Finite Group Databasebeta

← #21460895

Subgroups — #21460895

Order 7808.

136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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⋊M32C211yesmaximal, characteristic
2C2×#14519846C211yesmaximal, characteristic
3#108×D61C211yesmaximal, characteristic
4C2×C4⋊#6923—21no—
5#14519852C412yescomplemented
6#14519851—21no—
7D61⋊C16—21no—
8#14519846—21no—
9#14519846C412yes—
10M16×D61—21no—
11C2×C8×D61C2211yescharacteristic
12#14519713C411yescharacteristic, complemented
13#14519712—21no—
14#108×C61C411yescharacteristic, complemented
15C22×#6923—41no—
16C2×C4×D61D411yescharacteristic
17C4⋊#6923—22no—
18C4⋊#6923—41no—
19M16×C61—21no—
20C2×C8×C61C2×C411yescharacteristic
21#11758194—21no—
22C2×#92418D411yescharacteristic
23#11758189—41no—
24C8×D61—41no—
25C8×D61C2×C411yescharacteristic
26C8×D61C2×C411yescharacteristic
27C8×D61D411yescharacteristic
28C8×D61Q811yescharacteristic
29#11758187—22no—
30C22×D61SD1611yescharacteristic
31C2×#6923—42no—
32C2×#6923—82no—
33C2×C4×C61C22⋊C411yescharacteristic
34C2×Dic61Q1611yescharacteristic
35C4×D61C22⋊C411yescharacteristic
36C4×D61C4⋊C411yescharacteristic
37C4×D61D811yescharacteristic
38C4×D61SD1611yescharacteristic
39C8×C61—41no—
40C8×C61C4211yescharacteristic
41C8×C61C4⋊C411yescharacteristic
42#92418—41no—
43#92418C22⋊C411yescharacteristic
44#92418C4⋊C411yescharacteristic
45C22×C61#10311yescharacteristic
46C2×D61—21no—
47C2×D61—21no—
48C2×D61#10211yescharacteristic
49C2×D61#10611yescharacteristic
50#6923—82no—
51C4×C61#9511yescharacteristic
52C4×C61#10211yescharacteristic
53Dic61#10311yescharacteristic
54Dic61#10711yescharacteristic
55#1387—611nomaximal, Sylow
56C2×C61—21no—
57C2×C61#34011yescharacteristic
58D61—21no—
59D61#36111yescharacteristic
60D61#36211yescharacteristic
61C2×M32—611no—
62C2×#108—611no—
63C2×#107—611no—
64C61#138711yescharacteristic, complemented, Sylow
65C2×M16—1221no—
66C22×C8—611no—
67C2×C4⋊C4—1221no—
68M32—612no—
69M32—1221no—
70C2×C16—1221no—
71#108—611no—
72#108—1221no—
73#108#692311yescharacteristic, complemented
74#107—612no—
75#107—1221no—
76C22×C4—611no—
77C22×C4—2441no—
78M16—21no—
79M16—1221no—
80M16—2441no—
81C2×C8—611no—
82C2×C8—611no—
83C2×C8—611no—
84C2×C8—611no—
85C2×C8—611no—
86C2×C8—2441no—
87C2×C8C2×#692311yescharacteristic
88C4⋊C4—1222no—
89C4⋊C4—2441no—
90C16—1222no—
91C23—611no—
92C2×C4—611no—
93C2×C4—611no—
94C2×C4—611no—
95C2×C4—611no—
96C2×C4—611no—
97C2×C4—4882no—
98C2×C4—2442no—
99C2×C4C22⋊#692311yescharacteristic
100C8—41no—
101C8—611no—
102C8—611no—
103C8—2441no—
104C8C4×#692311yescharacteristic
105C8C4⋊#692311yescharacteristic
106C22—611no—
107C22—611no—
108C22—1221no—
109C22—1221no—
110C22#1451984011yescharacteristic
111C4—611no—
112C4—611no—
113C4—4882no—
114C4(C2×#6923)⋊C411yescharacteristic
115C4#1451983911yescharacteristic
116C2—21no—
117C2—611no—
118C2—611no—
119C2—1221no—
120C2#1684063511yescharacteristic
subgroupG/H
centerC2#16840635
commutatorC8×C61C42
FrattiniC2×C8C2×#6923
Fitting#108×C61C4
socleC2×C61#340
hypercenter#108#6923
hypocenterC61#1387
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
5. #14519852C4semidirect
12. #14519713C4semidirect
14. #108×C61C4semidirect
64. C61#1387semidirect
73. #108#6923semidirect