Finite Group Databasebeta

← #21447851

Subgroups — #21447851

Order 7808.

186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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×#14519718C212yesmaximal, complemented
2C4×D488C211yesmaximal, characteristic, complemented
3C4⋊#11758185C211yesmaximal, characteristic, complemented
4#16839563C212yesmaximal, complemented
5C61×#493C211yesmaximal, characteristic, complemented
6C2×D488C2211yescharacteristic
7C4×D244—21no—
8#14519718—24no—
9C2×#11758185C2212yes—
10#14519711C2211yescharacteristic
11#14519699—21no—
12C2×D8×C61—21no—
13C2×D8×C61C2212yes—
14#127×C61—21no—
15C4×C8×C61C2211yescharacteristic
16C2×D4×C61—22no—
17C2×D4×C61—41no—
18C2×D4×C61—41no—
19C2×D244—21no—
20C2×C4×D61—41no—
21D8×C61—22no—
22D8×C61—22no—
23D8×C61—42no—
24C2×C8×C61D411yescharacteristic
25C2×C8×C61C2311yescharacteristic
26C42×C61D411yescharacteristic
27#11758198—41no—
28C4⋊Dic61—21no—
29D488—21no—
30D488D412yescomplemented
31#11758185—22no—
32C23×C61—42no—
33C22×D61—41no—
34D4×C61—42no—
35D4×C61—42no—
36D4×C61—82no—
37D4×C61—82no—
38C2×C4×C61D811yescharacteristic
39C2×C4×C61D811yescharacteristic
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—41no—
42D244—22no—
43D244—41no—
44C4×D61—82no—
45C8×C61—21no—
46C8×C61C2×D411yescharacteristic
47C8×C61#4111yescharacteristic
48C22×C61—82no—
49C22×C61—82no—
50C22×C61—82no—
51C22×C61C2×D811yescharacteristic
52C2×D61—42no—
53C2×D61—81no—
54C2×D61—81no—
55C4×C61—21no—
56C4×C61D1612yescomplemented
57C4×C61#12111yescharacteristic
58C4×C61AGL(1,ℤ/8)11yescharacteristic
59Dic61—81no—
60#2206—611nomaximal, Sylow
61C2×C61—162no—
62C2×C61#45911yescharacteristic
63C2×C61C2×D1611yescharacteristic
64C2×C61#50911yescharacteristic
65D61—82no—
66C2×D16—612no—
67#493D6111yescharacteristic, complemented
68C4×D8—611no—
69C4⋊C16—611no—
70#357—612no—
71C61#220611yescharacteristic, complemented, Sylow
72C2×D8—21no—
73C2×D8—611no—
74C2×D8C2×D6112yes—
75#127—21no—
76C4×D4—1221no—
77D16—1224no—
78C2×C16—612no—
79#107—611no—
80#102—1221no—
81C4×C8C2×D6111yescharacteristic
82C2×D4—22no—
83C2×D4—41no—
84C2×D4—41no—
85C2×D4—1221no—
86C22×C4—2441no—
87D8—22no—
88D8—22no—
89D8—42no—
90D8—612no—
91D8—1221no—
92C2×C8C22⋊D6111yescharacteristic
93C2×C8C22×D6111yescharacteristic
94C4⋊C4—1221no—
95C22⋊C4—2441no—
96C42C22⋊D6111yescharacteristic
97C16—1222no—
98C23—42no—
99C23—2441no—
100D4—42no—
101D4—42no—
102D4—82no—
103D4—82no—
104D4—1222no—
105D4—2441no—
106C2×C4—4882no—
107C2×C4—2441no—
108C2×C4#1175819911yescharacteristic
109C2×C4#1175819911yescharacteristic
110C2×C4C2×C22⋊D6111yescharacteristic
111C8—21no—
112C8D4×D6111yescharacteristic
113C8#1175822411yescharacteristic
114C22—82no—
115C22—82no—
116C22—82no—
117C22—4881no—
118C22—4881no—
119C22—2442no—
120C22C2×#1175819911yescharacteristic
121C4—21no—
122C4—4881no—
123C4#1451971812yescomplemented
124C4#1451974811yescharacteristic
125C4#1451980311yescharacteristic
126C2—162no—
127C2—4882no—
128C2#1683995411yescharacteristic
129C2C2×#1451971811yescharacteristic
130C2#1684019811yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#493C2
socleC22×C61C2×D8
hypercenter#493D61
hypocenterC61#2206
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. C2×#14519718C2semidirect
2. C4×D488C2semidirect
3. C4⋊#11758185C2semidirect
4. #16839563C2semidirect
5. C61×#493C2semidirect
30. D488D4semidirect
56. C4×C61D16semidirect
67. #493D61semidirect
71. C61#2206semidirect
123. C4#14519718semidirect