Finite Group Databasebeta

← #21443705

Subgroups — #21443705

Order 7808.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#16839726C211yesmaximal, characteristic
2C4×C22⋊Dic61C211yesmaximal, characteristic
3C4×C22⋊C4×C61C211yesmaximal, characteristic
4C2×#11758194C412yescomplemented
5C2×C22⋊Dic61—21no—
6C2×C4×Dic61—21no—
7C22⋊#92418—21no—
8C22⋊#92418—21no—
9#14519684C412yescomplemented
10C23×C4×C61C2211yescharacteristic
11C2×C22⋊C4×C61—21no—
12C2×C42×C61—21no—
13#95×C61C412yescomplemented
14C24×C61D411yescharacteristic
15C22×C4×C61—22no—
16C22×C4×C61—42no—
17C22×C4×C61C2×C411yescharacteristic
18C22×C4×C61C2×C411yescharacteristic
19C22×C4×C61C2×C411yescharacteristic
20C22×C4×C61D411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61Q811yescharacteristic
23C22×Dic61—22no—
24C22⋊C4×C61—24no—
25C42×C61—42no—
26C22⋊Dic61—24no—
27C4×Dic61—42no—
28#11758194—42no—
29C2×#92418—22no—
30C23×C61—22no—
31C23×C61—22no—
32C23×C61—41no—
33C23×C61C22⋊C411yescharacteristic
34C23×C61C22⋊C411yescharacteristic
35C23×C61C4⋊C411yescharacteristic
36C2×C4×C61—22no—
37C2×C4×C61—22no—
38C2×C4×C61—22no—
39C2×C4×C61—24no—
40C2×C4×C61—41no—
41C2×C4×C61—41no—
42C2×C4×C61—41no—
43C2×C4×C61—42no—
44C2×C4×C61—42no—
45C2×C4×C61C4211yescharacteristic
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C4⋊C411yescharacteristic
48C2×C4×C61C4⋊C411yescharacteristic
49C2×Dic61—24no—
50C2×Dic61—42no—
51C2×Dic61—42no—
52#92418—42no—
53C22×C61—21no—
54C22×C61—21no—
55C22×C61—21no—
56C22×C61—21no—
57C22×C61—21no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61—44no—
61C22×C61#9511yescharacteristic
62C22×C61#10412yes—
63C22×C61#10412yes—
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—44no—
68C4×C61#9912yes—
69Dic61—44no—
70#1297—611nomaximal, Sylow
71C2×C61—22no—
72C2×C61—22no—
73C2×C61—41no—
74C2×C61#33911yescharacteristic
75C2×C61#33911yescharacteristic
76C2×C61#34211yescharacteristic
77#407—611no—
78C4×C22⋊C4—611no—
79C4×C22⋊C4D6111yescharacteristic
80C61#129711yescharacteristic, complemented, Sylow
81C23×C4C2×D6111yescharacteristic
82C2×M16—612no—
83C2×C22⋊C4—21no—
84C2×C22⋊C4—1221no—
85C2×C42—21no—
86C2×C42—1221no—
87C22⋊C8—1221no—
88C22⋊C8—1221no—
89#95—612no—
90#95Dic6112yescomplemented
91C24C22⋊D6111yescharacteristic
92C22×C4—22no—
93C22×C4—42no—
94C22×C4—1222no—
95C22×C4Dic12211yescharacteristic
96C22×C4C4×D6111yescharacteristic
97C22×C4C4×D6111yescharacteristic
98C22×C4D24411yescharacteristic
99C22×C4C2×Dic6111yescharacteristic
100C22×C4C22⋊D6111yescharacteristic
101M16—2442no—
102C2×C8—1222no—
103C22⋊C4—24no—
104C22⋊C4—1224no—
105C42—42no—
106C42—2442no—
107C23—22no—
108C23—22no—
109C23—41no—
110C23#1175819611yescharacteristic
111C23#1175819811yescharacteristic
112C23C22⋊Dic6111yescharacteristic
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—24no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—1224no—
123C2×C4—2442no—
124C2×C4—2442no—
125C2×C4C4×Dic6111yescharacteristic
126C2×C4#1175819611yescharacteristic
127C2×C4C4⋊Dic6111yescharacteristic
128C2×C4#1175819811yescharacteristic
129C8—2442no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22—44no—
138C22#1451968411yescharacteristic
139C22#1451970412yes—
140C22#1451970512yes—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—44no—
145C4—2444no—
146C4#1451969112yes—
147C2—22no—
148C2—22no—
149C2—41no—
150C2#1683952111yescharacteristic
151C2#1683952211yescharacteristic
152C2#1683952811yescharacteristic
subgroupG/H
centerC2×C4#11758198
commutatorC2×C4×C61C42
FrattiniC23×C4C2×D61
FittingC4×C22⋊C4×C61C2
socleC22×C61#95
hypercenterC4×C22⋊C4D61
hypocenterC61#1297
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#11758194C4semidirect
9. #14519684C4semidirect
13. #95×C61C4semidirect
80. C61#1297semidirect
90. #95Dic61semidirect