Finite Group Databasebeta

← #21460810

Subgroups — #21460810

Order 7808.

114 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 30 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
1#16840657C211yesmaximal, characteristic, complemented
2#16840638C211yesmaximal, characteristic, complemented
3#16839999C211yesmaximal, characteristic
4C2×#11758213—21no—
5C2×#11758187—21no—
6C2×D488C411yescharacteristic
7C2×C8×D61C2211yescharacteristic
8#14519752—21no—
9#14519697—21no—
10#107×C61C411yescharacteristic
11C2×D244—21no—
12C2×D244—41no—
13C2×C4×D61D411yescharacteristic
14C2×#92420—41no—
15#11758213—22no—
16#11758213—41no—
17C2×C8×C61C2×C411yescharacteristic
18C4⋊C4×C61—21no—
19#11758198—41no—
20C2×#92418D411yescharacteristic
21D488—41no—
22C8×D61—41no—
23#11758187—41no—
24C22×D61—41no—
25C22×D61SD1611yescharacteristic
26C2×C4×C61—41no—
27C2×C4×C61C22⋊C411yescharacteristic
28C2×Dic61D811yescharacteristic
29D244—41no—
30D244—41no—
31D244—82no—
32C4×D61—21no—
33C4×D61—21no—
34#92420—42no—
35C8×C61—21no—
36#92418—21no—
37C22×C61#10211yescharacteristic
38C2×D61—21no—
39C2×D61—21no—
40C2×D61—21no—
41C2×D61—81no—
42C2×D61—81no—
43C2×D61—81no—
44C4×C61—81no—
45C4×C61#9911yescharacteristic
46C4×C61#10411yescharacteristic
47Dic61—21no—
48#1349—611nomaximal, Sylow
49C2×C61#32711yescharacteristic
50C2×C61#35911yescharacteristic
51C2×C61#36111yescharacteristic
52D61—41no—
53D61—161no—
54#466—611no—
55C22⋊C16—611no—
56#341—611no—
57C61#134911yescharacteristic, complemented, Sylow
58C2×D8—611no—
59C2×M16—1221no—
60C22×C8—611no—
61#121—1221no—
62C2×C16—1221no—
63#107#692311yescharacteristic
64#102—1221no—
65C2×D4—1221no—
66C2×D4—2441no—
67C22×C4—611no—
68D8—2441no—
69M16—1222no—
70M16—2441no—
71C2×C8—611no—
72C2×C8—2441no—
73C2×C8—2441no—
74C2×C8C2×#692311yescharacteristic
75C4⋊C4—21no—
76C22⋊C4—2441no—
77C16—2441no—
78C23—611no—
79C23—2441no—
80D4—4882no—
81D4—2441no—
82D4—2441no—
83C2×C4—41no—
84C2×C4—611no—
85C2×C4—1221no—
86C2×C4—1221no—
87C2×C4C22⋊#692311yescharacteristic
88C8—21no—
89C8—1221no—
90C8—2442no—
91C22—1221no—
92C22—1221no—
93C22—1221no—
94C22—4881no—
95C22—4881no—
96C22—4881no—
97C22#1451983911yescharacteristic
98C4—81no—
99C4—1221no—
100C4#1451983611yescharacteristic
101C4#1451984211yescharacteristic
102C2—9761no—
103C2—2441no—
104C2#1684061411yescharacteristic
105C2#1684067711yescharacteristic
106C2#1684068011yescharacteristic
subgroupG/H
centerC22#14519839
commutatorC2×C8×C61C2×C4
FrattiniC2×C8C2×#6923
Fitting#107×C61C4
socleC22×C61#102
hypercenter#107#6923
hypocenterC61#1349
LCSG ▷ C2×C8×C61 ▷ C2×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
1. #16840657C2semidirect
2. #16840638C2semidirect
57. C61#1349semidirect