Finite Group Databasebeta

← #14580525

Subgroups — #14580525

Order 2624.

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#13050209C211yesmaximal, characteristic
2#13050147C212yesmaximal, complemented
3#13050079C211yesmaximal, characteristic, complemented
4#13050078C212yesmaximal, complemented
5#123×C41C211yesmaximal, characteristic, complemented
6C2×D4×C41C2211yescharacteristic
7C22×C4×C41C2211yescharacteristic, complemented
8C2×C22⋊D41—21no—
9C2×C22⋊D41C2212yes—
10#10620308—22no—
11D4×D41—22no—
12#10620306—21no—
13C4⋊C4×C41—21no—
14C22⋊C4×C41—21no—
15C22⋊C4×C41C2211yescharacteristic, complemented
16C22⋊Dic41C2212yescomplemented
17#10620281—22no—
18#10620279—22no—
19C23×C41D411yescharacteristic
20C23×C41C2311yescharacteristic
21C22×D41—21no—
22C22×D41D412yes—
23D4×C41—22no—
24C2×C4×C41—22no—
25C2×C4×C41—21no—
26C2×C4×C41—21no—
27C2×C4×C41D411yescharacteristic
28C22⋊D41—22no—
29C22⋊D41—22no—
30C22⋊D41—22no—
31C2×Dic41—21no—
32C2×Dic41—22no—
33C2×Dic41D412yes—
34D164—21no—
35C4×D41—22no—
36Dic82—21no—
37C22×C41—21no—
38C22×C41—41no—
39C22×C41—41no—
40C22×C41C2×D412yes—
41C22×C41C2×D411yescharacteristic
42C2×D41—22no—
43C2×D41—42no—
44C2×D41—81no—
45C4×C41—21no—
46C4×C41—41no—
47C4×C41—41no—
48Dic41—22no—
49Dic41—42no—
50C2×C41—22no—
51C2×C41—21no—
52C2×C41—41no—
53C2×C41#12011yescharacteristic
54D41—42no—
55#458—411nomaximal, Sylow
56C41#45811yescharacteristic, complemented, Sylow
57H(5,𝔽2)—411no—
58#123—412no—
59#123D4111yescharacteristic, complemented
60#99—411no—
61#99—412no—
62#41—822no—
63#41—821no—
64C2×D4—412no—
65C2×D4—822no—
66C2×D4—821no—
67C2×D4C2×D4111yescharacteristic
68C22×C4C2×D4111yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—822no—
71C22⋊C4—21no—
72C22⋊C4—412no—
73C22⋊C4—822no—
74C22⋊C4C2×D4111yescharacteristic, complemented
75C23—412no—
76C23—821no—
77C23C22⋊D4111yescharacteristic
78C23C22×D4111yescharacteristic
79Q8—821no—
80D4—22no—
81D4—821no—
82D4—822no—
83D4—822no—
84D4—822no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—412no—
89C2×C4—822no—
90C2×C4—821no—
91C2×C4—822no—
92C2×C4C22⋊D4111yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—3281no—
97C22—822no—
98C22—1642no—
99C22D4×D4112yes—
100C22C2×C22⋊D4111yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—822no—
105C4—1642no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—1642no—
110C2#1305013211yescharacteristic
subgroupG/H
centerC2#13050132
commutator, cosocleC23×C41C23
FrattiniC23C22×D41
Fitting#123×C41C2
socleC2×C41#120
prime radical#13050209C2
hypercenter#123D41
hypocenterC41#458
LCSG ▷ C23×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #13050147C2semidirect
3. #13050079C2semidirect
4. #13050078C2semidirect
5. #123×C41C2semidirect
7. C22×C4×C41C22semidirect
15. C22⋊C4×C41C22semidirect
16. C22⋊Dic41C22semidirect
56. C41#458semidirect
59. #123D41semidirect
68. C22×C4C2×D41semidirect
74. C22⋊C4C2×D41semidirect

Maximal subgroups

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

subgroupindex
#130502092
#130501472
#130500792
#130500782
#123×C412
#45841