Finite Group Databasebeta

← #37588539

Subgroups — #37588539

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#27133811C212yesmaximal, complemented
3#27133809C211yesmaximal, characteristic, complemented
4#27133755C212yesmaximal, complemented
5#99×C383C211yesmaximal, characteristic, complemented
6C23×D383C2211yescharacteristic, complemented
7#20259457—21no—
8#20259456—22no—
9C2×D1532—22no—
10C2×C22⋊D383—21no—
11C2×C22⋊D383—21no—
12C2×C22⋊D383C2212yes—
13D4×D383—22no—
14C22⋊Dic383C2211yescharacteristic, complemented
15(C2×D383)⋊C4—22no—
16(C2×D383)⋊C4—21no—
17C2×D4×C383C2211yescharacteristic
18C22⋊C4×C383C2212yescomplemented
19C22×D383—21no—
20C22×D383—22no—
21C22×D383—21no—
22C22×D383—42no—
23C22×D383D412yescomplemented
24Dic766—21no—
25D1532—21no—
26D1532—44no—
27C22⋊D383—22no—
28C22⋊D383—22no—
29C22⋊D383—22no—
30C22⋊D383—42no—
31C2×Dic383—21no—
32C2×Dic383—21no—
33C2×Dic383D412yescomplemented
34C4×D383—22no—
35C23×C383D411yescharacteristic, complemented
36C23×C383C2311yescharacteristic
37D4×C383—22no—
38C2×C4×C383—22no—
39C2×C4×C383D411yescharacteristic, complemented
40C22×C383—21no—
41C22×C383—41no—
42C22×C383—41no—
43C22×C383C2×D412yes—
44C22×C383C2×D411yescharacteristic
45C2×D383—22no—
46C2×D383—24no—
47C2×D383—22no—
48C2×D383—41no—
49C2×D383—42no—
50C2×D383—41no—
51C2×D383—42no—
52C2×D383—81no—
53C4×C383—21no—
54C4×C383—42no—
55Dic383—22no—
56Dic383—41no—
57C2×C383—21no—
58C2×C383—22no—
59C2×C383—41no—
60C2×C383#12011yescharacteristic
61D383—42no—
62D383—42no—
63C383B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—3831nomaximal, Sylow
65H(5,𝔽2)—3831no—
66#120—3831no—
67#120—3832no—
68#99—3832no—
69#99D38311yescharacteristic, complemented
70C24—3831no—
71#41—7662no—
72#41—7661no—
73C2×D4—3832no—
74C2×D4—7662no—
75C2×D4—7662no—
76C2×D4—7661no—
77C2×D4—7661no—
78C2×D4C2×D38311yescharacteristic
79C22⋊C4—3831no—
80C22⋊C4—7662no—
81C22⋊C4—7661no—
82C22⋊C4C2×D38312yescomplemented
83C23—3832no—
84C23—15322no—
85C23—7661no—
86C23—7662no—
87C23—7661no—
88C23D153211yescharacteristic, complemented
89C23C22×D38311yescharacteristic
90Q8—7661no—
91D4—22no—
92D4—15324no—
93D4—15322no—
94D4—7661no—
95D4—7662no—
96D4—7662no—
97D4—7662no—
98C2×C4—22no—
99C2×C4—3832no—
100C2×C4—7662no—
101C2×C4—7661no—
102C2×C4—7661no—
103C2×C4D153211yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—30641no—
108C22—15322no—
109C22—15322no—
110C22—15321no—
111C22—15321no—
112C22—7664no—
113C22—7662no—
114C22—7662no—
115C22D4×D38312yes—
116C22C2×D153211yescharacteristic
117C4—21no—
118C4—42no—
119C4—15321no—
120C4—7662no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—15322no—
125C2—15322no—
126C2#2713381111yescharacteristic
subgroupG/H
centerC2#27133811
commutator, cosocleC23×C383C23
FrattiniC23C22×D383
Fitting#99×C383C2
socleC2×C383#120
hypercenter#99D383
hypocenterC383B(4,𝔽2)
LCSG ▷ C23×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #27133886C2semidirect
2. #27133811C2semidirect
3. #27133809C2semidirect
4. #27133755C2semidirect
5. #99×C383C2semidirect
6. C23×D383C22semidirect
14. C22⋊Dic383C22semidirect
18. C22⋊C4×C383C22semidirect
23. C22×D383D4semidirect
33. C2×Dic383D4semidirect
35. C23×C383D4semidirect
39. C2×C4×C383D4semidirect
63. C383B(4,𝔽2)semidirect
69. #99D383semidirect
82. C22⋊C4C2×D383semidirect
88. C23D1532semidirect
103. C2×C4D1532semidirect

Maximal subgroups

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

subgroupindex
#271338862
#271338112
#271338092
#271337552
#99×C3832
B(4,𝔽2)383