Finite Group Databasebeta

← #14580522

Subgroups — #14580522

Order 2624.

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#13050209C211yesmaximal, characteristic, complemented
2#13050133C212yesmaximal, complemented
3#13050079C211yesmaximal, characteristic, complemented
4#13050078C212yesmaximal, complemented
5#120×C41C211yesmaximal, characteristic, complemented
6C24×C41C2211yescharacteristic, complemented
7C2×D4×C41—21no—
8C2×D4×C41C2211yescharacteristic
9C2×C22⋊D41—21no—
10C2×C22⋊D41—22no—
11C2×C22⋊D41C2212yes—
12#10620308—22no—
13D4×D41—22no—
14#10620306—21no—
15C22⋊C4×C41—21no—
16C22⋊C4×C41C2211yescharacteristic, complemented
17C22⋊Dic41—22no—
18C22⋊Dic41C2212yescomplemented
19C23×C41—22no—
20C23×C41—21no—
21C23×C41—42no—
22C23×C41D411yescharacteristic, complemented
23C23×C41C2311yescharacteristic
24C22×D41—21no—
25C22×D41D412yescomplemented
26D4×C41—22no—
27D4×C41—42no—
28C2×C4×C41—21no—
29C2×C4×C41D411yescharacteristic, complemented
30C22⋊D41—22no—
31C22⋊D41—22no—
32C22⋊D41—22no—
33C22⋊D41—44no—
34C2×Dic41—21no—
35C2×Dic41—22no—
36C2×Dic41D412yescomplemented
37D164—21no—
38C4×D41—22no—
39Dic82—21no—
40C22×C41—24no—
41C22×C41—22no—
42C22×C41—21no—
43C22×C41—41no—
44C22×C41—41no—
45C22×C41—42no—
46C22×C41—41no—
47C22×C41—41no—
48C22×C41C2×D412yes—
49C22×C41C2×D411yescharacteristic
50C2×D41—22no—
51C2×D41—42no—
52C2×D41—81no—
53C4×C41—21no—
54C4×C41—41no—
55Dic41—22no—
56Dic41—42no—
57C2×C41—22no—
58C2×C41—21no—
59C2×C41—41no—
60C2×C41—42no—
61C2×C41#12011yescharacteristic
62D41—42no—
63B(4,𝔽2)—411nomaximal, Sylow
64C41B(4,𝔽2)11yescharacteristic, complemented, Sylow
65H(5,𝔽2)—411no—
66#120—412no—
67#120D4111yescharacteristic, complemented
68#99—411no—
69#99—412no—
70C24C2×D4111yescharacteristic, complemented
71#41—822no—
72#41—821no—
73C2×D4—21no—
74C2×D4—412no—
75C2×D4—822no—
76C2×D4—821no—
77C2×D4—822no—
78C2×D4C2×D4111yescharacteristic
79C22⋊C4—21no—
80C22⋊C4—412no—
81C22⋊C4—822no—
82C22⋊C4C2×D4111yescharacteristic, complemented
83C23—22no—
84C23—21no—
85C23—42no—
86C23—412no—
87C23—821no—
88C23C22⋊D4111yescharacteristic, complemented
89C23C22×D4111yescharacteristic
90Q8—821no—
91D4—22no—
92D4—42no—
93D4—821no—
94D4—822no—
95D4—822no—
96D4—822no—
97D4—1644no—
98C2×C4—21no—
99C2×C4—412no—
100C2×C4—822no—
101C2×C4—821no—
102C2×C4—822no—
103C2×C4C22⋊D4111yescharacteristic, complemented
104C22—22no—
105C22—24no—
106C22—21no—
107C22—41no—
108C22—41no—
109C22—41no—
110C22—42no—
111C22—41no—
112C22—3281no—
113C22—822no—
114C22—1642no—
115C22D4×D4112yes—
116C22C2×C22⋊D4111yescharacteristic
117C4—21no—
118C4—41no—
119C4—822no—
120C4—1642no—
121C2—21no—
122C2—22no—
123C2—42no—
124C2—41no—
125C2—1642no—
126C2#1305013211yescharacteristic
subgroupG/H
centerC2#13050132
commutator, cosocleC23×C41C23
FrattiniC23C22×D41
Fitting#120×C41C2
socleC2×C41#120
hypercenter#120D41
hypocenterC41B(4,𝔽2)
LCSG ▷ C23×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #13050209C2semidirect
2. #13050133C2semidirect
3. #13050079C2semidirect
4. #13050078C2semidirect
5. #120×C41C2semidirect
6. C24×C41C22semidirect
16. C22⋊C4×C41C22semidirect
18. C22⋊Dic41C22semidirect
22. C23×C41D4semidirect
25. C22×D41D4semidirect
29. C2×C4×C41D4semidirect
36. C2×Dic41D4semidirect
64. C41B(4,𝔽2)semidirect
67. #120D41semidirect
70. C24C2×D41semidirect
82. C22⋊C4C2×D41semidirect
88. C23C22⋊D41semidirect
103. C2×C4C22⋊D41semidirect

Maximal subgroups

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

subgroupindex
#130502092
#130501332
#130500792
#130500782
#120×C412
B(4,𝔽2)41