Finite Group Databasebeta

← C22×C23×#99 #15670500

Subgroups — C22×C23×#99 #15670500

Order 2944.

1112 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 360 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×D4×C23C211yesmaximal, characteristic
2C22×C22⋊C4×C23C212yesmaximal, complemented
3C2×C23×#99C2112yesmaximal, direct product factor
4C25×C23C411yescharacteristic, complemented
5C25×C23C2211yescharacteristic
6C22×D4×C23—26no—
7C22×D4×C23—22no—
8C22×D4×C23C416yescomplemented
9C22×D4×C23C2216yes—
10C23×C4×C23—22no—
11C23×C4×C23C411yescharacteristic, complemented
12C2×C22⋊C4×C23—26no—
13C2×C22⋊C4×C23C22112yescomplemented
14C23×#99C22116yesdirect product factor
15C24×C23—23no—
16C24×C23—21no—
17C24×C23—44no—
18C24×C23—44no—
19C24×C23C2×C411yescharacteristic
20C24×C23C2×C413yes—
21C24×C23C2×C416yescomplemented
22C24×C23D412yes—
23C24×C23D416yes—
24C24×C23C2313yes—
25C2×D4×C23—212no—
26C2×D4×C23—212no—
27C2×D4×C23—212no—
28C2×D4×C23—212no—
29C2×D4×C23C2×C4112yescomplemented
30C2×D4×C23C2314yes—
31C22×C4×C23—23no—
32C22×C4×C23—21no—
33C22×C4×C23—212no—
34C22×C4×C23—48no—
35C22×C4×C23C2×C416yescomplemented
36C22⋊C4×C23—212no—
37C22⋊C4×C23C2318yescomplemented
38C23×C23—28no—
39C23×C23—24no—
40C23×C23—26no—
41C23×C23—26no—
42C23×C23—46no—
43C23×C23—412no—
44C23×C23—46no—
45C23×C23—412no—
46C23×C23—412no—
47C23×C23—44no—
48C23×C23C22⋊C413yes—
49C23×C23C22⋊C416yes—
50C23×C23C22⋊C416yes—
51C23×C23C22⋊C411yescharacteristic
52C23×C23C22×C413yes—
53C23×C23C22×C413yes—
54C23×C23C22×C414yescomplemented
55C23×C23C2×D416yes—
56C23×C23C2×D416yes—
57C23×C23C2411yescharacteristic
58D4×C23—224no—
59D4×C23—28no—
60C2×C4×C23—26no—
61C2×C4×C23—26no—
62C2×C4×C23—28no—
63C2×C4×C23—424no—
64C2×C4×C23C22×C414yescomplemented
65C22×#99C2311yesmaximal, characteristic, direct product factor, Sylow
66C22×C23—212no—
67C22×C23—26no—
68C22×C23—26no—
69C22×C23—212no—
70C22×C23—24no—
71C22×C23—46no—
72C22×C23—43no—
73C22×C23—46no—
74C22×C23—41no—
75C22×C23—44no—
76C22×C23—412no—
77C22×C23—412no—
78C22×C23#9914yesdirect product factor
79C22×C23C2×C22⋊C413yes—
80C22×C23C2×C22⋊C416yes—
81C22×C23C2×C22⋊C413yes—
82C22×C23C23×C411yescharacteristic
83C22×C23C22×D412yes—
84C4×C23—24no—
85C4×C23—48no—
86C23×D4C2×C2311yescharacteristic
87C22×C22⋊C4C2×C2312yescomplemented
88C2×#99C2×C23112yesdirect product factor
89C2×C23—22no—
90C2×C23—23no—
91C2×C23—21no—
92C2×C23—26no—
93C2×C23—44no—
94C2×C23C2×#9916yesdirect product factor
95C2×C23C22×C22⋊C411yescharacteristic
96C25C4×C2311yescharacteristic, complemented
97C25C22×C2311yescharacteristic
98C22×D4—22no—
99C22×D4—26no—
100C22×D4C4×C2316yescomplemented
101C22×D4C22×C2316yes—
102C23×C4—22no—
103C23×C4C4×C2311yescharacteristic, complemented
104C2×C22⋊C4—26no—
105C2×C22⋊C4C22×C23112yescomplemented
106#99C22×C23116yesdirect product factor
