Finite Group Databasebeta

← #21448034

Subgroups — #21448034

Order 7808.

134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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#16840015C211yesmaximal, characteristic
2#16839811C211yesmaximal, characteristic, complemented
3#16839585C212yesmaximal, complemented
4#16839576C212yesmaximal, complemented
5C61×#349C211yesmaximal, characteristic, complemented
6C2×D488C2211yescharacteristic
7C2×#11758194—21no—
8#14519751—21no—
9#14519713—21no—
10#14519713C2212yes—
11#14519709C2211yescharacteristic
12#14519699—21no—
13C2×M16×C61C2211yescharacteristic
14M32×C61C2212yes—
15C22×C4×C61D411yescharacteristic
16C2×C22⋊D61—41no—
17C2×D244—21no—
18M16×C61—22no—
19C2×C8×C61D411yescharacteristic
20C2×C8×C61C2311yescharacteristic
21#11758198—41no—
22C4⋊Dic61—21no—
23#11758194—22no—
24#11758194—41no—
25C2×#92418—41no—
26D488—22no—
27C16×C61—22no—
28C23×C61SD1611yescharacteristic
29C22×D61—41no—
30C2×C4×C61—21no—
31C2×C4×C61—21no—
32C2×C4×C61SD1611yescharacteristic
33C2×C4×C61C2×D411yescharacteristic
34C22⋊D61—82no—
35C2×Dic61—41no—
36D244—41no—
37D244—41no—
38C8×C61—21no—
39C8×C61#4112yes—
40#92418—42no—
41C22×C61—21no—
42C22×C61—41no—
43C22×C61C2×SD1611yescharacteristic
44C2×D61—81no—
45C2×D61—81no—
46C2×D61—81no—
47C4×C61—21no—
48C4×C61#12311yescharacteristic
49C4×C61AGL(1,ℤ/8)11yescharacteristic
50Dic61—81no—
51#2238—611nomaximal, Sylow
52C2×C61—21no—
53C2×C61—41no—
54C2×C61#48111yescharacteristic
55D61—161no—
56#469—611no—
57#430—611no—
58#365—612no—
59#361—612no—
60#349D6111yescharacteristic, complemented
61C61#223811yescharacteristic, complemented, Sylow
62C2×D8—611no—
63C2×M16—1221no—
64C2×M16C2×D6111yescharacteristic
65#121—1221no—
66M32C2×D6112yes—
67#108—612no—
68#108—1221no—
69#106—611no—
70#102—1221no—
71C2×D4—1221no—
72C2×D4—2441no—
73C22×C4D24411yescharacteristic
74D8—1222no—
75M16—22no—
76M16—1222no—
77M16—2441no—
78C2×C8—2441no—
79C2×C8D24411yescharacteristic
80C2×C8C22×D6111yescharacteristic
81C4⋊C4—1221no—
82C22⋊C4—2441no—
83C16—22no—
84C23—2441no—
85C23#1175819011yescharacteristic
86D4—4882no—
87D4—2441no—
88D4—2441no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—2441no—
92C2×C4#1175819011yescharacteristic
93C2×C4C2×D24411yescharacteristic
94C8—21no—
95C8—2442no—
96C8#1175822412yes—
97C22—21no—
98C22—41no—
99C22—4881no—
100C22—4881no—
101C22—4881no—
102C22C2×#1175819011yescharacteristic
103C4—21no—
104C4—4881no—
105C4#1451976111yescharacteristic
106C4#1451980511yescharacteristic
107C2—21no—
108C2—41no—
109C2—9761no—
110C2#1684008111yescharacteristic
subgroupG/H
centerC2#16840081
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#349C2
socleC2×C61#481
hypercenter#349D61
hypocenterC61#2238
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #16839811C2semidirect
3. #16839585C2semidirect
4. #16839576C2semidirect
5. C61×#349C2semidirect
60. #349D61semidirect
61. C61#2238semidirect