Finite Group Databasebeta

← #21460890

Subgroups — #21460890

Order 7808.

140 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 52 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
2C2×#14519845C211yesmaximal, characteristic
3#16839799C211yesmaximal, characteristic
4C2×C4⋊#6923—21no—
5#14519852—21no—
6#14519852C412yescomplemented
7C2×#11758187—21no—
8#14519845—21no—
9#14519845C412yescomplemented
10C2×C8×D61C2211yescharacteristic
11#14519735—21no—
12#14519711C411yescharacteristic, complemented
13#14519708—21no—
14#107×C61C411yescharacteristic, complemented
15C22×#6923—41no—
16C2×C4×D61D411yescharacteristic
17C4⋊#6923—22no—
18C4⋊#6923—41no—
19C2×C8×C61C2×C411yescharacteristic
20C4⋊C4×C61—21no—
21#11758198—41no—
22C4⋊Dic61—21no—
23C4×Dic61—41no—
24C2×#92418D411yescharacteristic
25C8×D61C2×C411yescharacteristic
26C8×D61C2×C411yescharacteristic
27C8×D61D411yescharacteristic
28C8×D61Q811yescharacteristic
29#11758187—22no—
30C22×D61D811yescharacteristic
31C2×#6923—42no—
32C2×#6923—81no—
33C2×#6923—81no—
34C2×C4×C61—41no—
35C2×C4×C61C22⋊C411yescharacteristic
36C2×Dic61—41no—
37C2×Dic61SD1611yescharacteristic
38C4×D61C22⋊C411yescharacteristic
39C4×D61C4⋊C411yescharacteristic
40C4×D61SD1611yescharacteristic
41C4×D61Q1611yescharacteristic
42C8×C61C4211yescharacteristic
43C8×C61C4⋊C411yescharacteristic
44#92418C22⋊C411yescharacteristic
45#92418C4⋊C411yescharacteristic
46C22×C61#10211yescharacteristic
47C2×D61—21no—
48C2×D61—21no—
49C2×D61#10211yescharacteristic
50C2×D61#10711yescharacteristic
51#6923—82no—
52C4×C61—81no—
53C4×C61#9511yescharacteristic
54C4×C61#10311yescharacteristic
55Dic61—81no—
56Dic61#10311yescharacteristic
57Dic61#10611yescharacteristic
58#1386—611nomaximal, Sylow
59C2×C61#34011yescharacteristic
60C2×C61#36011yescharacteristic
61C2×C61#36011yescharacteristic
62D61—21no—
63D61—21no—
64C2×M32—611no—
65#427—611no—
66C2×#106—611no—
67C61#138611yescharacteristic, complemented, Sylow
68C22×C8—611no—
69#117—1221no—
70C2×C4⋊C4—1221no—
71M32—612no—
72M32—1221no—
73C2×C16—1221no—
74#107—611no—
75#107#692311yescharacteristic, complemented
76#106—612no—
77#106—1221no—
78#106—1221no—
79C22×C4—611no—
80C22×C4—2441no—
81C2×C8—611no—
82C2×C8—611no—
83C2×C8—611no—
84C2×C8—611no—
85C2×C8—611no—
86C2×C8C2×#692311yescharacteristic
87C4⋊C4—21no—
88C4⋊C4—1222no—
89C4⋊C4—1221no—
90C4⋊C4—2441no—
91C22⋊C4—2441no—
92C42—2441no—
93C16—1222no—
94C23—611no—
95C2×C4—41no—
96C2×C4—611no—
97C2×C4—611no—
98C2×C4—611no—
99C2×C4—611no—
100C2×C4—611no—
101C2×C4—4881no—
102C2×C4—4881no—
103C2×C4—2442no—
104C2×C4—2441no—
105C2×C4C22⋊#692311yescharacteristic
106C8—611no—
107C8—611no—
108C8C4×#692311yescharacteristic
109C8C4⋊#692311yescharacteristic
110C22—611no—
111C22—611no—
112C22—1221no—
113C22—1221no—
114C22#1451983911yescharacteristic
115C4—81no—
116C4—611no—
117C4—611no—
118C4—4882no—
119C4—4881no—
120C4(C2×#6923)⋊C411yescharacteristic
121C4#1451984011yescharacteristic
122C2—1221no—
123C2—1221no—
124C2#1684063511yescharacteristic
125C2#1684067811yescharacteristic
126C2#1684067911yescharacteristic
subgroupG/H
centerC22#14519839
commutatorC8×C61C42
FrattiniC2×C8C2×#6923
Fitting#107×C61C4
socleC22×C61#102
hypercenter#107#6923
hypocenterC61#1386
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
6. #14519852C4semidirect
9. #14519845C4semidirect
12. #14519711C4semidirect
14. #107×C61C4semidirect
67. C61#1386semidirect
75. #107#6923semidirect