Finite Group Databasebeta

← #30594833

Subgroups — #30594833

Order 15616.

178 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460751C212yesmaximal
2#21445900C211yesmaximal, characteristic
3#16840658—22no—
4C2×#14519736C411yescharacteristic
5#16839726C2211yescharacteristic
6#16839530—22no—
7C61×#407C411yescharacteristic
8#14519851—42no—
9C2×#11758194D412yes—
10#14519736—41no—
11#14519736—41no—
12C2×C4⋊Dic61—21no—
13C2×C22⋊Dic61C812yes—
14C2×C4×Dic61—21no—
15C22⋊#92418—41no—
16C23×C4×C61C2×C411yescharacteristic
17C2×M16×C61—21no—
18C22⋊C8×C61—41no—
19C24×C61C2×C811yescharacteristic
20C22×C4×C61—21no—
21C22×C4×C61—21no—
22C22×C4×C61—42no—
23C22×C4×C61C22⋊C411yescharacteristic
24C22×C4×C61M1611yescharacteristic
25C22×Dic61—22no—
26M16×C61—42no—
27C2×C8×C61—41no—
28C22⋊Dic61—42no—
29C4⋊Dic61—41no—
30C4⋊Dic61—41no—
31C4×Dic61—42no—
32#11758194—42no—
33C2×#92418—22no—
34#11758187—82no—
35C23×C61—21no—
36C23×C61—41no—
37C23×C61—81no—
38C23×C61C22⋊C811yescharacteristic
39C2×C4×C61—22no—
40C2×C4×C61—21no—
41C2×C4×C61—42no—
42C2×C4×C61—42no—
43C2×C4×C61—41no—
44C2×C4×C61#9911yescharacteristic
45C2×C4×C61#10011yescharacteristic
46C2×Dic61—42no—
47C2×Dic61—82no—
48C8×C61—81no—
49#92418—42no—
50#7351—611nomaximal, Sylow
51C22×C61—21no—
52C22×C61—41no—
53C22×C61—42no—
54C22×C61—41no—
55C22×C61—82no—
56C22×C61#32311yescharacteristic
57C4×C61—21no—
58C4×C61—41no—
59C4×C61#35212yes—
60Dic61—82no—
61#1822—611no—
62#1320—612no—
63C2×C61—21no—
64C2×C61—41no—
65C2×C61—81no—
66C2×C61#131711yescharacteristic
67C2×#117—611no—
68#407—611no—
69#407#692311yescharacteristic
70#349—1222no—
71#343—1222no—
72C61#735111yescharacteristic, complemented, Sylow
73C23×C4C2×#692311yescharacteristic
74C2×M16—21no—
75C2×M16—612no—
76#117—2441no—
77#117—2441no—
78C2×C4⋊C4—1221no—
79C2×C22⋊C4—612no—
80C2×C42—1221no—
81M32—2442no—
82C22⋊C8—41no—
83C22⋊C8—2441no—
84C24D61⋊C811yescharacteristic
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—42no—
88C22×C4—1222no—
89C22×C4#1175821311yescharacteristic
90C22×C4C22⋊#692311yescharacteristic
91M16—42no—
92M16—2442no—
93C2×C8—41no—
94C2×C8—1222no—
95C4⋊C4—2441no—
96C4⋊C4—2441no—
97C22⋊C4—2442no—
98C42—2442no—
99C16—4882no—
100C23—21no—
101C23—41no—
102C23—81no—
103C23#1451983411yescharacteristic
104C2×C4—22no—
105C2×C4—21no—
106C2×C4—42no—
107C2×C4—42no—
108C2×C4—41no—
109C2×C4—4882no—
110C2×C4—2442no—
111C2×C4#1451983611yescharacteristic
112C2×C4#1451983711yescharacteristic
113C8—81no—
114C8—2442no—
115C22—21no—
116C22—41no—
117C22—42no—
118C22—41no—
119C22—82no—
120C22#1684060611yescharacteristic
121C4—21no—
122C4—41no—
123C4—4882no—
124C4#1684066512yes—
125C2—21no—
126C2—41no—
127C2—81no—
128C2#2146074611yescharacteristic
subgroupG/H
centerC2#21460746
commutator, prime radicalC24×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC61×#407C4
socleC2×C61#1317
cosocle#16839726C22
hypercenter#407#6923
hypocenterC61#7351
LCSG ▷ C24×C61 ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
72. C61#7351semidirect

Maximal subgroups

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

subgroupindex
#214607512
#214459002
#735161