Finite Group Databasebeta

← #21443820

Subgroups — #21443820

Order 7808.

146 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 35 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#16839687C211yesmaximal, characteristic
2#16839529C211yesmaximal, characteristic
3C61×#323C211yesmaximal, characteristic
4C2×C4⋊Dic61C411yescharacteristic, complemented
5C2×C22⋊Dic61—21no—
6C2×C22⋊Dic61—21no—
7#14519684—21no—
8#14519684C411yescharacteristic, complemented
9C2×C22⋊C4×C61C2211yescharacteristic
10C22⋊C8×C61—21no—
11C24×C61D411yescharacteristic
12C22×C4×C61C2×C411yescharacteristic
13C22×C4×C61D411yescharacteristic
14C22×Dic61—21no—
15C22×Dic61—21no—
16C22×Dic61—41no—
17C2×C8×C61—41no—
18C22⋊C4×C61—41no—
19C22⋊Dic61—22no—
20C22⋊Dic61—41no—
21C22⋊Dic61—41no—
22C22⋊Dic61—41no—
23C4⋊Dic61—41no—
24C23×C61—21no—
25C23×C61—21no—
26C23×C61—41no—
27C23×C61—41no—
28C23×C61C22⋊C411yescharacteristic
29C23×C61D811yescharacteristic
30C23×C61SD1611yescharacteristic
31C2×C4×C61—21no—
32C2×C4×C61—21no—
33C2×C4×C61—41no—
34C2×C4×C61—41no—
35C2×Dic61—42no—
36C2×Dic61—41no—
37C2×Dic61—41no—
38C2×Dic61—41no—
39C2×Dic61—41no—
40C2×Dic61—41no—
41C2×Dic61—41no—
42C2×Dic61—81no—
43C2×Dic61—81no—
44C8×C61—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#10211yescharacteristic
56C22×C61#10411yescharacteristic
57C4×C61—41no—
58C4×C61—41no—
59Dic61—81no—
60Dic61—82no—
61Dic61—81no—
62#1344—611nomaximal, Sylow
63C2×C61—21no—
64C2×C61—21no—
65C2×C61—41no—
66C2×C61—41no—
67C2×C61#32711yescharacteristic
68C2×C61#35211yescharacteristic
69C2×C61#35411yescharacteristic
70#397—611no—
71#342—611no—
72#323D6111yescharacteristic
73C61#134411yescharacteristic, complemented, Sylow
74C2×C4⋊C4—611no—
75C2×C22⋊C4—1221no—
76C2×C22⋊C4—1221no—
77C2×C22⋊C4C2×D6111yescharacteristic
78C22⋊C8—21no—
79#95—611no—
80#95—1221no—
81C24D24411yescharacteristic
82C22×C4—1221no—
83C22×C4—1221no—
84C22×C4—2441no—
85C22×C4C4×D6111yescharacteristic
86C22×C4C22⋊D6111yescharacteristic
87C2×C8—41no—
88C4⋊C4—2441no—
89C22⋊C4—41no—
90C22⋊C4—1222no—
91C22⋊C4—2441no—
92C22⋊C4—2441no—
93C22⋊C4—2441no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23#1175819011yescharacteristic
99C23D48811yescharacteristic
100C23#1175819811yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—4881no—
106C2×C4—4881no—
107C2×C4—2442no—
108C2×C4—2441no—
109C2×C4—2441no—
110C2×C4—2441no—
111C2×C4—2441no—
112C2×C4—2441no—
113C2×C4—2441no—
114C8—81no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#1451969111yescharacteristic
125C22#1451969911yescharacteristic
126C22#1451970311yescharacteristic
127C4—41no—
128C4—41no—
129C4—4881no—
130C4—4882no—
131C4—4881no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#1683949711yescharacteristic
137C2#1683955311yescharacteristic
138C2#1683955611yescharacteristic
subgroupG/H
centerC22#14519691
commutatorC22×C4×C61C2×C4
FrattiniC2×C22⋊C4C2×D61
FittingC61×#323C2
socleC22×C61#99
hypercenter#323D61
hypocenterC61#1344
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic61C4semidirect
8. #14519684C4semidirect
73. C61#1344semidirect