Finite Group Databasebeta

← C23×#2403 #15670022

Subgroups — C23×#2403 #15670022

Order 2944.

1564 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 1564 conjugacy classes of subgroups — too many to draw. Only its 280 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×C23C212yesmaximal, complemented
2C2×C23×#120C214yesmaximal, complemented
3C23×#392C214yesmaximal, complemented
4C23×#386C214yesmaximal, complemented
5C23×#379C211yesmaximal, characteristic, complemented
6C25×C23C2211yescharacteristic
7C25×C23C2212yescomplemented
8C22×D4×C23—28no—
9C22×D4×C23—216no—
10C22×D4×C23C2214yes—
11C22×D4×C23C2214yescomplemented
12C22×D4×C23C2214yescomplemented
13C23×C4×C23C2212yescomplemented
14C23×#120—216no—
15C2×C22⋊C4×C23C2214yescomplemented
16C2×C22⋊C4×C23C2218yescomplemented
17C2×C22⋊C4×C23C2212yescomplemented
18C23×#95C2214yescomplemented
19C24×C23—28no—
20C24×C23—24no—
21C24×C23—28no—
22C24×C23—28no—
23C24×C23—42no—
24C24×C23—44no—
25C24×C23D414yescomplemented
26C24×C23C2311yescharacteristic
27C24×C23C2314yes—
28C24×C23C2312yes—
29C2×D4×C23—264no—
30C2×D4×C23—28no—
31C2×D4×C23—28no—
32C2×D4×C23—28no—
33C2×D4×C23—28no—
34C2×D4×C23—216no—
35C2×D4×C23—28no—
36C2×D4×C23—44no—
37C2×D4×C23D4116yescomplemented
38C22×C4×C23—24no—
39C22×C4×C23—28no—
40C22×C4×C23C2314yes—
41C22×C4×C23C2314yes—
42C22⋊C4×C23—28no—
43C22⋊C4×C23—216no—
44C22⋊C4×C23—42no—
45C23×C23—24no—
46C23×C23—24no—
47C23×C23—216no—
48C23×C23—216no—
49C23×C23—28no—
50C23×C23—24no—
51C23×C23—24no—
52C23×C23—24no—
53C23×C23—22no—
54C23×C23—28no—
55C23×C23—44no—
56C23×C23—416no—
57C23×C23—432no—
58C23×C23—48no—
59C23×C23—48no—
60C23×C23C2×D412yes—
61C23×C23C2×D418yes—
62C23×C23C2×D414yes—
63C23×C23C2×D418yescomplemented
64C23×C23C2411yescharacteristic
65D4×C23—232no—
66D4×C23—232no—
67D4×C23—416no—
68C2×C4×C23—216no—
69C2×C4×C23—24no—
70C2×C4×C23—24no—
71C2×C4×C23—28no—
72C2×C4×C23—24no—
73C2×C4×C23C2×D418yescomplemented
74#2403C2311yesmaximal, characteristic, direct product factor, Sylow
75C22×C23—24no—
76C22×C23—24no—
77C22×C23—216no—
78C22×C23—24no—
79C22×C23—28no—
80C22×C23—22no—
81C22×C23—216no—
82C22×C23—416no—
83C22×C23—432no—
84C22×C23—44no—
85C22×C23—44no—
86C22×C23—48no—
87C22×C23—44no—
88C22×C23#12018yescomplemented
89C22×C23C22×D411yescharacteristic
90C22×C23C22×D414yes—
91C22×C23H(5,𝔽2)12yes—
92C4×C23—28no—
93C4×C23—44no—
94C23×D4C2×C2312yescomplemented
95C2×#120C2×C2314yescomplemented
96#392C2×C2314yescomplemented
97#386C2×C2314yescomplemented
98#379C2×C2311yescharacteristic, complemented
99C2×C23—28no—
100C2×C23—42no—
101C2×C23—48no—
102C2×C23C2×#12012yes—
103C2×C23#53411yescharacteristic
104C2×C23D4214yes—
105C25C22×C2311yescharacteristic
106C25C22×C2312yescomplemented
107C22×D4—28no—
108C22×D4—216no—
109C22×D4C22×C2314yes—
110C22×D4C22×C2314yescomplemented
111C22×D4C22×C2314yescomplemented
112C23×C4C22×C2312yescomplemented
113#120—216no—
