Finite Group Databasebeta

← #21444162

Subgroups — #21444162

Order 7808.

236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×Dic122C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic
3#16839487C214yesmaximal
4C61×#432C211yesmaximal, characteristic
5C22×Dic122C411yescharacteristic
6C4×Dic122—21no—
7C4×Dic122—21no—
8C4×Dic122—21no—
9C4×Dic122—21no—
10C2×C4⋊Dic61C411yescharacteristic
11C2×#11758196C2212yes—
12C2×C4×Dic61C412yes—
13C4⋊#92418—21no—
14C22⋊#92418C2212yes—
15#14519688—21no—
16C2×C42×C61C2211yescharacteristic
17C4⋊C8×C61—21no—
18C22⋊C8×C61C2212yes—
19#97×C61—21no—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61C2311yescharacteristic
23C22×Dic61C2×C412yes—
24C22×Dic61C2×C412yes—
25C2×Dic122—21no—
26C2×Dic122—21no—
27C2×Dic122—24no—
28C2×C8×C61—22no—
29C42×C61D411yescharacteristic
30C42×C61D411yescharacteristic
31C42×C61D411yescharacteristic
32C42×C61D411yescharacteristic
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35#11758196—22no—
36#11758196—22no—
37C4×Dic61—22no—
38C4×Dic61—22no—
39C2×#92418—22no—
40C23×C61C22×C411yescharacteristic
41C2×C4×C61—22no—
42C2×C4×C61—22no—
43C2×C4×C61—41no—
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C2×D411yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×Dic61—22no—
51C2×Dic61—22no—
52C2×Dic61—22no—
53C2×Dic61—42no—
54C2×Dic61M1614yes—
55Dic122—24no—
56Dic122—24no—
57C8×C61—42no—
58#92418—42no—
59C22×C61—21no—
60C22×C61—21no—
61C22×C61C2×C22⋊C411yescharacteristic
62C22×C61C2×M1612yes—
63C4×C61—21no—
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—21no—
68C4×C61#10112yes—
69Dic61—24no—
70Dic61—42no—
71#1467—611nomaximal, Sylow
72C2×C61—22no—
73C2×C61#40711yescharacteristic
74C2×C61#41011yescharacteristic
75C2×C61C2×#10111yescharacteristic
76C2×C4×Q8—611no—
77#432—611no—
78#432D6111yescharacteristic
79#324—614no—
80C61#146711yescharacteristic, complemented, Sylow
81C22×Q8—611no—
82C4×Q8—1221no—
83C4×Q8—1221no—
84C4×Q8—1221no—
85C4×Q8—1221no—
86C2×C4⋊C4—611no—
87C2×C4⋊C4—612no—
88C2×C42—612no—
89C2×C42C2×D6111yescharacteristic
90C4⋊C8—21no—
91C4⋊C8—1221no—
92C22⋊C8—612no—
93C22⋊C8C2×D6112yes—
94#97—21no—
95#97—1221no—
96C2×Q8—1224no—
97C2×Q8—1221no—
98C2×Q8—1221no—
99C22×C4—612no—
100C22×C4—612no—
101C22×C4C4×D6111yescharacteristic
102C22×C4C4×D6111yescharacteristic
103C22×C4C22×D6111yescharacteristic
104C2×C8—22no—
105C2×C8—1222no—
106C4⋊C4—1221no—
107C4⋊C4—1221no—
108C4⋊C4—1222no—
109C4⋊C4—1222no—
110C42—1222no—
111C42—1222no—
112C42D24411yescharacteristic
113C42D24411yescharacteristic
114C42C22⋊D6111yescharacteristic
115C42C22⋊D6111yescharacteristic
116C23C2×C4×D6111yescharacteristic
117Q8—1224no—
118Q8—1224no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4—614no—
123C2×C4—1222no—
124C2×C4—1222no—
125C2×C4—1222no—
126C2×C4—2442no—
127C2×C4#1175819811yescharacteristic
128C2×C4#1175819811yescharacteristic
129C2×C4#1175819811yescharacteristic
130C2×C4#1175819811yescharacteristic
131C2×C4C2×D24411yescharacteristic
132C2×C4C2×C22⋊D6111yescharacteristic
133C8—42no—
134C8—2442no—
135C22—21no—
136C22—21no—
137C22C2×#1175819811yescharacteristic
138C22M16×D6112yes—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—1224no—
145C4—2442no—
146C4#1451969512yes—
147C2—22no—
148C2#1683972511yescharacteristic
149C2#1683973511yescharacteristic
150C2C2×#1451969511yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1467
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
80. C61#1467semidirect