Finite Group Databasebeta

← #15675777

Subgroups — #15675777

Order 2944.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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×C4×D23C211yesmaximal, characteristic
2C2×#10625048C212yesmaximal, complemented
3#13092280C211yesmaximal, characteristic, complemented
4#13092276C214yesmaximal, complemented
5#13092272C212yesmaximal
6#13092264C214yesmaximal, complemented
7C23×#381C211yesmaximal, characteristic, complemented
8C24×D23C2211yescharacteristic
9C23×C4×C23C2211yescharacteristic
10C23×Dic23C2211yescharacteristic
11C22×C4×D23—28no—
12C22×C4×D23C418yescomplemented
13C22×C4×D23C2212yes—
14C22×C4×D23C2212yes—
15C2×C22⋊C4×C23C2212yes—
16C2×C22⋊Dic23C2212yes—
17C2×(C2×D23)⋊C4C2218yes—
18C2×Dic23⋊C4C2214yescomplemented
19C2×C4×Dic23C2214yescomplemented
20#10625048—28no—
21C23×#95C2214yescomplemented
22C23⋊#95C2214yescomplemented
23C24×C23C2311yescharacteristic
24C23×D23—24no—
25C23×D23—28no—
26C23×D23C2×C414yes—
27C23×D23C2312yes—
28C22×C4×C23—24no—
29C22×C4×C23C2×C414yes—
30C22×C4×C23C2314yes—
31C22×C4×C23C2312yes—
32C22×Dic23C2×C414yes—
33C22×Dic23D418yes—
34C22×Dic23C2314yes—
35C22×Dic23C2311yescharacteristic
36C22×Dic23C2311yescharacteristic
37C2×C4×D23—232no—
38C2×C4×D23—28no—
39C2×C4×D23—28no—
40C2×C4×D23C2×C418yes—
41C2×C4×D23C2×C418yes—
42C22⋊C4×C23—24no—
43C22⋊Dic23—24no—
44(C2×D23)⋊C4—216no—
45Dic23⋊C4—28no—
46C4×Dic23—28no—
47C23×C23—24no—
48C23×C23C22×C412yes—
49C23×C23C2×D414yes—
50C23×C23C2411yescharacteristic
51C22×D23—232no—
52C22×D23—28no—
53C22×D23—24no—
54C22×D23—24no—
55C22×D23—216no—
56C22×D23C22×C414yes—
57C22×D23#4118yes—
58C2×C4×C23—28no—
59C2×C4×C23—24no—
60C2×C4×C23—24no—
61C2×C4×C23—28no—
62C2×C4×C23C22×C414yes—
63C2×Dic23—24no—
64C2×Dic23—28no—
65C2×Dic23C22⋊C4116yescomplemented
66C2×Dic23C22×C412yes—
67C2×Dic23C22×C412yes—
68C2×Dic23C2×D414yes—
69C2×Dic23C2×D414yes—
70C4×D23—216no—
71C4×D23—216no—
72#2280—231nomaximal, Sylow
73C22×C23—24no—
74C22×C23—28no—
75C22×C23C2×C22⋊C414yes—
76C22×C23C23×C411yescharacteristic
77C22×C23C22×D412yes—
78C22×C23C2×#4114yes—
79C2×D23—232no—
80C2×D23—24no—
81C2×D23—24no—
82C2×D23—216no—
83C2×D23#11718yescomplemented
84C4×C23—24no—
85C4×C23—44no—
86Dic23—44no—
87Dic23C2×C22⋊C414yes—
88Dic23C2×C22⋊C414yes—
89C24×C4—231no—
90C2×#117—232no—
91#381—231no—
92#381D2311yescharacteristic, complemented
93#380—234no—
94#379—232no—
95C4×C22⋊C4—234no—
96C2×C23—24no—
97C2×C23C22×C22⋊C411yescharacteristic
98C2×C23C2×#11712yes—
99C2×C23#52514yes—
100D23—28no—
101C25—231no—
102C23×C4—231no—
103C23×C4—238no—
104C23×C4—232no—
105C23×C4—232no—
106C23×C4—468no—
107C23×C4C2×D2311yescharacteristic
108#117—468no—
109C2×C4⋊C4—234no—
110C2×C22⋊C4—232no—
111C2×C22⋊C4—238no—
112C2×C22⋊C4C2×D2312yes—
113C2×C42—234no—
114#95—234no—
115#95C2×D2314yescomplemented
116C23#228011yescharacteristic, complemented, Sylow
117C24—232no—
118C24—234no—
119C24—468no—
120C24—464no—
121C24C22×D2311yescharacteristic
122C22×C4—24no—
123C22×C4—234no—
124C22×C4—238no—
125C22×C4—231no—
126C22×C4—231no—
127C22×C4—238no—
128C22×C4—238no—
129C22×C4—234no—
130C22×C4—4632no—
131C22×C4—468no—
132C22×C4—468no—
133C22×C4C4×D2314yes—
134C22×C4C22×D2314yes—
135C22×C4C22×D2312yes—
136C4⋊C4—468no—
137C22⋊C4—24no—
138C22⋊C4—4616no—
139C22⋊C4—464no—
140C42—468no—
141C23—24no—
142C23—234no—
143C23—238no—
144C23—4616no—
145C23—4632no—
146C23—468no—
147C23—464no—
148C23—464no—
149C23C2×C4×D2312yes—
150C23D4×D2314yes—
151C23C23×D2311yescharacteristic
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—2316no—
157C2×C4—232no—
158C2×C4—232no—
159C2×C4—234no—
160C2×C4—234no—
161C2×C4—4616no—
162C2×C4—4616no—
163C2×C4—464no—
164C2×C4—468no—
165C2×C4C2×C4×D2314yes—
166C22—24no—
167C22—28no—
168C22—238no—
169C22—4632no—
170C22—464no—
171C22—4616no—
172C22—464no—
173C22C22⋊C4×D2314yes—
174C22C22×C4×D2311yescharacteristic
175C22C2×D4×D2312yes—
176C22#41×D2314yes—
177C4—24no—
178C4—44no—
179C4—234no—
180C4—234no—
181C4—924no—
182C2—24no—
183C2—468no—
184C2C2×C22⋊C4×D2311yescharacteristic
185C2#117×D2312yes—
186C2#1309292514yes—
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#381C2
socle, cosocleC23×C23C24
prime radicalC24×D23C22
hypercenter#381D23
hypocenterC23#2280
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#10625048C2semidirect
3. #13092280C2semidirect
4. #13092276C2semidirect
6. #13092264C2semidirect
7. C23×#381C2semidirect
12. C22×C4×D23C4semidirect
18. C2×Dic23⋊C4C22semidirect
19. C2×C4×Dic23C22semidirect
21. C23×#95C22semidirect
22. C23⋊#95C22semidirect
65. C2×Dic23C22⋊C4semidirect
83. C2×D23#117semidirect
92. #381D23semidirect
115. #95C2×D23semidirect
116. C23#2280semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D232
C2×#106250482
#130922802
#130922762
#130922722
#130922642
C23×#3812
#228023