2×Dic23⋊C4C411yescharacteristic
13C2×Dic23⋊C4C2211yescharacteristic
14C2×C4×Dic23C2211yescharacteristic
15#10625060—21no—
16#10625060—21no—
17#10625060—21no—
18#10625060—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×C22⋊C8C2211yescharacteristic
21C22⋊(C23⋊C8)C2211yescharacteristic
22C22⋊(C23⋊C8)C2211yescharacteristic
23#10624997—21no—
24Dic23⋊C8—21no—
25Dic23⋊C8—21no—
26C8×Dic23—21no—
27C22×C4×C23C2×C411yescharacteristic
28C22×C4×C23C2×C411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C22×Dic23C2×C411yescharacteristic
31C22×Dic23C2×C411yescharacteristic
32C22×Dic23C2×C411yescharacteristic
33C22×Dic23C2×C411yescharacteristic
34C2×C8×C23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊Dic23—21no—
39C4⋊Dic23—21no—
40Dic23⋊C4—21no—
41Dic23⋊C4—21no—
42Dic23⋊C4—21no—
43Dic23⋊C4—21no—
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48C4×Dic23D411yescharacteristic
49C4×Dic23D411yescharacteristic
50C4×Dic23D411yescharacteristic
51C4×Dic23D411yescharacteristic
52C2×C23⋊C8—21no—
53C2×C23⋊C8—21no—
54C23×C23C22×C411yescharacteristic
55C2×C4×C23—21no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—41no—
60C2×C4×C23—41no—
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—22no—
66C2×Dic23—21no—
67C2×Dic23—21no—
68C2×Dic23—21no—
69C2×Dic23—21no—
70C2×Dic23—41no—
71C2×Dic23C22⋊C411yescharacteristic
72C2×Dic23C22⋊C411yescharacteristic
73C2×Dic23C22⋊C411yescharacteristic
74C2×Dic23C22⋊C411yescharacteristic
75C8×C23—41no—
76C8×C23—41no—
77C23⋊C8—41no—
78C23⋊C8—41no—
79#1470—231nomaximal, Sylow
80C22×C23—21no—
81C22×C23—21no—
82C22×C23C2×C22⋊C411yescharacteristic
83C22×C23#13111yescharacteristic
84C22×C23#13111yescharacteristic
85C4×C23—21no—
86C4×C23—21no—
87C4×C23—41no—
88C4×C23—41no—
89Dic23—21no—
90Dic23—21no—
91Dic23—21no—
92Dic23—41no—
93Dic23—41no—
94Dic23#10112yes—
95C2×#125—231no—
96#432—231no—
97#431—231no—
98#324—231no—
99#324—231no—
100#324—231no—
101#324D2311yescharacteristic
102C2×C23—21no—
103C2×C23—21no—
104C2×C23#40811yescharacteristic
105C2×C23#41011yescharacteristic
106C2×C23C2×#10111yescharacteristic
107#125—461no—
108#125—461no—
109#125—461no—
110#125—461no—
111C2×C4⋊C4—231no—
112C2×C4⋊C4—231no—
113C2×C4⋊C4—231no—
114C2×C4⋊C4—231no—
115C2×C4⋊C4—231no—
116C2×C4⋊C4C2×D2311yescharacteristic
117C2×C42—231no—
118C4⋊C8—461no—
119C4⋊C8—461no—
120C22⋊C8—231no—
121C22⋊C8—231no—
122C22⋊C8C2×D2311yescharacteristic
123C22⋊C8C2×D2311yescharacteristic
124#97—461no—
125C4×C8—461no—
126C23#147011yescharacteristic, complemented, Sylow
127C22×C4—231no—
128C22×C4—231no—
129C22×C4—231no—
130C22×C4—231no—
131C22×C4C4×D2311yescharacteristic
132C22×C4C4×D2311yescharacteristic
133C22×C4C22×D2311yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—461no—
137C2×C8—461no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—461no—
141C4⋊C4—461no—
142C4⋊C4—461no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4—461no—
148C4⋊C4—461no—
149C4⋊C4—461no—
150C42—231no—
151C42—231no—
152C42—231no—
153C42—231no—
154C23C2×C4×D2311yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—231no—
162C2×C4—231no—
163C2×C4—231no—
164C2×C4—231no—
165C2×C4—462no—
166C2×C4—461no—
167C2×C4—461no—
168C2×C4—461no—
169C2×C4—461no—
170C2×C4—461no—
171C2×C4—461no—
172C2×C4—921no—
173C2×C4D4×D2311yescharacteristic
174C2×C4D4×D2311yescharacteristic
175C8—41no—
176C8—41no—
177C8—921no—
178C8—921no—
179C22—21no—
180C22—21no—
181C22C22⋊C4×D2311yescharacteristic
182C22#1062507211yescharacteristic
183C22#1062507811yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—232no—
189C4—461no—
190C4—461no—
191C4—461no—
192C4—921no—
193C4—921no—
194C2—21no—
195C2—21no—
196C2#1309238211yescharacteristic
197C2#1309238911yescharacteristic
198C2#101×D2311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutator, prime radicalC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#324C2
socleC22×C23C2×C22⋊C4
cosocleC22×C4×C23C23
hypercenter#324D23
hypocenterC23#1470
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
126. C23#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#106250602
#130924712
#130924672
#130921432
#130921422
C23×#3242
#147023