Finite Group Databasebeta

← #15675978

Subgroups — #15675978

Order 2944.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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×C22⋊D23C211yesmaximal, characteristic
2C2×#10625048C212yesmaximal, complemented
3#13092317C218yesmaximal, complemented
4#13092273C211yesmaximal, characteristic, complemented
5#13092272C212yesmaximal, complemented
6C23×#379C211yesmaximal, characteristic, complemented
7C25×C23C2211yescharacteristic
8C24×D23C2211yescharacteristic
9C22×C22⋊D23—28no—
10C22×C22⋊D23C418yescomplemented
11C22×C22⋊D23C2214yes—
12C23×Dic23C2211yescharacteristic
13C2×C22⋊C4×C23C2212yes—
14C2×C22⋊C4×C23C2214yescomplemented
15C2×C22⋊Dic23C2212yes—
16C2×C22⋊Dic23C2214yescomplemented
17C2×(C2×D23)⋊C4C2218yescomplemented
18C2×Dic23⋊C4C2214yescomplemented
19C2×C4×Dic23C2214yescomplemented
20#10625048—28no—
21C24×C23—24no—
22C24×C23—44no—
23C24×C23C2×C414yes—
24C24×C23C2312yes—
25C24×C23C2311yescharacteristic
26C23×D23—24no—
27C23×D23—44no—
28C23×D23C2×C414yes—
29C23×D23C2312yes—
30C22×C4×C23C2314yes—
31C2×C22⋊D23—232no—
32C2×C22⋊D23—28no—
33C2×C22⋊D23—28no—
34C2×C22⋊D23C2×C4116yes—
35C22×Dic23C2×C414yes—
36C22×Dic23D418yes—
37C22×Dic23C2314yes—
38C22×Dic23C2312yes—
39C22⋊C4×C23—24no—
40C22⋊C4×C23—44no—
41C22⋊Dic23—24no—
42C22⋊Dic23—44no—
43(C2×D23)⋊C4—48no—
44Dic23⋊C4—28no—
45C4×Dic23—28no—
46C23×C23—24no—
47C23×C23—28no—
48C23×C23—24no—
49C23×C23—24no—
50C23×C23—24no—
51C23×C23—48no—
52C23×C23—416no—
53C23×C23C22×C414yes—
54C23×C23C22×C412yes—
55C23×C23C2×D414yes—
56C23×C23C2411yescharacteristic
57C22×D23—28no—
58C22×D23—24no—
59C22×D23—28no—
60C22×D23—48no—
61C22×D23—416no—
62C22×D23C22×C414yes—
63C2×C4×C23—24no—
64C2×C4×C23—28no—
65C22⋊D23—232no—
66C2×Dic23—24no—
67C2×Dic23—28no—
68C2×Dic23C22⋊C4116yescomplemented
69C2×Dic23C22×C414yes—
70C2×Dic23C2×D414yes—
71C2×Dic23C2×D414yes—
72#2309—231nomaximal, Sylow
73C22×C23—24no—
74C22×C23—28no—
75C22×C23—24no—
76C22×C23—24no—
77C22×C23—24no—
78C22×C23—416no—
79C22×C23—48no—
80C22×C23C2×C22⋊C414yes—
81C22×C23C23×C411yescharacteristic
82C22×C23C22×D412yes—
83C22×C23H(5,𝔽2)14yes—
84C2×D23—24no—
85C2×D23—28no—
86C2×D23—416no—
87C2×D23—48no—
88C4×C23—44no—
89Dic23—44no—
90Dic23C2×C22⋊C418yes—
91C23×D4—231no—
92C2×#117—232no—
93#390—238no—
94#379—231no—
95#379—232no—
96#379D2311yescharacteristic, complemented
97C2×C23—24no—
98C2×C23—44no—
99C2×C23C22×C22⋊C411yescharacteristic
100C2×C23#51812yes—
101C2×C23#53514yes—
102D23—44no—
103C25—231no—
104C25C2×D2311yescharacteristic
105C22×D4—238no—
106C22×D4—234no—
107C22×D4—468no—
108C23×C4—231no—
109#117—468no—
110C2×C4⋊C4—234no—
111C2×C22⋊C4—232no—
112C2×C22⋊C4—234no—
113C2×C22⋊C4—238no—
114C2×C22⋊C4C2×D2312yes—
115C2×C22⋊C4C2×D2314yescomplemented
116C2×C42—234no—
117C23#230911yescharacteristic, complemented, Sylow
118C24—24no—
119C24—44no—
120C24—232no—
121C24—234no—
122C24—464no—
123C24—924no—
124C24C4×D2314yes—
125C24C22×D2312yes—
126C24C22×D2311yescharacteristic
127C2×D4—2316no—
128C2×D4—4632no—
129C2×D4—468no—
130C2×D4—468no—
131C22×C4—234no—
132C22×C4—238no—
133C22×C4—232no—
134C22×C4—234no—
135C22×C4C22×D2314yes—
136C4⋊C4—468no—
137C22⋊C4—24no—
138C22⋊C4—44no—
139C22⋊C4—464no—
140C22⋊C4—928no—
141C22⋊C4—924no—
142C42—468no—
143C23—24no—
144C23—28no—
145C23—24no—
146C23—24no—
147C23—24no—
148C23—48no—
149C23—416no—
150C23—234no—
151C23—468no—
152C23—464no—
153C23—468no—
154C23—928no—
155C23—9216no—
156C23C2×C4×D2314yes—
157C23C2×C4×D2312yes—
158C23D4×D2314yes—
159C23C23×D2311yescharacteristic
160D4—4632no—
161C2×C4—24no—
162C2×C4—28no—
163C2×C4—2316no—
164C2×C4—234no—
165C2×C4—234no—
166C2×C4—234no—
167C2×C4—464no—
168C2×C4—468no—
169C22—24no—
170C22—28no—
171C22—24no—
172C22—24no—
173C22—24no—
174C22—416no—
175C22—48no—
176C22—468no—
177C22—464no—
178C22—9216no—
179C22—928no—
180C22C22⋊C4×D2314yes—
181C22C22×C4×D2311yescharacteristic
182C22C2×D4×D2312yes—
183C22#1062515514yes—
184C4—44no—
185C4—238no—
186C4—924no—
187C2—24no—
188C2—44no—
189C2—924no—
190C2C2×C22⋊C4×D2311yescharacteristic
191C2#1309289012yes—
192C2#1309298214yes—
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#379C2
socle, cosocleC23×C23C24
prime radicalC23×C22⋊D23C2
hypercenter#379D23
hypocenterC23#2309
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#10625048C2semidirect
3. #13092317C2semidirect
4. #13092273C2semidirect
5. #13092272C2semidirect
6. C23×#379C2semidirect
10. C22×C22⋊D23C4semidirect
14. C2×C22⋊C4×C23C22semidirect
16. C2×C22⋊Dic23C22semidirect
17. C2×(C2×D23)⋊C4C22semidirect
18. C2×Dic23⋊C4C22semidirect
19. C2×C4×Dic23C22semidirect
68. C2×Dic23C22⋊C4semidirect
96. #379D23semidirect
115. C2×C22⋊C4C2×D23semidirect
117. C23#2309semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D232
C2×#106250482
#130923172
#130922732
#130922722
C23×#3792
#230923