Finite Group Databasebeta

← #44543284

Subgroups — #44543284

Order 31936.

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#30630396C211yesmaximal, characteristic, complemented
2#30630320C212yesmaximal, complemented
3#30630266C211yesmaximal, characteristic, complemented
4#30630265C212yesmaximal, complemented
5#120×C499C211yesmaximal, characteristic, complemented
6#22547811—21no—
7#22547810—22no—
8C2×C22⋊D499—21no—
9C2×C22⋊D499—22no—
10C2×C22⋊D499C2212yes—
11D4×D499—22no—
12C22⋊Dic499—22no—
13C22⋊Dic499C2212yescomplemented
14C24×C499C2211yescharacteristic, complemented
15C2×D4×C499—21no—
16C2×D4×C499C2211yescharacteristic
17C22⋊C4×C499—21no—
18C22⋊C4×C499C2211yescharacteristic, complemented
19C22×D499—21no—
20C22×D499D412yescomplemented
21Dic998—21no—
22D1996—21no—
23C22⋊D499—22no—
24C22⋊D499—22no—
25C22⋊D499—22no—
26C22⋊D499—44no—
27C2×Dic499—21no—
28C2×Dic499—22no—
29C2×Dic499D412yescomplemented
30C4×D499—22no—
31C23×C499—21no—
32C23×C499—22no—
33C23×C499—42no—
34C23×C499D411yescharacteristic, complemented
35C23×C499C2311yescharacteristic
36D4×C499—22no—
37D4×C499—42no—
38C2×C4×C499—21no—
39C2×C4×C499D411yescharacteristic, complemented
40C22×C499—24no—
41C22×C499—22no—
42C22×C499—21no—
43C22×C499—41no—
44C22×C499—41no—
45C22×C499—42no—
46C22×C499—41no—
47C22×C499—41no—
48C22×C499C2×D412yes—
49C22×C499C2×D411yescharacteristic
50C2×D499—22no—
51C2×D499—42no—
52C2×D499—81no—
53C4×C499—21no—
54C4×C499—41no—
55Dic499—22no—
56Dic499—42no—
57C2×C499—22no—
58C2×C499—21no—
59C2×C499—41no—
60C2×C499—42no—
61C2×C499#12011yescharacteristic
62D499—42no—
63C499B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—4991nomaximal, Sylow
65H(5,𝔽2)—4991no—
66#120—4992no—
67#120D49911yescharacteristic, complemented
68#99—4991no—
69#99—4992no—
70C24C2×D49911yescharacteristic, complemented
71#41—9982no—
72#41—9981no—
73C2×D4—21no—
74C2×D4—9982no—
75C2×D4—9982no—
76C2×D4—9981no—
77C2×D4—4992no—
78C2×D4C2×D49911yescharacteristic
79C22⋊C4—21no—
80C22⋊C4—9982no—
81C22⋊C4—4992no—
82C22⋊C4C2×D49911yescharacteristic, complemented
83C23—22no—
84C23—21no—
85C23—42no—
86C23—9981no—
87C23—4992no—
88C23C22⋊D49911yescharacteristic, complemented
89C23C22×D49911yescharacteristic
90Q8—9981no—
91D4—22no—
92D4—42no—
93D4—19964no—
94D4—9981no—
95D4—9982no—
96D4—9982no—
97D4—9982no—
98C2×C4—21no—
99C2×C4—9982no—
100C2×C4—9982no—
101C2×C4—9981no—
102C2×C4—4992no—
103C2×C4C22⋊D49911yescharacteristic, complemented
104C22—22no—
105C22—24no—
106C22—21no—
107C22—41no—
108C22—41no—
109C22—41no—
110C22—42no—
111C22—41no—
112C22—39921no—
113C22—19962no—
114C22—9982no—
115C22D4×D49912yes—
116C22C2×C22⋊D49911yescharacteristic
117C4—21no—
118C4—41no—
119C4—19962no—
120C4—9982no—
121C2—21no—
122C2—22no—
123C2—42no—
124C2—41no—
125C2—19962no—
126C2#3063031911yescharacteristic
subgroupG/H
centerC2#30630319
commutator, cosocleC23×C499C23
FrattiniC23C22×D499
Fitting#120×C499C2
socleC2×C499#120
hypercenter#120D499
hypocenterC499B(4,𝔽2)
LCSG ▷ C23×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #30630396C2semidirect
2. #30630320C2semidirect
3. #30630266C2semidirect
4. #30630265C2semidirect
5. #120×C499C2semidirect
13. C22⋊Dic499C22semidirect
14. C24×C499C22semidirect
18. C22⋊C4×C499C22semidirect
20. C22×D499D4semidirect
29. C2×Dic499D4semidirect
34. C23×C499D4semidirect
39. C2×C4×C499D4semidirect
63. C499B(4,𝔽2)semidirect
67. #120D499semidirect
70. C24C2×D499semidirect
82. C22⋊C4C2×D499semidirect
88. C23C22⋊D499semidirect
103. C2×C4C22⋊D499semidirect

Maximal subgroups

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

subgroupindex
#306303962
#306303202
#306302662
#306302652
#120×C4992
B(4,𝔽2)499