Finite Group Databasebeta

← #13092976

Subgroups — #13092976

Order 1472.

346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 111 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×D4×C23C211yesmaximal, characteristic, complemented
2C22×C22⋊D23C211yesmaximal, characteristic, complemented
3#10625124C212yesmaximal, complemented
4C2×C22⋊Dic23C211yesmaximal, characteristic, complemented
5#10625110C214yesmaximal, complemented
6#10625108C212yesmaximal, complemented
7#10625106C212yesmaximal, complemented
8#10625100C212yesmaximal, complemented
9C24×C23C2211yescharacteristic
10C24×C23C2211yescharacteristic, complemented
11C23×D23C2211yescharacteristic, complemented
12C2×D4×C23—24no—
13C2×D4×C23C2212yes—
14C2×D4×C23C2212yescomplemented
15C22×C4×C23C2211yescharacteristic, complemented
16C2×C22⋊D23—24no—
17C2×C22⋊D23C2212yes—
18C2×C22⋊D23C2212yescomplemented
19C2×C22⋊D23C2214yescomplemented
20C22×Dic23C2211yescharacteristic, complemented
21C22×Dic23C2212yescomplemented
22C22⋊Dic23C2212yescomplemented
23C22⋊Dic23C2212yescomplemented
24C22⋊Dic23C2214yescomplemented
25(C2×D23)⋊C4C2214yescomplemented
26Dic23⋊C4C2214yescomplemented
27C23×C23—22no—
28C23×C23—42no—
29C23×C23—42no—
30C23×C23D414yescomplemented
31C23×C23C2312yes—
32C23×C23C2311yescharacteristic
33C23×C23C2311yescharacteristic
34C23×C23C2311yescharacteristic
35C22×D23—22no—
36C22×D23—42no—
37C22×D23C2312yes—
38D4×C23—24no—
39D4×C23—24no—
40C2×C4×C23—22no—
41C2×C4×C23C2312yes—
42C22⋊D23—24no—
43C22⋊D23—24no—
44C22⋊D23—44no—
45C2×Dic23—22no—
46C2×Dic23—42no—
47C2×Dic23C2312yes—
48C2×Dic23C2314yes—
49C22×C23—22no—
50C22×C23—22no—
51C22×C23—22no—
52C22×C23—22no—
53C22×C23—24no—
54C22×C23—44no—
55C22×C23—44no—
56C22×C23C2×D412yes—
57C22×C23C2×D412yes—
58C22×C23C2×D412yes—
59C22×C23C2411yescharacteristic
60C2×D23—22no—
61C2×D23—24no—
62C2×D23—44no—
63C4×C23—22no—
64Dic23—22no—
65Dic23—24no—
66#534—231nomaximal, Sylow
67C2×C23—22no—
68C2×C23—22no—
69C2×C23—22no—
70C2×C23—42no—
71C2×C23C22×D411yescharacteristic
72C2×C23H(5,𝔽2)12yes—
73D23—42no—
74C22×D4—231no—
75C22×D4D2311yescharacteristic, complemented
76#123—232no—
77#123—232no—
78#121—234no—
79#120—232no—
80#120—232no—
81C2×C22⋊C4—231no—
82C23#53411yescharacteristic, complemented, Sylow
83C24—231no—
84C24C2×D2311yescharacteristic
85C24C2×D2311yescharacteristic, complemented
86C2×D4—24no—
87C2×D4—232no—
88C2×D4—232no—
89C2×D4—234no—
90C2×D4—464no—
91C2×D4C2×D2312yes—
92C2×D4C2×D2312yescomplemented
93C22×C4—231no—
94C22×C4—232no—
95C22×C4C2×D2311yescharacteristic, complemented
96C4⋊C4—234no—
97C22⋊C4—232no—
98C22⋊C4—232no—
99C22⋊C4—234no—
100C22⋊C4—234no—
101C23—22no—
102C23—42no—
103C23—42no—
104C23—232no—
105C23—462no—
106C23—922no—
107C23C22⋊D2314yescomplemented
108C23C22×D2312yes—
109C23C22×D2311yescharacteristic
110C23C22×D2311yescharacteristic
111C23C22×D2311yescharacteristic
112D4—24no—
113D4—24no—
114D4—464no—
115D4—464no—
116D4—924no—
117C2×C4—22no—
118C2×C4—234no—
119C2×C4—232no—
120C2×C4—462no—
121C2×C4—922no—
122C2×C4C22×D2312yes—
123C22—22no—
124C22—22no—
125C22—22no—
126C22—24no—
127C22—22no—
128C22—44no—
129C22—44no—
130C22—464no—
131C22—462no—
132C22—924no—
133C22C2×C22⋊D2312yes—
134C22C2×C22⋊D2312yes—
135C22C2×C22⋊D2312yes—
136C22C23×D2311yescharacteristic
137C4—22no—
138C4—464no—
139C4—462no—
140C2—22no—
141C2—22no—
142C2—22no—
143C2—42no—
144C2—922no—
145C2#1062515512yes—
146C2C22×C22⋊D2311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D23
commutator, socle, cosocleC22×C23C24
FittingC22×D4×C23C2
hypercenterC22×D4D23
hypocenterC23#534
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C23C2semidirect
2. C22×C22⋊D23C2semidirect
3. #10625124C2semidirect
4. C2×C22⋊Dic23C2semidirect
5. #10625110C2semidirect
6. #10625108C2semidirect
7. #10625106C2semidirect
8. #10625100C2semidirect
10. C24×C23C22semidirect
11. C23×D23C22semidirect
14. C2×D4×C23C22semidirect
15. C22×C4×C23C22semidirect
18. C2×C22⋊D23C22semidirect
19. C2×C22⋊D23C22semidirect
20. C22×Dic23C22semidirect
21. C22×Dic23C22semidirect
22. C22⋊Dic23C22semidirect
23. C22⋊Dic23C22semidirect
24. C22⋊Dic23C22semidirect
25. (C2×D23)⋊C4C22semidirect
26. Dic23⋊C4C22semidirect
30. C23×C23D4semidirect
75. C22×D4D23semidirect
82. C23#534semidirect
85. C24C2×D23semidirect
92. C2×D4C2×D23semidirect
95. C22×C4C2×D23semidirect
107. C23C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C232
C22×C22⋊D232
#106251242
C2×C22⋊Dic232
#106251102
#106251082
#106251062
#106251002
#53423