Finite Group Databasebeta

← #37588540

Subgroups — #37588540

Order 24512.

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#27133886C211yesmaximal, characteristic
2#27133824C212yesmaximal, complemented
3#27133756C211yesmaximal, characteristic, complemented
4#27133755C212yesmaximal, complemented
5#123×C383C211yesmaximal, characteristic, complemented
6#20259457—21no—
7#20259456—22no—
8C2×C22⋊D383—21no—
9C2×C22⋊D383C2212yes—
10D4×D383—22no—
11Dic383⋊C4—22no—
12C22⋊Dic383C2212yescomplemented
13(C2×D383)⋊C4—22no—
14C2×D4×C383C2211yescharacteristic
15C22×C4×C383C2211yescharacteristic, complemented
16C4⋊C4×C383—21no—
17C22⋊C4×C383—21no—
18C22⋊C4×C383C2211yescharacteristic, complemented
19C22×D383—21no—
20C22×D383D412yes—
21Dic766—21no—
22D1532—21no—
23C22⋊D383—22no—
24C22⋊D383—22no—
25C22⋊D383—22no—
26C2×Dic383—21no—
27C2×Dic383—22no—
28C2×Dic383D412yes—
29C4×D383—22no—
30C23×C383D411yescharacteristic
31C23×C383C2311yescharacteristic
32D4×C383—22no—
33C2×C4×C383—21no—
34C2×C4×C383—21no—
35C2×C4×C383—22no—
36C2×C4×C383D411yescharacteristic
37C22×C383—21no—
38C22×C383—41no—
39C22×C383—41no—
40C22×C383C2×D412yes—
41C22×C383C2×D411yescharacteristic
42C2×D383—22no—
43C2×D383—42no—
44C2×D383—81no—
45C4×C383—21no—
46C4×C383—41no—
47C4×C383—41no—
48Dic383—22no—
49Dic383—42no—
50C2×C383—22no—
51C2×C383—21no—
52C2×C383—41no—
53C2×C383#12011yescharacteristic
54D383—42no—
55C383#45811yescharacteristic, complemented, Sylow
56#458—3831nomaximal, Sylow
57H(5,𝔽2)—3831no—
58#123—3832no—
59#123D38311yescharacteristic, complemented
60#99—3831no—
61#99—3832no—
62#41—7662no—
63#41—7661no—
64C2×D4—3832no—
65C2×D4—7662no—
66C2×D4—7661no—
67C2×D4C2×D38311yescharacteristic
68C22×C4C2×D38311yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—7662no—
71C22⋊C4—21no—
72C22⋊C4—3832no—
73C22⋊C4—7662no—
74C22⋊C4C2×D38311yescharacteristic, complemented
75C23—3832no—
76C23—7661no—
77C23C22⋊D38311yescharacteristic
78C23C22×D38311yescharacteristic
79Q8—7661no—
80D4—22no—
81D4—7661no—
82D4—7662no—
83D4—7662no—
84D4—7662no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—3832no—
89C2×C4—7662no—
90C2×C4—7662no—
91C2×C4—7661no—
92C2×C4C22⋊D38311yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—30641no—
97C22—15322no—
98C22—7662no—
99C22D4×D38312yes—
100C22C2×C22⋊D38311yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—15322no—
105C4—7662no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—15322no—
110C2#2713380911yescharacteristic
subgroupG/H
centerC2#27133809
commutator, cosocleC23×C383C23
FrattiniC23C22×D383
Fitting#123×C383C2
socleC2×C383#120
prime radical#27133886C2
hypercenter#123D383
hypocenterC383#458
LCSG ▷ C23×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #27133824C2semidirect
3. #27133756C2semidirect
4. #27133755C2semidirect
5. #123×C383C2semidirect
12. C22⋊Dic383C22semidirect
15. C22×C4×C383C22semidirect
18. C22⋊C4×C383C22semidirect
55. C383#458semidirect
59. #123D383semidirect
68. C22×C4C2×D383semidirect
74. C22⋊C4C2×D383semidirect

Maximal subgroups

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

subgroupindex
#271338862
#271338242
#271337562
#271337552
#123×C3832
#458383