Finite Group Databasebeta

← #14583088

Subgroups — #14583088

Order 2752.

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#13063370C211yesmaximal, characteristic
2#13063308C212yesmaximal, complemented
3#13063240C211yesmaximal, characteristic, complemented
4#13063239C212yesmaximal, complemented
5#123×C43C211yesmaximal, characteristic, complemented
6C2×D4×C43C2211yescharacteristic
7C22×C4×C43C2211yescharacteristic, complemented
8C2×C22⋊D43—21no—
9C2×C22⋊D43C2212yes—
10#10621900—22no—
11D4×D43—22no—
12#10621898—21no—
13C4⋊C4×C43—21no—
14C22⋊C4×C43—21no—
15C22⋊C4×C43C2211yescharacteristic, complemented
16C22⋊Dic43C2212yescomplemented
17(C2×D43)⋊C4—22no—
18Dic43⋊C4—22no—
19C23×C43D411yescharacteristic
20C23×C43C2311yescharacteristic
21C22×D43—21no—
22C22×D43D412yes—
23D4×C43—22no—
24C2×C4×C43—22no—
25C2×C4×C43—21no—
26C2×C4×C43—21no—
27C2×C4×C43D411yescharacteristic
28C22⋊D43—22no—
29C22⋊D43—22no—
30C22⋊D43—22no—
31C2×Dic43—21no—
32C2×Dic43—22no—
33C2×Dic43D412yes—
34D172—21no—
35C4×D43—22no—
36Dic86—21no—
37C22×C43—21no—
38C22×C43—41no—
39C22×C43—41no—
40C22×C43C2×D412yes—
41C22×C43C2×D411yescharacteristic
42C2×D43—22no—
43C2×D43—42no—
44C2×D43—81no—
45C4×C43—21no—
46C4×C43—41no—
47C4×C43—41no—
48Dic43—22no—
49Dic43—42no—
50C2×C43—22no—
51C2×C43—21no—
52C2×C43—41no—
53C2×C43#12011yescharacteristic
54D43—42no—
55#458—431nomaximal, Sylow
56C43#45811yescharacteristic, complemented, Sylow
57H(5,𝔽2)—431no—
58#123—432no—
59#123D4311yescharacteristic, complemented
60#99—431no—
61#99—432no—
62#41—862no—
63#41—861no—
64C2×D4—432no—
65C2×D4—862no—
66C2×D4—861no—
67C2×D4C2×D4311yescharacteristic
68C22×C4C2×D4311yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—862no—
71C22⋊C4—21no—
72C22⋊C4—432no—
73C22⋊C4—862no—
74C22⋊C4C2×D4311yescharacteristic, complemented
75C23—432no—
76C23—861no—
77C23C22⋊D4311yescharacteristic
78C23C22×D4311yescharacteristic
79Q8—861no—
80D4—22no—
81D4—861no—
82D4—862no—
83D4—862no—
84D4—862no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—432no—
89C2×C4—862no—
90C2×C4—861no—
91C2×C4—862no—
92C2×C4C22⋊D4311yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—862no—
97C22—3441no—
98C22—1722no—
99C22D4×D4312yes—
100C22C2×C22⋊D4311yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—862no—
105C4—1722no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—1722no—
110C2#1306329311yescharacteristic
subgroupG/H
centerC2#13063293
commutator, cosocleC23×C43C23
FrattiniC23C22×D43
Fitting#123×C43C2
socleC2×C43#120
prime radical#13063370C2
hypercenter#123D43
hypocenterC43#458
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #13063308C2semidirect
3. #13063240C2semidirect
4. #13063239C2semidirect
5. #123×C43C2semidirect
7. C22×C4×C43C22semidirect
15. C22⋊C4×C43C22semidirect
16. C22⋊Dic43C22semidirect
56. C43#458semidirect
59. #123D43semidirect
68. C22×C4C2×D43semidirect
74. C22⋊C4C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633702
#130633082
#130632402
#130632392
#123×C432
#45843