Finite Group Databasebeta

← C23×#1465 #15669084

Subgroups — C23×#1465 #15669084

Order 2944.

316 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×C4×D4×C23C211yesmaximal, characteristic
2C23×#407C212yesmaximal, complemented
3C23×#324C212yesmaximal, complemented
4C23×#323C212yesmaximal, complemented
5C22×D4×C23C411yescharacteristic
6C23×C4×C23C411yescharacteristic
7C23×C4×C23C2211yescharacteristic
8C2×M16×C23—22no—
9C4×D4×C23—22no—
10C4×D4×C23—22no—
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×C22⋊C4×C23C411yescharacteristic
13C2×C22⋊C4×C23C2211yescharacteristic
14C2×C42×C23C411yescharacteristic
15C23×C22⋊C8—22no—
16C23×C22⋊C8C2214yes—
17C24×C23C2×C411yescharacteristic
18C24×C23C2×C411yescharacteristic
19C2×D4×C23—22no—
20C2×D4×C23—22no—
21C2×D4×C23—22no—
22C22×C4×C23—21no—
23C22×C4×C23—21no—
24C22×C4×C23—42no—
25C22×C4×C23—42no—
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23C2×C411yescharacteristic
28C22×C4×C23C2×C411yescharacteristic
29C22×C4×C23C2×C411yescharacteristic
30C22×C4×C23D412yes—
31C22×C4×C23D412yes—
32C22×C4×C23C2311yescharacteristic
33M16×C23—44no—
34C2×C8×C23—24no—
35C4⋊C4×C23—22no—
36C22⋊C4×C23—22no—
37C22⋊C4×C23—22no—
38C42×C23—21no—
39C42×C23—21no—
40C23×C23—21no—
41C23×C23—21no—
42C23×C23—21no—
43C23×C23—21no—
44C23×C23—41no—
45C23×C23—41no—
46C23×C23—41no—
47C23×C23—41no—
48C23×C23C22⋊C412yes—
49C23×C23M1612yescomplemented
50C23×C23C22×C411yescharacteristic
51D4×C23—28no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—24no—
55C2×C4×C23—22no—
56C2×C4×C23—21no—
57C2×C4×C23—21no—
58C2×C4×C23—42no—
59C2×C4×C23—41no—
60C2×C4×C23—42no—
61C2×C4×C23—42no—
62C2×C4×C23—41no—
63C2×C4×C23—41no—
64C2×C4×C23C22⋊C411yescharacteristic
65C2×C4×C23C22⋊C411yescharacteristic
66C2×C4×C23M1612yescomplemented
67C2×C4×C23C2×D412yes—
68C8×C23—44no—
69#1465C2311yesmaximal, characteristic, direct product factor, Sylow
70C22×C23—21no—
71C22×C23—21no—
72C22×C23—22no—
73C22×C23—22no—
74C22×C23—22no—
75C22×C23—22no—
76C22×C23—42no—
77C22×C23—42no—
78C22×C23—42no—
79C22×C23—42no—
80C22×C23—41no—
81C22×C23—41no—
82C22×C23C2×C22⋊C411yescharacteristic
83C22×C23C2×M1611yescharacteristic
84C22×C23C2×M1611yescharacteristic
85C4×C23—22no—
86C4×C23—22no—
87C4×C23—21no—
88C4×C23—41no—
89C4×C23—41no—
90C4×C23#9912yes—
91C2×C4×D4C2×C2311yescharacteristic
92#407C2×C2312yescomplemented
93#324C2×C2312yescomplemented
94#323C2×C2312yescomplemented
95C2×C23—21no—
96C2×C23—21no—
97C2×C23—42no—
98C2×C23—42no—
99C2×C23#40711yescharacteristic
100C2×C23C2×#9911yescharacteristic
101C2×C23#41311yescharacteristic
102C22×D4C4×C2311yescharacteristic
103C23×C4C4×C2311yescharacteristic
104C23×C4C22×C2311yescharacteristic
105C2×M16—22no—
106C4×D4—22no—
107C4×D4—22no—
108C2×C4⋊C4C22×C2311yescharacteristic
109C2×C22⋊C4C4×C2311yescharacteristic
110C2×C22⋊C4C22×C2311yescharacteristic
111C2×C42C4×C2311yescharacteristic
112C22⋊C8—22no—
113C22⋊C8C22×C2314yes—
114C23#146511yescharacteristic, direct product factor, Sylow
115C24C2×C4×C2311yescharacteristic
116C24C2×C4×C2311yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4—22no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—42no—
123C22×C4—42no—
124C22×C4C2×C4×C2311yescharacteristic
125C22×C4C2×C4×C2311yescharacteristic
126C22×C4C2×C4×C2311yescharacteristic
127C22×C4C2×C4×C2311yescharacteristic
128C22×C4D4×C2312yes—
129C22×C4D4×C2312yes—
130C22×C4C23×C2311yescharacteristic
131M16—44no—
132C2×C8—24no—
133C4⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C42—21no—
137C42—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23—21no—
142C23—41no—
143C23—41no—
144C23—41no—
145C23—41no—
146C23C22⋊C4×C2312yes—
147C23M16×C2312yescomplemented
148C23C22×C4×C2311yescharacteristic
149D4—28no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—24no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4C22⋊C4×C2311yescharacteristic
163C2×C4C22⋊C4×C2311yescharacteristic
164C2×C4M16×C2312yescomplemented
165C2×C4C2×D4×C2312yes—
166C8—44no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—42no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—41no—
179C22C2×C22⋊C4×C2311yescharacteristic
180C22C2×M16×C2311yescharacteristic
181C22C2×M16×C2311yescharacteristic
182C4—22no—
183C4—22no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4C23×#9912yes—
188C2—21no—
189C2—21no—
190C2—42no—
191C2—42no—
192C2C23×#40711yescharacteristic
193C2C2×C23×#9911yescharacteristic
194C2C23×#41311yescharacteristic
subgroupG/H
center, socleC22×C23C2×C22⋊C4
commutatorC23C22×C4×C23
Frattini, cosocleC22×C4C23×C23
prime radicalC22×D4×C23C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#407C2semidirect
3. C23×#324C2semidirect
4. C23×#323C2semidirect
49. C23×C23M16semidirect
66. C2×C4×C23M16semidirect
69. #1465C23direct (N × H)
92. #407C2×C23semidirect
93. #324C2×C23semidirect
94. #323C2×C23semidirect
114. C23#1465direct (N × H)
147. C23M16×C23semidirect
164. C2×C4M16×C23semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C232
C23×#4072
C23×#3242
C23×#3232
#146523