Finite Group Databasebeta

← #21443827

Subgroups — #21443827

Order 7808.

126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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#16839998C211yesmaximal, characteristic
2C22⋊#11758185C211yesmaximal, characteristic, complemented
3C61×#340C211yesmaximal, characteristic, complemented
4C2×D488C411yescharacteristic, complemented
5#14519751—21no—
6C2×#11758185—21no—
7#14519711C411yescharacteristic, complemented
8#14519699—21no—
9C22×C8×C61C2211yescharacteristic
10C2×C4⋊C4×C61—21no—
11C22×C4×C61—41no—
12C22×C4×C61D411yescharacteristic
13C2×C22⋊D61—41no—
14C2×D244—21no—
15C2×C8×C61—41no—
16C2×C8×C61C2×C411yescharacteristic
17C2×C8×C61D411yescharacteristic
18C4⋊C4×C61—22no—
19C4⋊C4×C61—41no—
20#11758198—41no—
21C4⋊Dic61—21no—
22D488—41no—
23#11758185—41no—
24C23×C61D811yescharacteristic
25C22×D61—41no—
26C2×C4×C61—21no—
27C2×C4×C61—21no—
28C2×C4×C61—42no—
29C2×C4×C61—81no—
30C2×C4×C61—81no—
31C2×C4×C61C22⋊C411yescharacteristic
32C2×C4×C61SD1611yescharacteristic
33C22⋊D61—81no—
34C22⋊D61—81no—
35C2×Dic61—41no—
36D244—41no—
37D244—41no—
38C8×C61—21no—
39C8×C61—21no—
40C22×C61—21no—
41C22×C61—21no—
42C22×C61#10211yescharacteristic
43C22×C61D1611yescharacteristic
44C22×C61SD3211yescharacteristic
45C2×D61—81no—
46C2×D61—81no—
47C2×D61—81no—
48C4×C61—21no—
49C4×C61—82no—
50C4×C61#9911yescharacteristic
51C4×C61#10411yescharacteristic
52Dic61—81no—
53#1347—611nomaximal, Sylow
54C2×C61—21no—
55C2×C61—21no—
56C2×C61#32711yescharacteristic
57C2×C61#35711yescharacteristic
58C2×C61#36011yescharacteristic
59D61—161no—
60#466—611no—
61C22⋊C16—611no—
62#340D6111yescharacteristic, complemented
63C61#134711yescharacteristic, complemented, Sylow
64C2×D8—611no—
65C22×C8C2×D6111yescharacteristic
66#121—1221no—
67C2×C4⋊C4—21no—
68C2×C16—1221no—
69#107—611no—
70#102—1221no—
71C2×D4—1221no—
72C2×D4—2441no—
73C22×C4—41no—
74C22×C4C22⋊D6111yescharacteristic
75D8—2441no—
76C2×C8—41no—
77C2×C8C4×D6111yescharacteristic
78C2×C8D24411yescharacteristic
79C4⋊C4—22no—
80C4⋊C4—41no—
81C4⋊C4—1221no—
82C22⋊C4—2441no—
83C16—2441no—
84C23—2441no—
85C23#1175819911yescharacteristic
86D4—4881no—
87D4—4881no—
88D4—2441no—
89D4—2441no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—42no—
93C2×C4—81no—
94C2×C4—81no—
95C2×C4—2441no—
96C2×C4#1175819811yescharacteristic
97C2×C4#1175820111yescharacteristic
98C8—21no—
99C8—21no—
100C22—21no—
101C22—21no—
102C22—4881no—
103C22—4881no—
104C22—4881no—
105C22#1451969711yescharacteristic
106C22#1451971811yescharacteristic
107C22#1451972011yescharacteristic
108C4—21no—
109C4—82no—
110C4—4881no—
111C4#1451969111yescharacteristic
112C4#1451970511yescharacteristic
113C2—21no—
114C2—21no—
115C2—9761no—
116C2#1683949511yescharacteristic
117C2#1683956211yescharacteristic
118C2#1683957111yescharacteristic
subgroupG/H
centerC22#14519697
commutatorC2×C8×C61C2×C4
FrattiniC22×C8C2×D61
FittingC61×#340C2
socleC22×C61#102
hypercenter#340D61
hypocenterC61#1347
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C22⋊#11758185C2semidirect
3. C61×#340C2semidirect
4. C2×D488C4semidirect
7. #14519711C4semidirect
62. #340D61semidirect
63. C61#1347semidirect