Finite Group Databasebeta

← #13092608

Subgroups — #13092608

Order 1472.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#10625155C211yesmaximal, characteristic
2#10625106C211yesmaximal, characteristic, complemented
3#10625057C212yesmaximal, complemented
4C23×#99C211yesmaximal, characteristic, complemented
5#10624988C212yesmaximal, complemented
6C2×D4×C23C2211yescharacteristic
7C2×C22⋊D23—21no—
8C2×C22⋊D23C2212yes—
9C22×Dic23C2211yescharacteristic, complemented
10#67290—22no—
11D4×D23—22no—
12#67288—21no—
13C22⋊C4×C23C2212yescomplemented
14C22⋊Dic23—21no—
15C22⋊Dic23C2211yescharacteristic, complemented
16(C2×D23)⋊C4—22no—
17C4⋊Dic23—22no—
18Dic23⋊C4—21no—
19C23×C23D411yescharacteristic
20C23×C23C2311yescharacteristic
21C22×D23—21no—
22C22×D23D412yes—
23D4×C23—22no—
24C2×C4×C23—22no—
25C2×C4×C23D411yescharacteristic
26C22⋊D23—22no—
27C22⋊D23—22no—
28C22⋊D23—22no—
29C2×Dic23—21no—
30C2×Dic23—21no—
31C2×Dic23—21no—
32C2×Dic23—22no—
33C2×Dic23D412yes—
34D92—21no—
35C4×D23—22no—
36Dic46—21no—
37C22×C23—21no—
38C22×C23—41no—
39C22×C23—41no—
40C22×C23C2×D411yescharacteristic
41C22×C23C2×D412yes—
42C2×D23—22no—
43C2×D23—42no—
44C2×D23—81no—
45C4×C23—21no—
46C4×C23—42no—
47Dic23—22no—
48Dic23—41no—
49Dic23—41no—
50#458—231nomaximal, Sylow
51C2×C23—21no—
52C2×C23—22no—
53C2×C23—41no—
54C2×C23#12011yescharacteristic
55D23—42no—
56H(5,𝔽2)—231no—
57#123—231no—
58#123—232no—
59#99—232no—
60#99D2311yescharacteristic, complemented
61C23#45811yescharacteristic, complemented, Sylow
62#41—462no—
63#41—461no—
64C2×D4—232no—
65C2×D4—462no—
66C2×D4—461no—
67C2×D4C2×D2311yescharacteristic
68C22×C4—231no—
69C4⋊C4—462no—
70C4⋊C4—461no—
71C22⋊C4—231no—
72C22⋊C4—462no—
73C22⋊C4—461no—
74C22⋊C4C2×D2312yescomplemented
75C23—232no—
76C23—461no—
77C23D9211yescharacteristic
78C23C22×D2311yescharacteristic
79Q8—461no—
80D4—22no—
81D4—461no—
82D4—462no—
83D4—462no—
84D4—462no—
85C2×C4—22no—
86C2×C4—232no—
87C2×C4—462no—
88C2×C4—461no—
89C2×C4—461no—
90C2×C4—461no—
91C2×C4—462no—
92C2×C4D9211yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—462no—
97C22—922no—
98C22—1841no—
99C22C2×D9211yescharacteristic
100C22D4×D2312yes—
101C4—21no—
102C4—42no—
103C4—462no—
104C4—921no—
105C4—921no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—922no—
110C2#1062505311yescharacteristic
subgroupG/H
centerC2#10625053
commutator, cosocleC23×C23C23
FrattiniC23C22×D23
FittingC23×#99C2
socleC2×C23#120
prime radical#10625155C2
hypercenter#99D23
hypocenterC23#458
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #10625106C2semidirect
3. #10625057C2semidirect
4. C23×#99C2semidirect
5. #10624988C2semidirect
9. C22×Dic23C22semidirect
13. C22⋊C4×C23C22semidirect
15. C22⋊Dic23C22semidirect
60. #99D23semidirect
61. C23#458semidirect
74. C22⋊C4C2×D23semidirect

Maximal subgroups

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

subgroupindex
#106251552
#106251062
#106250572
C23×#992
#106249882
#45823