Finite Group Databasebeta

← #21448016

Subgroups — #21448016

Order 7808.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840003C211yesmaximal, characteristic
2#16839589C212yesmaximal, complemented
3#16839565C212yesmaximal, complemented
4C22⋊#11758185C211yesmaximal, characteristic
5C2×#107×C61C211yesmaximal, characteristic
6C2×Dic244C2211yescharacteristic
7#14519756—21no—
8C2×#11758185C2212yes—
9#14519711C2211yescharacteristic
10#14519702—21no—
11C22×C8×C61C2211yescharacteristic
12C2×C4⋊C4×C61—21no—
13#107×C61—21no—
14#107×C61C2212yes—
15C22×C4×C61—41no—
16C22×C4×C61D411yescharacteristic
17C2×Dic122—21no—
18C2×C8×C61—22no—
19C2×C8×C61D411yescharacteristic
20C2×C8×C61C2311yescharacteristic
21C4⋊C4×C61—22no—
22C4⋊C4×C61—41no—
23C22⋊Dic61—41no—
24C4⋊Dic61—21no—
25#11758196—41no—
26Dic244—22no—
27#11758185—22no—
28C23×C61D811yescharacteristic
29C2×C4×C61—21no—
30C2×C4×C61—21no—
31C2×C4×C61—42no—
32C2×C4×C61—82no—
33C2×C4×C61D811yescharacteristic
34C2×C4×C61C2×D411yescharacteristic
35C2×Dic61—41no—
36C2×Dic61—41no—
37Dic122—41no—
38Dic122—41no—
39C8×C61—21no—
40C8×C61#4112yes—
41C22×C61—21no—
42C22×C61—21no—
43C22×C61SD3212yes—
44C22×C61C2×D811yescharacteristic
45C4×C61—21no—
46C4×C61—82no—
47C4×C61#12311yescharacteristic
48C4×C61#13711yescharacteristic
49Dic61—81no—
50Dic61—81no—
51#2235—611nomaximal, Sylow
52C2×C61—22no—
53C2×C61#48011yescharacteristic
54C2×C61C2×SD3211yescharacteristic
55C2×C61#51011yescharacteristic
56#467—611no—
57C2×#107D6111yescharacteristic
58#367—612no—
59#358—612no—
60C22⋊C16—611no—
61C61#223511yescharacteristic, complemented, Sylow
62C2×Q16—611no—
63C22×C8C2×D6111yescharacteristic
64C22⋊Q8—1221no—
65C2×C4⋊C4—21no—
66C2×C16—612no—
67#107—21no—
68#107—611no—
69#107C2×D6112yes—
70#103—1221no—
71C2×Q8—1221no—
72C22×C4—41no—
73C22×C4C22⋊D6111yescharacteristic
74Q16—1222no—
75C2×C8—22no—
76C2×C8C22⋊D6111yescharacteristic
77C2×C8C22×D6111yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C4⋊C4—1221no—
81C4⋊C4—2441no—
82C22⋊C4—2441no—
83C16—1222no—
84C23#1175819911yescharacteristic
85Q8—2441no—
86Q8—2441no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—42no—
90C2×C4—82no—
91C2×C4—2441no—
92C2×C4—2441no—
93C2×C4#1175819911yescharacteristic
94C2×C4C2×C22⋊D6111yescharacteristic
95C8—21no—
96C8#1175822212yes—
97C22—21no—
98C22—21no—
99C22#1451972112yes—
100C22C2×#1175819911yescharacteristic
101C4—21no—
102C4—82no—
103C4—4881no—
104C4—4881no—
105C4#1451976011yescharacteristic
106C4#1451980811yescharacteristic
107C2—22no—
108C2#1684007511yescharacteristic
109C2C2×#1451972111yescharacteristic
110C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×#107×C61C2
socleC22×C61C2×D8
hypercenterC2×#107D61
hypocenterC61#2235
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #16839589C2semidirect
3. #16839565C2semidirect
61. C61#2235semidirect