Finite Group Databasebeta

← C2×C23×#442 #15670561

Subgroups — C2×C23×#442 #15670561

Order 2944.

608 conjugacy classes of subgroups; only the 296 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 296 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
1C22×D8×C23C211yesmaximal, characteristic
2C2×C4×D4×C23C212yesmaximal, complemented
3C23×#442C218yesmaximal, direct product factor
4C2×C23×#106C211yesmaximal, characteristic, complemented
5C2×C23×#102C212yesmaximal, complemented
6C2×C23×#97C211yesmaximal, characteristic, complemented
7C22×D4×C23C2212yes—
8C23×C4×C23—22no—
9C2×D8×C23C418yescomplemented
10C2×D8×C23C2214yes—
11C22×C8×C23C2211yescharacteristic
12C22×C8×C23C2211yescharacteristic
13C4×D4×C23—24no—
14C4×D4×C23C2218yescomplemented
15C2×C4⋊C4×C23C2212yes—
16C2×C22⋊C4×C23—22no—
17C2×C42×C23C2211yescharacteristic
18C23×#106C2214yescomplemented
19C23×#102C2218yescomplemented
20C23×#97C2214yescomplemented
21C24×C23—22no—
22C2×D4×C23—22no—
23C2×D4×C23—24no—
24C2×D4×C23C2×C418yescomplemented
25C2×D4×C23C2314yes—
26C22×C4×C23—22no—
27C22×C4×C23—28no—
28C22×C4×C23—48no—
29C22×C4×C23D412yes—
30C22×C4×C23C2311yescharacteristic
31D8×C23C2×C4116yescomplemented
32C2×C8×C23—22no—
33C2×C8×C23C2×C414yescomplemented
34C2×C8×C23C2312yes—
35C2×C8×C23C2312yes—
36C4⋊C4×C23—22no—
37C4⋊C4×C23C2314yes—
38C22⋊C4×C23—28no—
39C42×C23D412yes—
40C42×C23C2312yes—
41C23×C23—28no—
42C23×C23—24no—
43C23×C23—44no—
44C23×C23—44no—
45C23×C23C2×D411yescharacteristic
46D4×C23—28no—
47D4×C23—24no—
48D4×C23C22×C418yescomplemented
49C2×C4×C23—24no—
50C2×C4×C23—24no—
51C2×C4×C23—416no—
52C2×C4×C23—44no—
53C2×C4×C23C22×C412yes—
54C2×C4×C23C2×D414yes—
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23#4112yes—
57C2×C4×C23C2411yescharacteristic
58C8×C23—22no—
59C8×C23C22×C414yescomplemented
60C2×#442C2311yesmaximal, characteristic, direct product factor, Sylow
61C22×C23—28no—
62C22×C23—44no—
63C22×C23—44no—
64C22×C23—416no—
65C22×C23C4×D412yes—
66C22×C23AGL(1,ℤ/8)14yes—
67C22×C23C22×D411yescharacteristic
68C4×C23—24no—
69C4×C23—44no—
70C4×C23C4×D412yes—
71C4×C23C23×C411yescharacteristic
72C4×C23C2×#4111yescharacteristic
73C22×D8C2×C2311yescharacteristic
74C2×C4×D4C2×C2312yescomplemented
75#442C2×C2318yesdirect product factor
76C2×#106C2×C2311yescharacteristic, complemented
77C2×#102C2×C2312yescomplemented
78C2×#97C2×C2311yescharacteristic, complemented
79C2×C23—48no—
80C2×C23#44214yesdirect product factor
81C2×C23C2×C4×D411yescharacteristic
82C2×C23C2×AGL(1,ℤ/8)12yes—
83C22×D4C22×C2312yes—
84C23×C4—22no—
85C2×D8C4×C2318yescomplemented
86C2×D8C22×C2314yes—
87C22×C8C22×C2311yescharacteristic
88C22×C8C22×C2311yescharacteristic
89C4×D4—24no—
