Finite Group Databasebeta

← #21447997

Subgroups — #21447997

Order 7808.

150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14519711C211yesmaximal, characteristic, complemented
2#16839587C212yesmaximal, complemented
3#16839563C212yesmaximal, complemented
4C22⋊#11758185C211yesmaximal, characteristic, complemented
5C61×#466C211yesmaximal, characteristic
6C2×C4⋊Dic61—21no—
7C2×#11758185C2212yes—
8#14519711—21no—
9#14519711C2212yes—
10C2×D8×C61C2211yescharacteristic
11C22×C8×C61C2211yescharacteristic
12#121×C61—21no—
13#107×C61C2211yescharacteristic
14#102×C61—21no—
15C2×D4×C61—21no—
16C2×D4×C61—41no—
17C22×C4×C61D411yescharacteristic
18C22×Dic61—41no—
19D8×C61—22no—
20C2×C8×C61—22no—
21C2×C8×C61D411yescharacteristic
22C2×C8×C61C2311yescharacteristic
23C4⋊C4×C61—21no—
24C22⋊C4×C61—41no—
25C4⋊Dic61—22no—
26C4⋊Dic61—41no—
27#11758185—22no—
28C23×C61—41no—
29C23×C61D811yescharacteristic
30D4×C61—41no—
31D4×C61—41no—
32D4×C61—82no—
33C2×C4×C61—21no—
34C2×C4×C61—21no—
35C2×C4×C61—41no—
36C2×C4×C61D811yescharacteristic
37C2×C4×C61C2×D411yescharacteristic
38C2×Dic61—42no—
39C2×Dic61—82no—
40C8×C61—21no—
41C8×C61#4112yes—
42C22×C61—21no—
43C22×C61—21no—
44C22×C61—81no—
45C22×C61—81no—
46C22×C61—81no—
47C22×C61D1612yes—
48C22×C61C2×D811yescharacteristic
49C4×C61—21no—
50C4×C61—81no—
51C4×C61#12311yescharacteristic
52C4×C61#13711yescharacteristic
53Dic61—82no—
54#2232—611nomaximal, Sylow
55C2×C61—22no—
56C2×C61—161no—
57C2×C61#48011yescharacteristic
58C2×C61C2×D1611yescharacteristic
59C2×C61#51011yescharacteristic
60#466D6111yescharacteristic
61C2×#107—611no—
62#366—612no—
63#357—612no—
64C22⋊C16—611no—
65C61#223211yescharacteristic, complemented, Sylow
66C2×D8C2×D6111yescharacteristic
67C22×C8C2×D6111yescharacteristic
68#121—21no—
69C2×C4⋊C4—1221no—
70C2×C16—612no—
71#107—612no—
72#107—1221no—
73#107C2×D6111yescharacteristic
74#102—21no—
75C2×D4—21no—
76C2×D4—41no—
77C22×C4—2441no—
78C22×C4C22⋊D6111yescharacteristic
79D8—22no—
80C2×C8—22no—
81C2×C8C22⋊D6111yescharacteristic
82C2×C8C22×D6111yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—1222no—
85C4⋊C4—2441no—
86C22⋊C4—41no—
87C16—1222no—
88C23—41no—
89C23#1175819911yescharacteristic
90D4—41no—
91D4—41no—
92D4—82no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—41no—
96C2×C4—4882no—
97C2×C4—2442no—
98C2×C4#1175819911yescharacteristic
99C2×C4C2×C22⋊D6111yescharacteristic
100C8—21no—
101C8#1175822412yes—
102C22—21no—
103C22—21no—
104C22—81no—
105C22—81no—
106C22—81no—
107C22#1451971812yes—
108C22C2×#1175819911yescharacteristic
109C4—21no—
110C4—81no—
111C4—4882no—
112C4#1451975811yescharacteristic
113C4#1451980711yescharacteristic
114C2—22no—
115C2—161no—
116C2#1684007311yescharacteristic
117C2C2×#1451971811yescharacteristic
118C2#1684020211yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#466C2
socleC22×C61C2×D8
hypercenter#466D61
hypocenterC61#2232
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#14519711C2semidirect
2. #16839587C2semidirect
3. #16839563C2semidirect
4. C22⋊#11758185C2semidirect
65. C61#2232semidirect