Finite Group Databasebeta

← #21447928

Subgroups — #21447928

Order 7808.

150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C2×Dic488C211yesmaximal, characteristic, complemented
2C2×#14519716C211yesmaximal, characteristic
3#16840004C212yesmaximal
4#16839565C212yesmaximal, complemented
5C61×#367C211yesmaximal, characteristic, complemented
6C2×Dic244C2212yes—
7C2×C8×D61C2211yescharacteristic
8#14519757—22no—
9Dic488—22no—
10#14519716—22no—
11C2×#11758185C2211yescharacteristic
12#14519700—22no—
13C2×C16×C61C2211yescharacteristic
14#107×C61C2212yes—
15C2×C4×D61D411yescharacteristic
16C2×Dic122—22no—
17C2×C8×C61C2311yescharacteristic
18C4⋊C4×C61—22no—
19#11758198—42no—
20C4⋊Dic61—42no—
21C2×#92418D411yescharacteristic
22Dic244—22no—
23Dic244—22no—
24C8×D61—21no—
25C8×D61—21no—
26C16×C61D412yes—
27#11758185—21no—
28C22×D61D811yescharacteristic
29C2×C4×C61—42no—
30C2×C4×C61C2×D411yescharacteristic
31C2×Dic61—42no—
32C2×Dic61D811yescharacteristic
33C4×D61—21no—
34C4×D61—21no—
35Dic122—42no—
36Dic122—42no—
37C8×C61C2×D411yescharacteristic
38C8×C61#4111yescharacteristic
39#92418—21no—
40C22×C61C2×D811yescharacteristic
41C2×D61—21no—
42C2×D61—22no—
43C4×C61—82no—
44C4×C61#12111yescharacteristic
45C4×C61#13511yescharacteristic
46Dic61—21no—
47Dic61—82no—
48#2219—611nomaximal, Sylow
49C2×C61#46611yescharacteristic
50C2×C61#51012yes—
51D61—41no—
52C2×Q32—611no—
53C2×M32—611no—
54#467—612no—
55#367D6111yescharacteristic, complemented
56#358—612no—
57C61#221911yescharacteristic, complemented, Sylow
58C2×Q16—612no—
59C22×C8—611no—
60C22⋊Q8—1222no—
61Q32—1222no—
62M32—1222no—
63C2×C16—611no—
64C2×C16C2×D6111yescharacteristic
65#107C2×D6112yes—
66#103—1222no—
67C2×Q8—1222no—
68C22×C4—611no—
69Q16—1222no—
70Q16—1222no—
71C2×C8—611no—
72C2×C8—1221no—
73C2×C8—1221no—
74C2×C8C22×D6111yescharacteristic
75C4⋊C4—22no—
76C4⋊C4—2442no—
77C22⋊C4—2442no—
78C16—1221no—
79C16D24412yes—
80C23—611no—
81Q8—2442no—
82Q8—2442no—
83C2×C4—42no—
84C2×C4—611no—
85C2×C4—1221no—
86C2×C4—1221no—
87C2×C4—2442no—
88C2×C4D4×D6111yescharacteristic
89C8—1221no—
90C8C2×D24411yescharacteristic
91C8#1175822611yescharacteristic
92C22—1222no—
93C22—1221no—
94C22D8×D6111yescharacteristic
95C4—82no—
96C4—1221no—
97C4—4882no—
98C4#1451975211yescharacteristic
99C4#1451980011yescharacteristic
100C2—2441no—
101C2#1683999911yescharacteristic
102C2#1684020112yes—
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#367C2
socleC22×C61C2×D8
hypercenter#367D61
hypocenterC61#2219
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
1. C2×Dic488C2semidirect
4. #16839565C2semidirect
5. C61×#367C2semidirect
55. #367D61semidirect
57. C61#2219semidirect