Finite Group Databasebeta

← #21447605

Subgroups — #21447605

Order 7808.

156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14519717C211yesmaximal, characteristic
2#16839800C211yesmaximal, characteristic
3#16839589C212yesmaximal, complemented
4#16839587C212yesmaximal, complemented
5C2×#107×C61C211yesmaximal, characteristic
6#14519736—21no—
7#14519717C414yescomplemented
8C2×#11758185C2212yes—
9#14519711C2211yescharacteristic
10#14519711C2211yescharacteristic
11#14519709—21no—
12C22×C8×C61C2211yescharacteristic
13C2×C4⋊C4×C61—21no—
14#107×C61—21no—
15#107×C61C2212yes—
16C22×C4×C61—41no—
17C22×C4×C61D411yescharacteristic
18C2×C8×C61C2×C412yes—
19C2×C8×C61D411yescharacteristic
20C2×C8×C61Q812yes—
21C2×C8×C61C2311yescharacteristic
22C4⋊C4×C61—22no—
23C4⋊C4×C61—41no—
24C22⋊Dic61—41no—
25C4⋊Dic61—21no—
26C4⋊Dic61—21no—
27C4×Dic61—41no—
28#11758185C2×C414yescomplemented
29C23×C61D811yescharacteristic
30C2×C4×C61—42no—
31C2×C4×C61—82no—
32C2×C4×C61C4⋊C412yes—
33C2×C4×C61D811yescharacteristic
34C2×C4×C61Q1612yes—
35C2×C4×C61C2×D411yescharacteristic
36C2×Dic61—41no—
37C2×Dic61—41no—
38C8×C61C4⋊C412yes—
39C8×C61C22×C411yescharacteristic
40C8×C61C2×Q811yescharacteristic
41C22×C61—21no—
42C22×C61—21no—
43C22×C61#10712yes—
44C22×C61C2×D811yescharacteristic
45C4×C61—82no—
46C4×C61#10712yes—
47C4×C61C2×C4⋊C411yescharacteristic
48C4×C61C2×Q1611yescharacteristic
49Dic61—81no—
50Dic61—81no—
51#2159—611nomaximal, Sylow
52C2×C61—22no—
53C2×C61C2×#10711yescharacteristic
54C2×C61#50911yescharacteristic
55C2×C61#51011yescharacteristic
56C2×M32—611no—
57#427—611no—
58C2×#107D6111yescharacteristic
59#367—612no—
60#366—612no—
61C61#215911yescharacteristic, complemented, Sylow
62C22×C8C2×D6111yescharacteristic
63#117—1221no—
64C2×C4⋊C4—21no—
65M32—614no—
66C2×C16—612no—
67#107—21no—
68#107—611no—
69#107—611no—
70#107C2×D6112yes—
71#106—1221no—
72C22×C4—41no—
73C22×C4C22⋊D6111yescharacteristic
74C2×C8Dic12212yes—
75C2×C8C4×D6112yes—
76C2×C8C22⋊D6111yescharacteristic
77C2×C8C22×D6111yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C4⋊C4—1221no—
81C4⋊C4—1221no—
82C22⋊C4—2441no—
83C42—2441no—
84C16—614no—
85C23#1175819911yescharacteristic
86C2×C4—42no—
87C2×C4—82no—
88C2×C4—2441no—
89C2×C4—2441no—
90C2×C4#1175819612yes—
91C2×C4#1175819911yescharacteristic
92C2×C4#1175820212yes—
93C2×C4C2×C22⋊D6111yescharacteristic
94C8#1175819612yes—
95C8C2×Dic12211yescharacteristic
96C8C2×C4×D6111yescharacteristic
97C22—21no—
98C22—21no—
99C22#1451971012yes—
100C22C2×#1175819911yescharacteristic
101C4—82no—
102C4—4881no—
103C4—4881no—
104C4#1451971012yes—
105C4C2×#1175819611yescharacteristic
106C4C2×#1175820211yescharacteristic
107C2—22no—
108C2C2×#1451971011yescharacteristic
109C2#1684019811yescharacteristic
110C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC2×#107×C61C2
socleC22×C61C2×D8
hypercenterC2×#107D61
hypocenterC61#2159
LCSG ▷ 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
3. #16839589C2semidirect
4. #16839587C2semidirect
7. #14519717C4semidirect
28. #11758185C2×C4semidirect
61. C61#2159semidirect