90C4×D4C22×C2318yescomplemented
91C2×C4⋊C4C22×C2312yes—
92C2×C22⋊C4—22no—
93C2×C42C22×C2311yescharacteristic
94#106C22×C2314yescomplemented
95#102C22×C2318yescomplemented
96#97C22×C2314yescomplemented
97C23C2×#44211yescharacteristic, direct product factor, Sylow
98C24—22no—
99C2×D4—22no—
100C2×D4—24no—
101C2×D4C2×C4×C2318yescomplemented
102C2×D4C23×C2314yes—
103C22×C4—22no—
104C22×C4—28no—
105C22×C4—48no—
106C22×C4D4×C2312yes—
107C22×C4C23×C2311yescharacteristic
108D8C2×C4×C23116yescomplemented
109C2×C8—22no—
110C2×C8C2×C4×C2314yescomplemented
111C2×C8C23×C2312yes—
112C2×C8C23×C2312yes—
113C4⋊C4—22no—
114C4⋊C4C23×C2314yes—
115C22⋊C4—28no—
116C42D4×C2312yes—
117C42C23×C2312yes—
118C23—28no—
119C23—24no—
120C23—44no—
121C23—44no—
122C23C2×D4×C2311yescharacteristic
123D4—28no—
124D4—24no—
125D4C22×C4×C2318yescomplemented
126C2×C4—24no—
127C2×C4—24no—
128C2×C4—416no—
129C2×C4—44no—
130C2×C4C22×C4×C2312yes—
131C2×C4C2×D4×C2314yes—
132C2×C4C2×D4×C2311yescharacteristic
133C2×C4#41×C2312yes—
134C2×C4C24×C2311yescharacteristic
135C8—22no—
136C8C22×C4×C2314yescomplemented
137C22—28no—
138C22—44no—
139C22—44no—
140C22—416no—
141C22C4×D4×C2312yes—
142C22C23×AGL(1,ℤ/8)14yes—
143C22C22×D4×C2311yescharacteristic
144C4—24no—
145C4—44no—
146C4C4×D4×C2312yes—
147C4C23×C4×C2311yescharacteristic
148C4C2×#41×C2311yescharacteristic
149C2—48no—
150C2C23×#44214yesdirect product factor
151C2C2×C4×D4×C2311yescharacteristic
152C2C2×C23×AGL(1,ℤ/8)12yes—
subgroupG/H
center, socleC23×C23C2×D4
commutatorC4C23×C4×C23
Frattini, cosocleC2×C4C24×C23
prime radicalC22×D8×C23C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×C23C2semidirect
3. C23×#442C2direct (N × H)
4. C2×C23×#106C2semidirect
5. C2×C23×#102C2semidirect
6. C2×C23×#97C2semidirect
9. C2×D8×C23C4semidirect
14. C4×D4×C23C22semidirect
18. C23×#106C22semidirect
19. C23×#102C22semidirect
20. C23×#97C22semidirect
24. C2×D4×C23C2×C4semidirect
31. D8×C23C2×C4semidirect
33. C2×C8×C23C2×C4semidirect
48. D4×C23C22×C4semidirect
59. C8×C23C22×C4semidirect
60. C2×#442C23direct (N × H)
74. C2×C4×D4C2×C23semidirect
75. #442C2×C23direct (N × H)
76. C2×#106C2×C23semidirect
77. C2×#102C2×C23semidirect
78. C2×#97C2×C23semidirect
80. C2×C23#442direct (N × H)
85. C2×D8C4×C23semidirect
90. C4×D4C22×C23semidirect
94. #106C22×C23semidirect
95. #102C22×C23semidirect
96. #97C22×C23semidirect
97. C23C2×#442direct (N × H)
101. C2×D4C2×C4×C23semidirect
108. D8C2×C4×C23semidirect
110. C2×C8C2×C4×C23semidirect
125. D4C22×C4×C23semidirect
136. C8C22×C4×C23semidirect
150. C2C23×#442direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D8×C232
C2×C4×D4×C232
C23×#4422
C2×C23×#1062
C2×C23×#1022
C2×C23×#972
C2×#44223