114C2×C22⋊C4C22×C2314yescomplemented
115C2×C22⋊C4C22×C2318yescomplemented
116C2×C22⋊C4C22×C2312yescomplemented
117#95C22×C2314yescomplemented
118C23#240311yescharacteristic, direct product factor, Sylow
119C24—28no—
120C24—24no—
121C24—28no—
122C24—28no—
123C24—42no—
124C24—44no—
125C24D4×C2314yescomplemented
126C24C23×C2311yescharacteristic
127C24C23×C2314yes—
128C24C23×C2312yes—
129C2×D4—264no—
130C2×D4—28no—
131C2×D4—28no—
132C2×D4—28no—
133C2×D4—28no—
134C2×D4—216no—
135C2×D4—28no—
136C2×D4—44no—
137C2×D4D4×C23116yescomplemented
138C22×C4—24no—
139C22×C4—28no—
140C22×C4C23×C2314yes—
141C22×C4C23×C2314yes—
142C22⋊C4—28no—
143C22⋊C4—216no—
144C22⋊C4—42no—
145C23—24no—
146C23—24no—
147C23—216no—
148C23—216no—
149C23—28no—
150C23—24no—
151C23—24no—
152C23—24no—
153C23—22no—
154C23—28no—
155C23—44no—
156C23—416no—
157C23—432no—
158C23—48no—
159C23—48no—
160C23C2×D4×C2312yes—
161C23C2×D4×C2318yes—
162C23C2×D4×C2314yes—
163C23C2×D4×C2318yescomplemented
164C23C24×C2311yescharacteristic
165D4—232no—
166D4—232no—
167D4—416no—
168C2×C4—216no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—28no—
172C2×C4—24no—
173C2×C4C2×D4×C2318yescomplemented
174C22—24no—
175C22—24no—
176C22—216no—
177C22—24no—
178C22—28no—
179C22—22no—
180C22—216no—
181C22—416no—
182C22—432no—
183C22—44no—
184C22—44no—
185C22—48no—
186C22—44no—
187C22C23×#12018yescomplemented
188C22C22×D4×C2311yescharacteristic
189C22C22×D4×C2314yes—
190C22C23×H(5,𝔽2)12yes—
191C4—28no—
192C4—44no—
193C2—28no—
194C2—42no—
195C2—48no—
196C2C2×C23×#12012yes—
197C2C23×#53411yescharacteristic
198C2D42×C2314yes—
subgroupG/H
center, socleC23×C23C24
commutator, Frattini, cosocleC23C24×C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×D4×C23C2semidirect
2. C2×C23×#120C2semidirect
3. C23×#392C2semidirect
4. C23×#386C2semidirect
5. C23×#379C2semidirect
7. C25×C23C22semidirect
11. C22×D4×C23C22semidirect
12. C22×D4×C23C22semidirect
13. C23×C4×C23C22semidirect
15. C2×C22⋊C4×C23C22semidirect
16. C2×C22⋊C4×C23C22semidirect
17. C2×C22⋊C4×C23C22semidirect
18. C23×#95C22semidirect
25. C24×C23D4semidirect
37. C2×D4×C23D4semidirect
63. C23×C23C2×D4semidirect
73. C2×C4×C23C2×D4semidirect
74. #2403C23direct (N × H)
88. C22×C23#120semidirect
94. C23×D4C2×C23semidirect
95. C2×#120C2×C23semidirect
96. #392C2×C23semidirect
97. #386C2×C23semidirect
98. #379C2×C23semidirect
106. C25C22×C23semidirect
110. C22×D4C22×C23semidirect
111. C22×D4C22×C23semidirect
112. C23×C4C22×C23semidirect
114. C2×C22⋊C4C22×C23semidirect
115. C2×C22⋊C4C22×C23semidirect
116. C2×C22⋊C4C22×C23semidirect
117. #95C22×C23semidirect
118. C23#2403direct (N × H)
125. C24D4×C23semidirect
137. C2×D4D4×C23semidirect
163. C23C2×D4×C23semidirect
173. C2×C4C2×D4×C23semidirect
187. C22C23×#120semidirect

Maximal subgroups

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

subgroupindex
C23×D4×C232
C2×C23×#1202
C23×#3922
C23×#3862
C23×#3792
#240323