Finite Group Databasebeta

← #21447334

Subgroups — #21447334

Order 7808.

222 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 63 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#16839810C212yesmaximal, complemented
2#16839725C212yesmaximal
3#16839725C211yesmaximal, characteristic
4#16839520C211yesmaximal, characteristic, complemented
5C61×#430C211yesmaximal, characteristic, complemented
6C22×C4×D61C2211yescharacteristic
7C2×#11758194C2211yescharacteristic
8C2×#11758194C2212yes—
9#14519712—24no—
10#14519689—22no—
11#14519689—24no—
12C2×M16×C61C2212yes—
13C2×M16×C61C2211yescharacteristic
14#108×C61—22no—
15C23×D61Q811yescharacteristic
16C22×C4×C61C2311yescharacteristic
17C22×Dic61Q811yescharacteristic
18C2×C4×D61—22no—
19C2×C4×D61—21no—
20C2×C4×D61—22no—
21C2×C4×D61—21no—
22M16×C61—22no—
23M16×C61—22no—
24M16×C61—22no—
25C2×C8×C61—22no—
26C2×C8×C61D412yes—
27#11758194—22no—
28#11758194—22no—
29#11758194—22no—
30C2×#92418—21no—
31C2×#92418D414yes—
32C23×C61C2×Q811yescharacteristic
33C22×D61—21no—
34C22×D61—22no—
35C22×D61—42no—
36C2×C4×C61C2×D412yes—
37C2×C4×C61C2×D411yescharacteristic
38C2×C4×C61#4112yes—
39C2×C4×C61#4111yescharacteristic
40C2×Dic61—21no—
41C2×Dic61—22no—
42C4×D61—41no—
43C4×D61—42no—
44C4×D61—41no—
45C8×C61—22no—
46C8×C61—42no—
47#92418—24no—
48#92418—41no—
49C22×C61—41no—
50C22×C61C22⋊Q811yescharacteristic
51C22×C61C22⋊Q812yes—
52C2×D61—22no—
53C2×D61—24no—
54C2×D61—41no—
55C2×D61—42no—
56C2×D61—41no—
57C4×C61#12311yescharacteristic
58C4×C61#12312yes—
59C4×C61#12711yescharacteristic
60Dic61—41no—
61#2091—611nomaximal, Sylow
62C2×C61—21no—
63C2×C61—22no—
64C2×C61#39911yescharacteristic
65D61—42no—
66#430—612no—
67#430D6111yescharacteristic, complemented
68#407—612no—
69#407—611no—
70#338—611no—
71C61#209111yescharacteristic, complemented, Sylow
72C23×C4—611no—
73C2×M16—612no—
74C2×M16—611no—
75C2×M16C2×D6112yes—
76C2×M16C2×D6111yescharacteristic
77#108—22no—
78#108—1224no—
79C22⋊C8—1224no—
80C22⋊C8—1222no—
81C24—611no—
82C22×C4—611no—
83C22×C4—1222no—
84C22×C4—1222no—
85C22×C4—1221no—
86C22×C4—1221no—
87C22×C4C22×D6111yescharacteristic
88M16—22no—
89M16—22no—
90M16—22no—
91M16—1222no—
92M16—1222no—
93M16—1222no—
94C2×C8—22no—
95C2×C8—614no—
96C2×C8—1221no—
97C2×C8C22⋊D6112yes—
98C23—1221no—
99C23—1222no—
100C23—2442no—
101C23Q8×D6111yescharacteristic
102C2×C4—1221no—
103C2×C4—1222no—
104C2×C4—2441no—
105C2×C4—2442no—
106C2×C4—2441no—
107C2×C4#1175822212yes—
108C2×C4D4×D6112yes—
109C2×C4#1175822611yescharacteristic
110C2×C4C2×C22⋊D6111yescharacteristic
111C8—22no—
112C8—42no—
113C8—1224no—
114C8—2441no—
115C22—41no—
116C22—1222no—
117C22—1224no—
118C22—2441no—
119C22—2442no—
120C22—2441no—
121C22#1451975311yescharacteristic
122C22#1451975512yes—
123C4—2441no—
124C4#1451976011yescharacteristic
125C4#1451976212yes—
126C4#1451977311yescharacteristic
127C2—21no—
128C2—22no—
129C2—2442no—
130C2#1683969711yescharacteristic
subgroupG/H
centerC4#14519773
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#430C2
socleC2×C61#399
hypercenter#430D61
hypocenterC61#2091
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
1. #16839810C2semidirect
4. #16839520C2semidirect
5. C61×#430C2semidirect
67. #430D61semidirect
71. C61#2091semidirect