Finite Group Databasebeta

← #21447910

Subgroups — #21447910

Order 7808.

154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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
2#16840003C212yesmaximal
3#16839588C211yesmaximal, characteristic, complemented
4#16839567C212yesmaximal, complemented
5C22×C16×C61C211yesmaximal, characteristic
6C2×Dic244C2212yes—
7#14519756—22no—
8Dic488—22no—
9#14519711C2212yes—
10#14519702—22no—
11C22×C8×C61C2211yescharacteristic
12C2×C16×C61—22no—
13C2×C16×C61C2211yescharacteristic
14C2×C16×C61C2211yescharacteristic
15C22×C4×C61D411yescharacteristic
16C2×Dic122—22no—
17C2×C8×C61—21no—
18C2×C8×C61—21no—
19C2×C8×C61D411yescharacteristic
20C2×C8×C61C2311yescharacteristic
21C22⋊Dic61—42no—
22C4⋊Dic61—22no—
23#11758196—42no—
24Dic244—22no—
25Dic244—22no—
26C16×C61—21no—
27C16×C61D412yes—
28C23×C61D811yescharacteristic
29C2×C4×C61—21no—
30C2×C4×C61—21no—
31C2×C4×C61D811yescharacteristic
32C2×C4×C61C2×D411yescharacteristic
33C2×Dic61—42no—
34C2×Dic61—42no—
35Dic122—42no—
36Dic122—42no—
37C8×C61—21no—
38C8×C61C2×D411yescharacteristic
39C8×C61#4111yescharacteristic
40C22×C61—21no—
41C22×C61—21no—
42C22×C61Q3212yescomplemented
43C22×C61C2×D811yescharacteristic
44C4×C61—21no—
45C4×C61#12111yescharacteristic
46C4×C61#13511yescharacteristic
47Dic61—82no—
48Dic61—82no—
49#2216—611nomaximal, Sylow
50C2×C61—22no—
51C2×C61#46611yescharacteristic
52C2×C61C2×Q3211yescharacteristic
53C2×C61#50811yescharacteristic
54C2×Q32—611no—
55C22×C16D6111yescharacteristic
56#467—612no—
57#366—611no—
58#358—612no—
59C61#221611yescharacteristic, complemented, Sylow
60C2×Q16—612no—
61C22×C8C2×D6111yescharacteristic
62C22⋊Q8—1222no—
63Q32—1222no—
64C2×C16—22no—
65C2×C16C2×D6111yescharacteristic
66C2×C16C2×D6111yescharacteristic
67#107—612no—
68#103—1222no—
69C2×Q8—1222no—
70C22×C4D24411yescharacteristic
71Q16—1222no—
72Q16—1222no—
73C2×C8—21no—
74C2×C8—21no—
75C2×C8D24411yescharacteristic
76C2×C8C22×D6111yescharacteristic
77C4⋊C4—1222no—
78C4⋊C4—2442no—
79C22⋊C4—2442no—
80C16—21no—
81C16C22⋊D6112yes—
82C23D48811yescharacteristic
83Q8—2442no—
84Q8—2442no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—2442no—
88C2×C4—2442no—
89C2×C4D48811yescharacteristic
90C2×C4C2×D24411yescharacteristic
91C8—21no—
92C8#1175822211yescharacteristic
93C8C2×C22⋊D6111yescharacteristic
94C22—21no—
95C22—21no—
96C22Dic48812yescomplemented
97C22C2×D48811yescharacteristic
98C4—21no—
99C4—4882no—
100C4—4882no—
101C4#1451975111yescharacteristic
102C4#1451979911yescharacteristic
103C2—22no—
104C2#1683999811yescharacteristic
105C2C2×Dic48811yescharacteristic
106C2#1684019411yescharacteristic
subgroupG/H
centerC22C2×D488
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC22×C16×C61C2
socleC22×C61C2×D8
hypercenterC22×C16D61
hypocenterC61#2216
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
1. C2×Dic488C2semidirect
3. #16839588C2semidirect
4. #16839567C2semidirect
42. C22×C61Q32semidirect
59. C61#2216semidirect
96. C22Dic488semidirect