Finite Group Databasebeta

← #21460806

Subgroups — #21460806

Order 7808.

126 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 32 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#16840636C211yesmaximal, characteristic, complemented
3#16839999C211yesmaximal, characteristic
4C2×C4⋊#6923—21no—
5C2×#11758187—21no—
6C2×D488C411yescharacteristic, complemented
7C2×C8×D61C2211yescharacteristic
8#14519752—21no—
9#14519697—21no—
10#107×C61C411yescharacteristic, complemented
11C22×#6923—41no—
12C2×D244—21no—
13C2×D244—41no—
14C2×C4×D61D411yescharacteristic
15C4⋊#6923—22no—
16C4⋊#6923—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×D61D811yescharacteristic
26C2×#6923—42no—
27C2×#6923—81no—
28C2×#6923—81no—
29C2×C4×C61—41no—
30C2×C4×C61C22⋊C411yescharacteristic
31C2×Dic61SD1611yescharacteristic
32D244—41no—
33D244—41no—
34D244—81no—
35D244—81no—
36C4×D61—21no—
37C4×D61—21no—
38C8×C61—21no—
39#92418—21no—
40C22×C61#10211yescharacteristic
41C2×D61—21no—
42C2×D61—21no—
43C2×D61—81no—
44C2×D61—81no—
45C2×D61—81no—
46C2×D61D1611yescharacteristic
47C2×D61SD3211yescharacteristic
48#6923—82no—
49C4×C61—81no—
50C4×C61#9911yescharacteristic
51C4×C61#10411yescharacteristic
52Dic61—21no—
53#1347—611nomaximal, Sylow
54C2×C61#32711yescharacteristic
55C2×C61#35711yescharacteristic
56C2×C61#36011yescharacteristic
57D61—21no—
58D61—21no—
59D61—161no—
60#466—611no—
61C22⋊C16—611no—
62#340—611no—
63C61#134711yescharacteristic, complemented, Sylow
64C2×D8—611no—
65C22×C8—611no—
66#121—1221no—
67C2×C4⋊C4—1221no—
68C2×C16—1221no—
69#107#692311yescharacteristic, complemented
70#102—1221no—
71C2×D4—1221no—
72C2×D4—2441no—
73C22×C4—611no—
74C22×C4—2441no—
75D8—2441no—
76C2×C8—611no—
77C2×C8—2441no—
78C2×C8C2×#692311yescharacteristic
79C4⋊C4—21no—
80C4⋊C4—1222no—
81C4⋊C4—2441no—
82C22⋊C4—2441no—
83C16—2441no—
84C23—611no—
85C23—2441no—
86D4—4881no—
87D4—4881no—
88D4—2441no—
89D4—2441no—
90C2×C4—41no—
91C2×C4—611no—
92C2×C4—1221no—
93C2×C4—1221no—
94C2×C4—4881no—
95C2×C4—4881no—
96C2×C4—2442no—
97C2×C4C22⋊#692311yescharacteristic
98C8—21no—
99C8—1221no—
100C22—611no—
101C22—611no—
102C22—1221no—
103C22—1221no—
104C22—4881no—
105C22—4881no—
106C22—4881no—
107C22#1451983911yescharacteristic
108C4—81no—
109C4—1221no—
110C4—4882no—
111C4#1451983611yescharacteristic
112C4#1451984211yescharacteristic
113C2—1221no—
114C2—1221no—
115C2—9761no—
116C2#1684061411yescharacteristic
117C2#1684067411yescharacteristic
118C2#1684067911yescharacteristic
subgroupG/H
centerC22#14519839
commutatorC2×C8×C61C2×C4
FrattiniC2×C8C2×#6923
Fitting#107×C61C4
socleC22×C61#102
hypercenter#107#6923
hypocenterC61#1347
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. #16840636C2semidirect
6. C2×D488C4semidirect
10. #107×C61C4semidirect
63. C61#1347semidirect
69. #107#6923semidirect