Finite Group Databasebeta

← #21447911

Subgroups — #21447911

Order 7808.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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×C16×D61C211yesmaximal, characteristic
3#16840004C212yesmaximal
4#16839565C212yesmaximal, complemented
5C61×#366C211yesmaximal, characteristic, complemented
6C2×Dic244C2212yes—
7C2×C8×D61C2211yescharacteristic
8#14519757—22no—
9Dic488—22no—
10C2×#11758185C2211yescharacteristic
11C16×D61—22no—
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—21no—
43C2×D61Q3212yescomplemented
44C4×C61—82no—
45C4×C61#12111yescharacteristic
46C4×C61#13511yescharacteristic
47Dic61—21no—
48Dic61—82no—
49#2216—611nomaximal, Sylow
50C2×C61#46611yescharacteristic
51C2×C61C2×Q3211yescharacteristic
52C2×C61#50811yescharacteristic
53D61—22no—
54C2×Q32—611no—
55C22×C16—611no—
56#467—612no—
57#366D6111yescharacteristic, complemented
58#358—612no—
59C61#221611yescharacteristic, complemented, Sylow
60C2×Q16—612no—
61C22×C8—611no—
62C22⋊Q8—1222no—
63Q32—1222no—
64C2×C16—611no—
65C2×C16—1222no—
66C2×C16C2×D6111yescharacteristic
67#107C2×D6112yes—
68#103—1222no—
69C2×Q8—1222no—
70C22×C4—611no—
71Q16—1222no—
72Q16—1222no—
73C2×C8—611no—
74C2×C8—1221no—
75C2×C8—1221no—
76C2×C8C22×D6111yescharacteristic
77C4⋊C4—22no—
78C4⋊C4—2442no—
79C22⋊C4—2442no—
80C16—1221no—
81C16D24412yes—
82C23—611no—
83Q8—2442no—
84Q8—2442no—
85C2×C4—42no—
86C2×C4—611no—
87C2×C4—1221no—
88C2×C4—1221no—
89C2×C4—2442no—
90C2×C4D4×D6111yescharacteristic
91C8—1221no—
92C8C2×D24411yescharacteristic
93C8#1175822611yescharacteristic
94C22—612no—
95C22—1221no—
96C22—1221no—
97C22D8×D6111yescharacteristic
98C4—82no—
99C4—1221no—
100C4—4882no—
101C4#1451975211yescharacteristic
102C4#1451980011yescharacteristic
103C2—1222no—
104C2#1683999911yescharacteristic
105C2Q32×D6111yescharacteristic
106C2#1684019111yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#366C2
socleC22×C61C2×D8
hypercenter#366D61
hypocenterC61#2216
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. C2×Dic488C2semidirect
4. #16839565C2semidirect
5. C61×#366C2semidirect
43. C2×D61Q32semidirect
57. #366D61semidirect
59. C61#2216semidirect