Finite Group Databasebeta

← #37588537

Subgroups — #37588537

Order 24512.

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

normal subgroups only

This group has 198 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, complemented
2#27133810C212yesmaximal, complemented
3#27133756C211yesmaximal, characteristic, complemented
4#27133755C212yesmaximal, complemented
5#120×C383C211yesmaximal, characteristic, complemented
6#20259457—21no—
7#20259456—22no—
8C2×C22⋊D383—22no—
9C2×C22⋊D383—21no—
10C2×C22⋊D383C2212yes—
11D4×D383—22no—
12C22⋊Dic383—22no—
13C22⋊Dic383C2212yescomplemented
14C24×C383C2211yescharacteristic, complemented
15C2×D4×C383—21no—
16C2×D4×C383C2211yescharacteristic
17C22⋊C4×C383—21no—
18C22⋊C4×C383C2211yescharacteristic, complemented
19C22×D383—21no—
20C22×D383D412yescomplemented
21Dic766—21no—
22D1532—21no—
23C22⋊D383—22no—
24C22⋊D383—22no—
25C22⋊D383—22no—
26C22⋊D383—44no—
27C2×Dic383—21no—
28C2×Dic383—22no—
29C2×Dic383D412yescomplemented
30C4×D383—22no—
31C23×C383—21no—
32C23×C383—22no—
33C23×C383—42no—
34C23×C383D411yescharacteristic, complemented
35C23×C383C2311yescharacteristic
36D4×C383—22no—
37D4×C383—42no—
38C2×C4×C383—21no—
39C2×C4×C383D411yescharacteristic, complemented
40C22×C383—22no—
41C22×C383—24no—
42C22×C383—21no—
43C22×C383—41no—
44C22×C383—41no—
45C22×C383—42no—
46C22×C383—41no—
47C22×C383—41no—
48C22×C383C2×D412yes—
49C22×C383C2×D411yescharacteristic
50C2×D383—22no—
51C2×D383—42no—
52C2×D383—81no—
53C4×C383—21no—
54C4×C383—41no—
55Dic383—22no—
56Dic383—42no—
57C2×C383—22no—
58C2×C383—21no—
59C2×C383—41no—
60C2×C383—42no—
61C2×C383#12011yescharacteristic
62D383—42no—
63C383B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—3831nomaximal, Sylow
65H(5,𝔽2)—3831no—
66#120—3832no—
67#120D38311yescharacteristic, complemented
68#99—3831no—
69#99—3832no—
70C24C2×D38311yescharacteristic, complemented
71#41—7662no—
72#41—7661no—
73C2×D4—21no—
74C2×D4—3832no—
75C2×D4—7662no—
76C2×D4—7662no—
77C2×D4—7661no—
78C2×D4C2×D38311yescharacteristic
79C22⋊C4—21no—
80C22⋊C4—3832no—
81C22⋊C4—7662no—
82C22⋊C4C2×D38311yescharacteristic, complemented
83C23—22no—
84C23—21no—
85C23—42no—
86C23—3832no—
87C23—7661no—
88C23C22⋊D38311yescharacteristic, complemented
89C23C22×D38311yescharacteristic
90Q8—7661no—
91D4—22no—
92D4—42no—
93D4—15324no—
94D4—7661no—
95D4—7662no—
96D4—7662no—
97D4—7662no—
98C2×C4—21no—
99C2×C4—3832no—
100C2×C4—7662no—
101C2×C4—7662no—
102C2×C4—7661no—
103C2×C4C22⋊D38311yescharacteristic, complemented
104C22—22no—
105C22—24no—
106C22—21no—
107C22—41no—
108C22—41no—
109C22—41no—
110C22—42no—
111C22—41no—
112C22—30641no—
113C22—15322no—
114C22—7662no—
115C22D4×D38312yes—
116C22C2×C22⋊D38311yescharacteristic
117C4—21no—
118C4—41no—
119C4—15322no—
120C4—7662no—
121C2—21no—
122C2—22no—
123C2—42no—
124C2—41no—
125C2—15322no—
126C2#2713380911yescharacteristic
subgroupG/H
centerC2#27133809
commutator, cosocleC23×C383C23
FrattiniC23C22×D383
Fitting#120×C383C2
socleC2×C383#120
hypercenter#120D383
hypocenterC383B(4,𝔽2)
LCSG ▷ C23×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #27133886C2semidirect
2. #27133810C2semidirect
3. #27133756C2semidirect
4. #27133755C2semidirect
5. #120×C383C2semidirect
13. C22⋊Dic383C22semidirect
14. C24×C383C22semidirect
18. C22⋊C4×C383C22semidirect
20. C22×D383D4semidirect
29. C2×Dic383D4semidirect
34. C23×C383D4semidirect
39. C2×C4×C383D4semidirect
63. C383B(4,𝔽2)semidirect
67. #120D383semidirect
70. C24C2×D383semidirect
82. C22⋊C4C2×D383semidirect
88. C23C22⋊D383semidirect
103. C2×C4C22⋊D383semidirect

Maximal subgroups

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

subgroupindex
#271338862
#271338102
#271337562
#271337552
#120×C3832
B(4,𝔽2)383