Finite Group Databasebeta

← #16840749

Subgroups — #16840749

Order 3904.

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

normal subgroups only

This group has 150 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
1C2×#11758217C212yesmaximal, complemented
2#14519838C212yesmaximal, complemented
3#14519837C212yesmaximal, complemented
4C2×#11758224C211yesmaximal, characteristic
5C2×D4×C61C411yescharacteristic
6C2×C22⋊D61C411yescharacteristic
7C2×C22⋊D61C2211yescharacteristic
8C22×Dic61C411yescharacteristic
9C22×Dic61C2211yescharacteristic
10#11758224—22no—
11#11758224—22no—
12C2×C4×D61C411yescharacteristic
13C2×Dic122C2211yescharacteristic
14#11758217—22no—
15#11758217C2214yes—
16C2×#92420—22no—
17C23×C61C2×C411yescharacteristic
18C23×C61C2×C411yescharacteristic
19C22×D61C2×C411yescharacteristic
20D4×C61—22no—
21C2×C4×C61C2×C411yescharacteristic
22C22⋊D61—22no—
23C22⋊D61—22no—
24C2×Dic61—21no—
25C2×Dic61—21no—
26C2×Dic61C2×C411yescharacteristic
27C2×Dic61C2×C411yescharacteristic
28C2×Dic61D412yes—
29C2×Dic61D412yes—
30C2×Dic61C2311yescharacteristic
31C4×D61—21no—
32C4×D61—21no—
33Dic122—22no—
34#92420—24no—
35C22×C61—21no—
36C22×C61—41no—
37C22×C61—41no—
38C22×C61C22⋊C412yes—
39C22×C61C22×C411yescharacteristic
40C2×D61—21no—
41C2×D61—41no—
42C4×C61—21no—
43Dic61—21no—
44Dic61C22⋊C411yescharacteristic
45Dic61C22⋊C411yescharacteristic
46Dic61C2×D412yes—
47C2×C61—21no—
48C2×C61—22no—
49C2×C61—41no—
50C2×C61C2×C22⋊C411yescharacteristic
51D61—41no—
52#413—611nomaximal, Sylow
53C61#41311yescharacteristic, complemented, Sylow
54C2×#41—611no—
55C2×M16—612no—
56#101—612no—
57#100—612no—
58#41—1222no—
59#41—1222no—
60C2×Q8—611no—
61C2×D4—611no—
62C2×D4—611no—
63C2×D4#692311yescharacteristic
64C22×C4—611no—
65C22×C4—611no—
66C22×C4—611no—
67M16—614no—
68M16—1222no—
69C2×C8—1222no—
70C23—611no—
71C23C2×#692311yescharacteristic
72C23C2×#692311yescharacteristic
73Q8—1222no—
74D4—22no—
75D4—1222no—
76D4—1222no—
77C2×C4—612no—
78C2×C4—612no—
79C2×C4—611no—
80C2×C4—611no—
81C2×C4—611no—
82C2×C4—1221no—
83C2×C4—1221no—
84C2×C4—1221no—
85C2×C4—1221no—
86C2×C4C2×#692311yescharacteristic
87C8—1224no—
88C22—21no—
89C22—41no—
90C22—41no—
91C22—1221no—
92C22—2441no—
93C22C22⋊#692312yes—
94C22C22×#692311yescharacteristic
95C4—21no—
96C4—611no—
97C4—611no—
98C4—612no—
99C4—1221no—
100C2—21no—
101C2—22no—
102C2—41no—
103C2—2441no—
104C2C2×C22⋊#692311yescharacteristic
subgroupG/H
centerC2C2×C22⋊#6923
commutatorC22×C61C22×C4
FrattiniC22C22×#6923
FittingC2×D4×C61C4
socleC2×C61C2×C22⋊C4
prime radicalC2×#11758224C2
cosocleC2×Dic61C23
hypercenterC2×D4#6923
hypocenterC61#413
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#11758217C2semidirect
2. #14519838C2semidirect
3. #14519837C2semidirect
53. C61#413semidirect

Maximal subgroups

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

subgroupindex
C2×#117582172
#145198382
#145198372
C2×#117582242
#41361