107C23C22×#9911yescharacteristic, direct product factor, Sylow
108C24—23no—
109C24—21no—
110C24—44no—
111C24—44no—
112C24C2×C4×C2311yescharacteristic
113C24C2×C4×C2313yes—
114C24C2×C4×C2316yescomplemented
115C24D4×C2312yes—
116C24D4×C2316yes—
117C24C23×C2313yes—
118C2×D4—212no—
119C2×D4—212no—
120C2×D4—212no—
121C2×D4—212no—
122C2×D4C2×C4×C23112yescomplemented
123C2×D4C23×C2314yes—
124C22×C4—23no—
125C22×C4—21no—
126C22×C4—212no—
127C22×C4—48no—
128C22×C4C2×C4×C2316yescomplemented
129C22⋊C4—212no—
130C22⋊C4C23×C2318yescomplemented
131C23—28no—
132C23—24no—
133C23—26no—
134C23—26no—
135C23—46no—
136C23—412no—
137C23—46no—
138C23—412no—
139C23—412no—
140C23—44no—
141C23C22⋊C4×C2313yes—
142C23C22⋊C4×C2316yes—
143C23C22⋊C4×C2316yes—
144C23C22⋊C4×C2311yescharacteristic
145C23C22×C4×C2313yes—
146C23C22×C4×C2313yes—
147C23C22×C4×C2314yescomplemented
148C23C2×D4×C2316yes—
149C23C2×D4×C2316yes—
150C23C24×C2311yescharacteristic
151D4—224no—
152D4—28no—
153C2×C4—26no—
154C2×C4—26no—
155C2×C4—28no—
156C2×C4—424no—
157C2×C4C22×C4×C2314yescomplemented
158C22—212no—
159C22—26no—
160C22—26no—
161C22—212no—
162C22—24no—
163C22—46no—
164C22—43no—
165C22—46no—
166C22—41no—
167C22—44no—
168C22—412no—
169C22—412no—
170C22C23×#9914yesdirect product factor
171C22C2×C22⋊C4×C2313yes—
172C22C2×C22⋊C4×C2316yes—
173C22C2×C22⋊C4×C2313yes—
174C22C23×C4×C2311yescharacteristic
175C22C22×D4×C2312yes—
176C4—24no—
177C4—48no—
178C2—22no—
179C2—23no—
180C2—21no—
181C2—26no—
182C2—44no—
183C2C2×C23×#9916yesdirect product factor
184C2C22×C22⋊C4×C2311yescharacteristic
subgroupG/H
center, socleC23×C23C22⋊C4
commutatorC22C23×C4×C23
Frattini, cosocleC23C24×C23
prime radicalC23×D4×C23C2
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C25×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊C4×C23C2semidirect
3. C2×C23×#99C2direct (N × H)
4. C25×C23C4semidirect
8. C22×D4×C23C4semidirect
11. C23×C4×C23C4semidirect
13. C2×C22⋊C4×C23C22semidirect
14. C23×#99C22direct (N × H)
21. C24×C23C2×C4semidirect
29. C2×D4×C23C2×C4semidirect
35. C22×C4×C23C2×C4semidirect
37. C22⋊C4×C23C23semidirect
54. C23×C23C22×C4semidirect
64. C2×C4×C23C22×C4semidirect
65. C22×#99C23direct (N × H)
78. C22×C23#99direct (N × H)
87. C22×C22⋊C4C2×C23semidirect
88. C2×#99C2×C23direct (N × H)
94. C2×C23C2×#99direct (N × H)
96. C25C4×C23semidirect
100. C22×D4C4×C23semidirect
103. C23×C4C4×C23semidirect
105. C2×C22⋊C4C22×C23semidirect
106. #99C22×C23direct (N × H)
107. C23C22×#99direct (N × H)
114. C24C2×C4×C23semidirect
122. C2×D4C2×C4×C23semidirect
128. C22×C4C2×C4×C23semidirect
130. C22⋊C4C23×C23semidirect
147. C23C22×C4×C23semidirect
157. C2×C4C22×C4×C23semidirect
170. C22C23×#99direct (N × H)
183. C2C2×C23×#99direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×C232
C22×C22⋊C4×C232
C2×C23×#992
C22×#9923