Finite Group Databasebeta

← D61⋊#368 #21462173

Subgroups — D61⋊#368 #21462173

Order 7808.

144 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 64 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
1D61⋊#108C212yesmaximal
2#16840691C212yesmaximal, complemented
3#16840690C212yesmaximal, complemented
4C2×C16×D61C211yesmaximal, characteristic
5D61⋊M16—22no—
6#14519848C2214yes—
7#14519847—22no—
8C2×C8×D61C2211yescharacteristic
9C2×#11758185C411yescharacteristic
10C16×D61C411yescharacteristic
11C16×D61C411yescharacteristic
12C16×D61C2211yescharacteristic
13C16×D61C2211yescharacteristic
14C2×C16×C61C411yescharacteristic
15C2×C4×D61D411yescharacteristic
16#11758217—42no—
17#11758213—24no—
18D61⋊C8—42no—
19C2×C8×C61C2×C411yescharacteristic
20C2×#92418Q811yescharacteristic
21C8×D61C2×C411yescharacteristic
22C8×D61D411yescharacteristic
23C8×D61Q811yescharacteristic
24C8×D61C2311yescharacteristic
25C16×C61C2×C411yescharacteristic
26C16×C61C2×C411yescharacteristic
27#11758185C2×C411yescharacteristic
28#11758185C2×C411yescharacteristic
29C22×D61Q1611yescharacteristic
30C2×C4×C61C4⋊C411yescharacteristic
31C2×Dic61D811yescharacteristic
32C4×D61C4⋊C411yescharacteristic
33C4×D61D811yescharacteristic
34C4×D61Q1611yescharacteristic
35C4×D61C2×D411yescharacteristic
36#92420—44no—
37C8×C61C4⋊C411yescharacteristic
38C8×C61C22×C411yescharacteristic
39#92418C4⋊C411yescharacteristic
40#92418C2×Q811yescharacteristic
41C22×C61#10711yescharacteristic
42C2×D61—22no—
43C2×D61#10711yescharacteristic
44C2×D61C2×Q1611yescharacteristic
45C4×C61#10711yescharacteristic
46C4×C61C2×C4⋊C411yescharacteristic
47Dic61#10711yescharacteristic
48Dic61C2×D811yescharacteristic
49C2×#368—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61C2×#10711yescharacteristic
52D61—21no—
53D61#36812yescomplemented
54C22×C16—611no—
55C2×#108—612no—
56#368—612no—
57#368—612no—
58C61C2×#36811yescharacteristic, complemented, Sylow
59C2×M16—1222no—
60C22×C8—611no—
61C2×C16—611no—
62C2×C16—611no—
63C2×C16—611no—
64C2×C16—611no—
65C2×C16—611no—
66C2×C16#692311yescharacteristic
67#108—614no—
68#108—1222no—
69C22×C4—611no—
70M16—1224no—
71M16—2442no—
72C2×C8—611no—
73C2×C8—611no—
74C2×C8—611no—
75C2×C8—611no—
76C2×C8—611no—
77C2×C8—2442no—
78C2×C8C2×#692311yescharacteristic
79C16—611no—
80C16—611no—
81C16C2×#692311yescharacteristic
82C16C2×#692311yescharacteristic
83C23—611no—
84C2×C4—611no—
85C2×C4—611no—
86C2×C4—611no—
87C2×C4—611no—
88C2×C4—611no—
89C2×C4C4⋊#692311yescharacteristic
90C8—611no—
91C8—611no—
92C8—2444no—
93C8C4⋊#692311yescharacteristic
94C8C22×#692311yescharacteristic
95C22—611no—
96C22—611no—
97C22—1222no—
98C22#1451984611yescharacteristic
99C4—611no—
100C4—611no—
101C4#1451984611yescharacteristic
102C4C2×C4⋊#692311yescharacteristic
103C2—21no—
104C2—612no—
105C2—1221no—
106C2C2×#1451984611yescharacteristic
subgroupG/H
centerC4#14519846
commutatorC8×C61C22×C4
FrattiniC8C22×#6923
FittingC2×C16×C61C4
socleC2×C61C2×#107
hypercenterC2×C16#6923
hypocenterC61C2×#368
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. #16840691C2semidirect
3. #16840690C2semidirect
53. D61#368semidirect
58. C61C2×#368semidirect