Finite Group Databasebeta

← #16840741

Subgroups — #16840741

Order 3904.

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#14519856C212yesmaximal, complemented
2#14519836C212yesmaximal, complemented
3#14519835C212yesmaximal, complemented
4C2×#11758222C211yesmaximal, characteristic
5C22×C4×C61C411yescharacteristic, complemented
6C2×C22⋊D61C411yescharacteristic, complemented
7C2×C22⋊D61C2211yescharacteristic
8#11758222—22no—
9#11758222—22no—
10C2×D244C2211yescharacteristic
11C2×C4×D61C411yescharacteristic, complemented
12C2×C4×D61C2211yescharacteristic
13C2×Dic122C411yescharacteristic, complemented
14C22⋊#6923C2214yes—
15C4⋊#6923—22no—
16C4×#6923—22no—
17C23×C61C2×C411yescharacteristic
18C22×D61C2×C411yescharacteristic
19C22×D61C2311yescharacteristic
20C2×#6923—24no—
21C2×C4×C61—21no—
22C2×C4×C61—21no—
23C2×C4×C61C2×C411yescharacteristic
24C2×C4×C61C2×C411yescharacteristic
25C22⋊D61—22no—
26C22⋊D61—22no—
27C2×Dic61C2×C411yescharacteristic
28C2×Dic61C2×C411yescharacteristic
29D244—22no—
30C4×D61—21no—
31C4×D61—21no—
32C4×D61D412yes—
33C4×D61D412yes—
34Dic122—22no—
35C22×C61—21no—
36C22×C61—41no—
37C22×C61C22×C411yescharacteristic
38C2×D61—21no—
39C2×D61—41no—
40C2×D61—41no—
41C2×D61C2×D412yes—
42#6923—44no—
43C4×C61—21no—
44C4×C61C22⋊C411yescharacteristic
45C4×C61C22⋊C411yescharacteristic
46Dic61—21no—
47Dic61C22⋊C412yes—
48C2×C61—21no—
49C2×C61—41no—
50C2×C61C2×C22⋊C411yescharacteristic
51D61—22no—
52D61—41no—
53#410—611nomaximal, Sylow
54C61#41011yescharacteristic, complemented, Sylow
55C2×#41—611no—
56#117—612no—
57#99—612no—
58#99—612no—
59#41—1222no—
60#41—1222no—
61C2×Q8—611no—
62C2×D4—611no—
63C2×D4—611no—
64C2×D4—611no—
65C22×C4—611no—
66C22×C4—611no—
67C22×C4#692311yescharacteristic, complemented
68C4⋊C4—1222no—
69C22⋊C4—614no—
70C42—1222no—
71C23—611no—
72C23—611no—
73C23C2×#692311yescharacteristic
74Q8—1222no—
75D4—1222no—
76D4—1222no—
77D4—1222no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—611no—
81C2×C4—612no—
82C2×C4—612no—
83C2×C4—611no—
84C2×C4—1221no—
85C2×C4—1221no—
86C2×C4—1224no—
87C2×C4C2×#692311yescharacteristic
88C2×C4C2×#692311yescharacteristic
89C22—21no—
90C22—41no—
91C22—612no—
92C22—1221no—
93C22—2441no—
94C22—2441no—
95C22C22×#692311yescharacteristic
96C4—21no—
97C4—612no—
98C4—1221no—
99C4—2444no—
100C4C22⋊#692311yescharacteristic
101C4C22⋊#692311yescharacteristic
102C2—21no—
103C2—41no—
104C2—1222no—
105C2—2441no—
106C2C2×C22⋊#692311yescharacteristic
subgroupG/H
centerC4C22⋊#6923
commutatorC22×C61C22×C4
FrattiniC22C22×#6923
FittingC22×C4×C61C4
socleC2×C61C2×C22⋊C4
prime radicalC2×#11758222C2
cosocleC22×D61C23
hypercenterC22×C4#6923
hypocenterC61#410
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #14519856C2semidirect
2. #14519836C2semidirect
3. #14519835C2semidirect
5. C22×C4×C61C4semidirect
6. C2×C22⋊D61C4semidirect
11. C2×C4×D61C4semidirect
13. C2×Dic122C4semidirect
54. C61#410semidirect
67. C22×C4#6923semidirect

Maximal subgroups

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

subgroupindex
#145198562
#145198362
#145198352
C2×#117582222
#41061