Finite Group Databasebeta

← C23×#2613 #15670232

Subgroups — C23×#2613 #15670232

Order 2944.

1134 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 232 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, complemented
2C2×C23×#123C211yesmaximal, characteristic, complemented
3C2×C23×#120C212yesmaximal, complemented
4C23×#394C214yesmaximal, complemented
5C23×#392C214yesmaximal, complemented
6C23×#381C211yesmaximal, characteristic, complemented
7C23×#379C212yesmaximal, complemented
8C25×C23C2212yes—
9C22×D4×C23—28no—
10C22×D4×C23—24no—
11C22×D4×C23C2214yes—
12C22×D4×C23C2211yescharacteristic
13C22×D4×C23C2214yescomplemented
14C23×C4×C23C2211yescharacteristic
15C23×#123—24no—
16C23×#120—28no—
17C2×C4⋊C4×C23C2212yescomplemented
18C2×C22⋊C4×C23C2211yescharacteristic
19C2×C22⋊C4×C23C2212yes—
20C2×C22⋊C4×C23C2212yescomplemented
21C2×C22⋊C4×C23C2214yescomplemented
22C2×C22⋊C4×C23C2218yescomplemented
23C23×#95C2214yescomplemented
24C24×C23—24no—
25C24×C23—24no—
26C24×C23—48no—
27C24×C23D418yescomplemented
28C24×C23C2311yescharacteristic
29C24×C23C2314yes—
30C24×C23C2311yescharacteristic
31C2×D4×C23—232no—
32C2×D4×C23—216no—
33C2×D4×C23—24no—
34C2×D4×C23—28no—
35C2×D4×C23—22no—
36C2×D4×C23—28no—
37C2×D4×C23—48no—
38C22×C4×C23—24no—
39C22×C4×C23D414yescomplemented
40C22×C4×C23C2312yes—
41C22×C4×C23C2314yes—
42C22×C4×C23C2311yescharacteristic
43C22×C4×C23C2312yes—
44C4⋊C4×C23—24no—
45C22⋊C4×C23—24no—
46C22⋊C4×C23—22no—
47C22⋊C4×C23—28no—
48C22⋊C4×C23—24no—
49C22⋊C4×C23—48no—
50C23×C23—24no—
51C23×C23—216no—
52C23×C23—24no—
53C23×C23—24no—
54C23×C23—28no—
55C23×C23—28no—
56C23×C23—21no—
57C23×C23—22no—
58C23×C23—24no—
59C23×C23—416no—
60C23×C23—416no—
61C23×C23—416no—
62C23×C23C2×D418yes—
63C23×C23C2×D414yes—
64C23×C23C2×D412yes—
65C23×C23C2411yescharacteristic
66D4×C23—232no—
67D4×C23—416no—
68D4×C23—44no—
69C2×C4×C23—28no—
70C2×C4×C23—24no—
71C2×C4×C23—22no—
72C2×C4×C23—22no—
73C2×C4×C23—24no—
74C2×C4×C23—21no—
75C2×C4×C23—24no—
76C2×C4×C23—28no—
77C2×C4×C23C2×D414yes—
78#2613C2311yesmaximal, characteristic, direct product factor, Sylow
79C22×C23—28no—
80C22×C23—24no—
81C22×C23—28no—
82C22×C23—28no—
83C22×C23—28no—
84C22×C23—432no—
85C22×C23—48no—
86C22×C23—48no—
87C22×C23—41no—
88C22×C23—44no—
89C22×C23—42no—
90C22×C23#12014yes—
91C22×C23C22×D412yes—
92C22×C23C22×D411yescharacteristic
93C22×C23H(5,𝔽2)14yes—
94C4×C23—24no—
95C4×C23—41no—
96C4×C23—44no—
97C4×C23—42no—
98C23×D4C2×C2311yescharacteristic, complemented
99C2×#123C2×C2311yescharacteristic, complemented
100C2×#120C2×C2312yescomplemented
101#394C2×C2314yescomplemented
102#392C2×C2314yescomplemented
103#381C2×C2311yescharacteristic, complemented
104#379C2×C2312yescomplemented
105C2×C23—24no—
106C2×C23—48no—
107C2×C23—81no—
108C2×C23C2×#12011yescharacteristic
109C2×C23#53414yes—
110C2×C23#53512yes—
111C25C22×C2312yes—
112C22×D4—28no—
