Finite Group Databasebeta

← #30594855

Subgroups — #30594855

Order 15616.

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

normal subgroups only

This group has 184 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#21460765C212yesmaximal
2#21446796C211yesmaximal, characteristic
3#16840658—22no—
4#16840319C411yescharacteristic
5#16839786C2211yescharacteristic
6#16839522—22no—
7C43×C61C411yescharacteristic
8#14519851—42no—
9C2×#11758194D412yes—
10#14519777—21no—
11#14519769C812yes—
12#14519756—41no—
13C4×Dic122—41no—
14#14519736—21no—
15C4⋊#92418—41no—
16C2×C42×C61—21no—
17C2×C42×C61—41no—
18C2×C42×C61C2×C411yescharacteristic
19C22×C4×C61—21no—
20C22×C4×C61—41no—
21C22×C4×C61C22⋊C411yescharacteristic
22C2×Dic122—41no—
23C42×C61—21no—
24C42×C61—22no—
25C42×C61—41no—
26C42×C61—44no—
27C42×C61C2×C811yescharacteristic
28C42×C61M1611yescharacteristic
29C22⋊Dic61—41no—
30C4⋊Dic61—22no—
31C4⋊Dic61—41no—
32#11758196—42no—
33C4×Dic61—41no—
34#11758194—42no—
35C2×#92418—22no—
36#11758187—82no—
37C23×C61#10011yescharacteristic
38C2×C4×C61—21no—
39C2×C4×C61—21no—
40C2×C4×C61—21no—
41C2×C4×C61—21no—
42C2×C4×C61—42no—
43C2×C4×C61—42no—
44C2×C4×C61—44no—
45C2×C4×C61C22⋊C811yescharacteristic
46C2×C4×C61#9911yescharacteristic
47C2×Dic61—42no—
48Dic122—82no—
49#92418—42no—
50#7361—611nomaximal, Sylow
51C22×C61—21no—
52C22×C61—41no—
53C22×C61#32311yescharacteristic
54C4×C61—22no—
55C4×C61—21no—
56C4×C61—41no—
57C4×C61—44no—
58C4×C61#35411yescharacteristic
59C4×C61#35611yescharacteristic
60Dic61—82no—
61#1994—611no—
62#1327—612no—
63C2×C61—21no—
64C2×C61—41no—
65C2×C61#131911yescharacteristic
66#533—611no—
67#423—611no—
68C43#692311yescharacteristic
69#349—1222no—
70#339—1222no—
71C61#736111yescharacteristic, complemented, Sylow
72C2×M16—612no—
73C4⋊Q8—1221no—
74#125—612no—
75C22⋊Q8—2441no—
76C4×Q8—2441no—
77#117—1221no—
78C2×C42—21no—
79C2×C42—41no—
80C2×C42C2×#692311yescharacteristic
81M32—2442no—
82C4⋊C8—2441no—
83C2×Q8—2441no—
84C22×C4—21no—
85C22×C4—41no—
86C22×C4C22⋊#692311yescharacteristic
87M16—2442no—
88C2×C8—1222no—
89C4⋊C4—1222no—
90C4⋊C4—2442no—
91C4⋊C4—2441no—
92C22⋊C4—2441no—
93C42—21no—
94C42—22no—
95C42—41no—
96C42—44no—
97C42—2441no—
98C42D61⋊C811yescharacteristic
99C42#1175821311yescharacteristic
100C16—4882no—
101C23#1451983711yescharacteristic
102Q8—4882no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—42no—
108C2×C4—42no—
109C2×C4—44no—
110C2×C4—2442no—
111C2×C4#1451983411yescharacteristic
112C2×C4#1451983611yescharacteristic
113C8—2442no—
114C22—21no—
115C22—41no—
116C22#1684060611yescharacteristic
117C4—22no—
118C4—21no—
119C4—41no—
120C4—44no—
121C4—4882no—
122C4#1684066911yescharacteristic
123C4#1684067311yescharacteristic
124C2—21no—
125C2—41no—
126C2#2146075011yescharacteristic
subgroupG/H
centerC4#16840669
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC43×C61C4
socleC2×C61#1319
prime radicalC23×C61#100
cosocle#16839786C22
hypercenterC43#6923
hypocenterC61#7361
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
71. C61#7361semidirect

Maximal subgroups

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

subgroupindex
#214607652
#214467962
#736161