Finite Group Databasebeta

← #21443843

Subgroups — #21443843

Order 7808.

154 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 37 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#16839529C211yesmaximal, characteristic
2#16839486C211yesmaximal, characteristic
3C61×#399C211yesmaximal, characteristic
4C2×C22⋊Dic61—21no—
5C22⋊#92418—21no—
6C2×C4⋊C4×C61—21no—
7C2×C4⋊C4×C61C411yescharacteristic, complemented
8C2×C22⋊C4×C61—21no—
9C2×C22⋊C4×C61C2211yescharacteristic
10#95×C61C411yescharacteristic, complemented
11C24×C61D411yescharacteristic
12C22×C4×C61—21no—
13C22×C4×C61—21no—
14C22×C4×C61C2×C411yescharacteristic
15C22×C4×C61D411yescharacteristic
16C22×Dic61—41no—
17C4⋊C4×C61—42no—
18C4⋊C4×C61—41no—
19C22⋊C4×C61—41no—
20C22⋊C4×C61—42no—
21C22⋊Dic61—22no—
22C22⋊Dic61—41no—
23C2×#92418—41no—
24C23×C61—21no—
25C23×C61—21no—
26C23×C61—41no—
27C23×C61—41no—
28C23×C61C22⋊C411yescharacteristic
29C23×C61SD1611yescharacteristic
30C23×C61Q1611yescharacteristic
31C2×C4×C61—22no—
32C2×C4×C61—21no—
33C2×C4×C61—21no—
34C2×C4×C61—41no—
35C2×C4×C61—41no—
36C2×C4×C61—41no—
37C2×C4×C61—41no—
38C2×C4×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61—41no—
41C2×Dic61—42no—
42C2×Dic61—81no—
43C2×Dic61—81no—
44#92418—81no—
45C22×C61—21no—
46C22×C61—21no—
47C22×C61—21no—
48C22×C61—21no—
49C22×C61—41no—
50C22×C61—41no—
51C22×C61—41no—
52C22×C61—41no—
53C22×C61—81no—
54C22×C61#9911yescharacteristic
55C22×C61#10311yescharacteristic
56C22×C61#10411yescharacteristic
57C4×C61—42no—
58C4×C61—41no—
59C4×C61—41no—
60C4×C61—81no—
61Dic61—82no—
62#1352—611nomaximal, Sylow
63C2×C61—21no—
64C2×C61—21no—
65C2×C61—41no—
66C2×C61—41no—
67C2×C61#32811yescharacteristic
68C2×C61#35211yescharacteristic
69C2×C61#35311yescharacteristic
70#399D6111yescharacteristic
71#342—611no—
72#323—611no—
73C61#135211yescharacteristic, complemented, Sylow
74C2×C4⋊C4—21no—
75C2×C4⋊C4Dic6111yescharacteristic, complemented
76C2×C22⋊C4—21no—
77C2×C22⋊C4—1221no—
78C2×C22⋊C4C2×D6111yescharacteristic
79C22⋊C8—1221no—
80#95Dic6111yescharacteristic, complemented
81C24C22⋊D6111yescharacteristic
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—2441no—
85C22×C4C2×Dic6111yescharacteristic
86C22×C4C22⋊D6111yescharacteristic
87C2×C8—2441no—
88C4⋊C4—41no—
89C4⋊C4—42no—
90C22⋊C4—41no—
91C22⋊C4—42no—
92C22⋊C4—1222no—
93C22⋊C4—2441no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23#1175820111yescharacteristic
99C23#1175820211yescharacteristic
100C23C22⋊Dic6111yescharacteristic
101C2×C4—22no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—4881no—
112C2×C4—4881no—
113C2×C4—2442no—
114C8—4881no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#1451969211yescharacteristic
125C22#1451970111yescharacteristic
126C22#1451970411yescharacteristic
127C4—42no—
128C4—41no—
129C4—41no—
130C4—81no—
131C4—4882no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#1683949911yescharacteristic
137C2#1683955211yescharacteristic
138C2#1683955511yescharacteristic
subgroupG/H
centerC22#14519692
commutatorC22×C4×C61C2×C4
FrattiniC2×C22⋊C4C2×D61
FittingC61×#399C2
socleC22×C61#99
hypercenter#399D61
hypocenterC61#1352
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #399

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊C4×C61C4semidirect
10. #95×C61C4semidirect
73. C61#1352semidirect
75. C2×C4⋊C4Dic61semidirect
80. #95Dic61semidirect