Finite Group Databasebeta

← #21460899

Subgroups — #21460899

Order 7808.

128 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 128 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
1C2×#14519852C211yesmaximal, characteristic
2#16840772C211yesmaximal, characteristic
3#108×D61C211yesmaximal, characteristic
4#14519856—21no—
5#14519852—21no—
6#14519852C412yescomplemented
7C2×#11758187—21no—
8#14519846—21no—
9#14519845C412yes—
10M16×D61—21no—
11C2×C8×D61C2211yescharacteristic
12#14519713C411yescharacteristic, complemented
13#14519712—21no—
14#108×C61C411yescharacteristic, complemented
15C2×C4×D61D411yescharacteristic
16C22⋊#6923—41no—
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×C4×C61C22⋊C411yescharacteristic
33C2×Dic61Q1611yescharacteristic
34C4×D61C22⋊C411yescharacteristic
35C4×D61C4⋊C411yescharacteristic
36C4×D61D811yescharacteristic
37C4×D61SD1611yescharacteristic
38C8×C61—41no—
39C8×C61C4211yescharacteristic
40C8×C61C4⋊C411yescharacteristic
41#92418—41no—
42#92418C22⋊C411yescharacteristic
43#92418C4⋊C411yescharacteristic
44C22×C61#10311yescharacteristic
45C2×D61—41no—
46C2×D61#10211yescharacteristic
47C2×D61#10611yescharacteristic
48#6923—82no—
49C4×C61#9511yescharacteristic
50C4×C61#10211yescharacteristic
51Dic61#10311yescharacteristic
52Dic61#10711yescharacteristic
53#1389—611nomaximal, Sylow
54C2×C61—21no—
55C2×C61#34011yescharacteristic
56D61—21no—
57D61—21no—
58C2×M32—611no—
59C2×#108—611no—
60#427—611no—
61C61#138911yescharacteristic, complemented, Sylow
62C2×M16—1221no—
63C22×C8—611no—
64#117—1221no—
65M32—612no—
66M32—1221no—
67C2×C16—1221no—
68#108—611no—
69#108—1221no—
70#108#692311yescharacteristic, complemented
71#107—1221no—
72#106—612no—
73C22×C4—611no—
74M16—21no—
75M16—1221no—
76M16—2441no—
77C2×C8—611no—
78C2×C8—611no—
79C2×C8—611no—
80C2×C8—611no—
81C2×C8—611no—
82C2×C8—2441no—
83C2×C8C2×#692311yescharacteristic
84C4⋊C4—1222no—
85C22⋊C4—2441no—
86C42—2441no—
87C16—1222no—
88C23—611no—
89C2×C4—611no—
90C2×C4—611no—
91C2×C4—611no—
92C2×C4—611no—
93C2×C4—611no—
94C2×C4—2442no—
95C2×C4C22⋊#692311yescharacteristic
96C8—41no—
97C8—611no—
98C8—611no—
99C8—2441no—
100C8C4×#692311yescharacteristic
101C8C4⋊#692311yescharacteristic
102C22—611no—
103C22—611no—
104C22—2441no—
105C22#1451984011yescharacteristic
106C4—611no—
107C4—611no—
108C4—4882no—
109C4(C2×#6923)⋊C411yescharacteristic
110C4#1451983911yescharacteristic
111C2—21no—
112C2—1221no—
113C2—1221no—
114C2#1684063511yescharacteristic
subgroupG/H
centerC4#14519839
commutatorC8×C61C42
FrattiniC2×C8C2×#6923
Fitting#108×C61C4
socleC2×C61#340
hypercenter#108#6923
hypocenterC61#1389
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
6. #14519852C4semidirect
12. #14519713C4semidirect
14. #108×C61C4semidirect
61. C61#1389semidirect
70. #108#6923semidirect