113C22×D4—24no—
114C22×D4C22×C2311yescharacteristic
115C22×D4C22×C2314yes—
116C22×D4C22×C2314yescomplemented
117C23×C4C22×C2311yescharacteristic
118#123—24no—
119#120—28no—
120C2×C4⋊C4C22×C2312yescomplemented
121C2×C22⋊C4C22×C2312yes—
122C2×C22⋊C4C22×C2311yescharacteristic
123C2×C22⋊C4C22×C2314yescomplemented
124C2×C22⋊C4C22×C2312yescomplemented
125C2×C22⋊C4C22×C2318yescomplemented
126#95C22×C2314yescomplemented
127C23#261311yescharacteristic, direct product factor, Sylow
128C24—24no—
129C24—24no—
130C24—48no—
131C24D4×C2318yescomplemented
132C24C23×C2311yescharacteristic
133C24C23×C2314yes—
134C24C23×C2311yescharacteristic
135C2×D4—232no—
136C2×D4—216no—
137C2×D4—24no—
138C2×D4—28no—
139C2×D4—22no—
140C2×D4—28no—
141C2×D4—48no—
142C22×C4—24no—
143C22×C4D4×C2314yescomplemented
144C22×C4C23×C2314yes—
145C22×C4C23×C2312yes—
146C22×C4C23×C2311yescharacteristic
147C22×C4C23×C2312yes—
148C4⋊C4—24no—
149C22⋊C4—24no—
150C22⋊C4—22no—
151C22⋊C4—28no—
152C22⋊C4—24no—
153C22⋊C4—48no—
154C23—24no—
155C23—216no—
156C23—24no—
157C23—24no—
158C23—28no—
159C23—28no—
160C23—21no—
161C23—22no—
162C23—24no—
163C23—416no—
164C23—416no—
165C23—416no—
166C23C2×D4×C2318yes—
167C23C2×D4×C2314yes—
168C23C2×D4×C2312yes—
169C23C24×C2311yescharacteristic
170D4—232no—
171D4—416no—
172D4—44no—
173C2×C4—28no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—21no—
179C2×C4—24no—
180C2×C4—28no—
181C2×C4C2×D4×C2314yes—
182C22—28no—
183C22—24no—
184C22—28no—
185C22—28no—
186C22—28no—
187C22—432no—
188C22—48no—
189C22—48no—
190C22—41no—
191C22—44no—
192C22—42no—
193C22C23×#12014yes—
194C22C22×D4×C2312yes—
195C22C22×D4×C2311yescharacteristic
196C22C23×H(5,𝔽2)14yes—
197C4—24no—
198C4—41no—
199C4—44no—
200C4—42no—
201C2—24no—
202C2—48no—
203C2—81no—
204C2C2×C23×#12011yescharacteristic
205C2C23×#53414yes—
206C2C23×#53512yes—
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×#123C2semidirect
3. C2×C23×#120C2semidirect
4. C23×#394C2semidirect
5. C23×#392C2semidirect
6. C23×#381C2semidirect
7. C23×#379C2semidirect
13. C22×D4×C23C22semidirect
17. C2×C4⋊C4×C23C22semidirect
20. C2×C22⋊C4×C23C22semidirect
21. C2×C22⋊C4×C23C22semidirect
22. C2×C22⋊C4×C23C22semidirect
23. C23×#95C22semidirect
27. C24×C23D4semidirect
39. C22×C4×C23D4semidirect
78. #2613C23direct (N × H)
98. C23×D4C2×C23semidirect
99. C2×#123C2×C23semidirect
100. C2×#120C2×C23semidirect
101. #394C2×C23semidirect
102. #392C2×C23semidirect
103. #381C2×C23semidirect
104. #379C2×C23semidirect
116. C22×D4C22×C23semidirect
120. C2×C4⋊C4C22×C23semidirect
123. C2×C22⋊C4C22×C23semidirect
124. C2×C22⋊C4C22×C23semidirect
125. C2×C22⋊C4C22×C23semidirect
126. #95C22×C23semidirect
127. C23#2613direct (N × H)
131. C24D4×C23semidirect
143. C22×C4D4×C23semidirect

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×#1232
C2×C23×#1202
C23×#3942
C23×#3922
C23×#3812
C23×#3792
#261323