Finite Group Databasebeta

← #21460892

Subgroups — #21460892

Order 7808.

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

normal subgroups only

This group has 140 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
2#16840772C211yesmaximal, characteristic
3#106×D61C211yesmaximal, characteristic
4#14519856—21no—
5#14519852C412yescomplemented
6#14519851—21no—
7D61⋊C16—21no—
8#14519846C412yescomplemented
9#14519845—21no—
10C2×C8×D61C2211yescharacteristic
11C4⋊C4×D61—21no—
12#14519709C411yescharacteristic, complemented
13#14519708—21no—
14#106×C61C411yescharacteristic, complemented
15C2×C4×D61—41no—
16C2×C4×D61D411yescharacteristic
17C22⋊#6923—41no—
18C4⋊#6923—22no—
19C4×#6923—41no—
20C2×C8×C61C2×C411yescharacteristic
21C4⋊C4×C61—21no—
22C4⋊Dic61—21no—
23#11758196—41no—
24C2×#92418D411yescharacteristic
25C8×D61C2×C411yescharacteristic
26C8×D61C2×C411yescharacteristic
27C8×D61D411yescharacteristic
28C8×D61Q811yescharacteristic
29#11758187—22no—
30C22×D61D811yescharacteristic
31C2×#6923—42no—
32C2×C4×C61—41no—
33C2×C4×C61C22⋊C411yescharacteristic
34C2×Dic61—41no—
35C2×Dic61SD1611yescharacteristic
36C4×D61—82no—
37C4×D61C22⋊C411yescharacteristic
38C4×D61C4⋊C411yescharacteristic
39C4×D61SD1611yescharacteristic
40C4×D61Q1611yescharacteristic
41C8×C61C4211yescharacteristic
42C8×C61C4⋊C411yescharacteristic
43#92418C22⋊C411yescharacteristic
44#92418C4⋊C411yescharacteristic
45C22×C61#10211yescharacteristic
46C2×D61—22no—
47C2×D61#10211yescharacteristic
48C2×D61#10711yescharacteristic
49#6923—82no—
50C4×C61—81no—
51C4×C61#9511yescharacteristic
52C4×C61#10311yescharacteristic
53Dic61—81no—
54Dic61#10311yescharacteristic
55Dic61#10611yescharacteristic
56#1386—611nomaximal, Sylow
57C2×C61—21no—
58C2×C61#34011yescharacteristic
59D61—21no—
60D61#36012yes—
61C2×M32—611no—
62#427—611no—
63C2×#106—611no—
64C61#138611yescharacteristic, complemented, Sylow
65C22×C8—611no—
66#117—1221no—
67C2×C4⋊C4—1221no—
68M32—612no—
69M32—1221no—
70C2×C16—1221no—
71#107—612no—
72#106—611no—
73#106—1221no—
74#106—1221no—
75#106#692311yescharacteristic, complemented
76C22×C4—611no—
77C22×C4—2441no—
78C2×C8—611no—
79C2×C8—611no—
80C2×C8—611no—
81C2×C8—611no—
82C2×C8—611no—
83C2×C8C2×#692311yescharacteristic
84C4⋊C4—21no—
85C4⋊C4—1222no—
86C4⋊C4—1221no—
87C4⋊C4—2441no—
88C22⋊C4—2441no—
89C42—2441no—
90C16—1222no—
91C23—611no—
92C2×C4—41no—
93C2×C4—611no—
94C2×C4—611no—
95C2×C4—611no—
96C2×C4—611no—
97C2×C4—611no—
98C2×C4—4882no—
99C2×C4—2442no—
100C2×C4—2441no—
101C2×C4C22⋊#692311yescharacteristic
102C8—611no—
103C8—611no—
104C8C4×#692311yescharacteristic
105C8C4⋊#692311yescharacteristic
106C22—611no—
107C22—611no—
108C22—1222no—
109C22#1451983911yescharacteristic
110C4—81no—
111C4—611no—
112C4—611no—
113C4—4881no—
114C4—4882no—
115C4(C2×#6923)⋊C411yescharacteristic
116C4#1451984011yescharacteristic
117C2—21no—
118C2—612no—
119C2—1221no—
120C2#1684063511yescharacteristic
subgroupG/H
centerC2#16840635
commutatorC8×C61C42
FrattiniC2×C8C2×#6923
Fitting#106×C61C4
socleC2×C61#340
hypercenter#106#6923
hypocenterC61#1386
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
5. #14519852C4semidirect
8. #14519846C4semidirect
12. #14519709C4semidirect
14. #106×C61C4semidirect
64. C61#1386semidirect
75. #106#6923semidirect