Finite Group Databasebeta

← #14581315

Subgroups — #14581315

Order 2624.

158 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 48 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#13050243C212yesmaximal, complemented
2#13050223C212yesmaximal, complemented
3#13050222C212yesmaximal, complemented
4C2×#10620306C211yesmaximal, characteristic
5C22×C4×C41C411yescharacteristic, complemented
6C2×C22⋊D41C411yescharacteristic, complemented
7C2×C22⋊D41C2211yescharacteristic
8#10620306—22no—
9#10620306—22no—
10C2×D164C2211yescharacteristic
11C2×C4×D41C411yescharacteristic, complemented
12C2×C4×D41C2211yescharacteristic
13C2×Dic82C411yescharacteristic, complemented
14C22⋊#4223C2214yes—
15C4⋊#4223—22no—
16C4×#4223—22no—
17C23×C41C2×C411yescharacteristic
18C22×D41C2×C411yescharacteristic
19C22×D41C2311yescharacteristic
20C2×#4223—24no—
21C2×C4×C41—21no—
22C2×C4×C41—21no—
23C2×C4×C41C2×C411yescharacteristic
24C2×C4×C41C2×C411yescharacteristic
25C22⋊D41—22no—
26C22⋊D41—22no—
27C2×Dic41C2×C411yescharacteristic
28C2×Dic41C2×C411yescharacteristic
29D164—22no—
30C4×D41—21no—
31C4×D41—21no—
32C4×D41D412yes—
33C4×D41D412yes—
34Dic82—22no—
35C22×C41—21no—
36C22×C41—41no—
37C22×C41C22×C411yescharacteristic
38C2×D41—21no—
39C2×D41—41no—
40C2×D41—41no—
41C2×D41C2×D412yes—
42#4223—44no—
43C4×C41—21no—
44C4×C41C22⋊C411yescharacteristic
45C4×C41C22⋊C411yescharacteristic
46Dic41—21no—
47Dic41C22⋊C412yes—
48C2×C41—21no—
49C2×C41—41no—
50C2×C41C2×C22⋊C411yescharacteristic
51D41—22no—
52D41—41no—
53#410—411nomaximal, Sylow
54C41#41011yescharacteristic, complemented, Sylow
55C2×#41—411no—
56#117—412no—
57#99—412no—
58#99—412no—
59#41—822no—
60#41—822no—
61C2×Q8—411no—
62C2×D4—411no—
63C2×D4—411no—
64C2×D4—411no—
65C22×C4—411no—
66C22×C4—411no—
67C22×C4#422311yescharacteristic, complemented
68C4⋊C4—822no—
69C22⋊C4—414no—
70C42—822no—
71C23—411no—
72C23—411no—
73C23C2×#422311yescharacteristic
74Q8—822no—
75D4—822no—
76D4—822no—
77D4—822no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—411no—
81C2×C4—412no—
82C2×C4—412no—
83C2×C4—411no—
84C2×C4—821no—
85C2×C4—821no—
86C2×C4—824no—
87C2×C4C2×#422311yescharacteristic
88C2×C4C2×#422311yescharacteristic
89C22—21no—
90C22—41no—
91C22—412no—
92C22—821no—
93C22—1641no—
94C22—1641no—
95C22C22×#422311yescharacteristic
96C4—21no—
97C4—412no—
98C4—821no—
99C4—1644no—
100C4C22⋊#422311yescharacteristic
101C4C22⋊#422311yescharacteristic
102C2—21no—
103C2—41no—
104C2—822no—
105C2—1641no—
106C2C2×C22⋊#422311yescharacteristic
subgroupG/H
centerC4C22⋊#4223
commutatorC22×C41C22×C4
FrattiniC22C22×#4223
FittingC22×C4×C41C4
socleC2×C41C2×C22⋊C4
prime radicalC2×#10620306C2
cosocleC22×D41C23
hypercenterC22×C4#4223
hypocenterC41#410
LCSG ▷ C22×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #13050243C2semidirect
2. #13050223C2semidirect
3. #13050222C2semidirect
5. C22×C4×C41C4semidirect
6. C2×C22⋊D41C4semidirect
11. C2×C4×D41C4semidirect
13. C2×Dic82C4semidirect
54. C41#410semidirect
67. C22×C4#4223semidirect

Maximal subgroups

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

subgroupindex
#130502432
#130502232
#130502222
C2×#106203062
#41041