Finite Group Databasebeta

← #21461069

Subgroups — #21461069

Order 7808.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840732C212yesmaximal
2#16840608C214yesmaximal, complemented
3C22×#11758196C211yesmaximal, characteristic
4C2×#11758217—22no—
5C22⋊#92420—22no—
6C22⋊#92420C2214yes—
7C23×Dic61C411yescharacteristic
8C23×Dic61C2211yescharacteristic
9C2×#11758196—22no—
10C2×#11758196—22no—
11C2×#11758196C412yes—
12C2×#11758196C2212yes—
13C23×C4×C61C411yescharacteristic
14C24×C61C2×C411yescharacteristic
15C22×C4×C61—21no—
16C22×C4×C61—21no—
17C22×C4×C61—42no—
18C22×C4×C61C2×C412yes—
19C22×Dic61—21no—
20C22×Dic61—21no—
21C22×Dic61—24no—
22C22×Dic61—42no—
23C22×Dic61C2×C412yes—
24C22×Dic61C2×C411yescharacteristic
25C22×Dic61D412yes—
26C22×Dic61D412yes—
27C22×Dic61C2311yescharacteristic
28#11758217—44no—
29C2×#92420—24no—
30#11758196—24no—
31#11758196—24no—
32C23×C61—22no—
33C23×C61—22no—
34C23×C61—22no—
35C23×C61C22⋊C411yescharacteristic
36C23×C61C22⋊C411yescharacteristic
37C23×C61C22×C411yescharacteristic
38C2×C4×C61—22no—
39C2×C4×C61—42no—
40C2×C4×C61—42no—
41C2×C4×C61—42no—
42C2×Dic61—24no—
43C2×Dic61—24no—
44C2×Dic61—24no—
45C2×Dic61—22no—
46C2×Dic61—22no—
47C2×Dic61—41no—
48C2×Dic61—42no—
49C2×Dic61—41no—
50C2×Dic61C22⋊C412yes—
51C2×Dic61M1614yescomplemented
52C2×Dic61C2×D412yes—
53#92420—44no—
54C22×C61—28no—
55C22×C61—21no—
56C22×C61—21no—
57C22×C61—21no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61—21no—
61C22×C61#9912yes—
62C22×C61#10112yes—
63C22×C61C2×C22⋊C411yescharacteristic
64C22×C61C2×M1612yes—
65C4×C61—42no—
66Dic61—24no—
67Dic61—22no—
68Dic61—22no—
69#1463—611nomaximal, Sylow
70C2×C61—22no—
71C2×C61—22no—
72C2×C61—22no—
73C2×C61#40711yescharacteristic
74C2×C61C2×#9911yescharacteristic
75C2×C61C2×#10111yescharacteristic
76C22×C4⋊C4—611no—
77#407—612no—
78#324—614no—
79C61#146311yescharacteristic, complemented, Sylow
80C23×C4—611no—
81C23×C4—611no—
82C23×C4#692311yescharacteristic
83C2×M16—1222no—
84C2×C4⋊C4—612no—
85C2×C4⋊C4—612no—
86C2×C4⋊C4—1222no—
87C2×C4⋊C4—1222no—
88C22⋊C8—614no—
89C22⋊C8—1222no—
90C24C2×#692311yescharacteristic
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—42no—
94C22×C4—612no—
95C22×C4—612no—
96C22×C4—612no—
97C22×C4—611no—
98C22×C4—611no—
99C22×C4—1224no—
100C22×C4—1221no—
101C22×C4—1221no—
102C22×C4—2442no—
103C22×C4C2×#692312yes—
104M16—2444no—
105C2×C8—1224no—
106C4⋊C4—1224no—
107C4⋊C4—1224no—
108C23—22no—
109C23—22no—
110C23—22no—
111C23C22⋊#692311yescharacteristic
112C23C22⋊#692311yescharacteristic
113C23C22×#692311yescharacteristic
114C2×C4—22no—
115C2×C4—42no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—612no—
119C2×C4—612no—
120C2×C4—614no—
121C2×C4—1224no—
122C2×C4—1224no—
123C2×C4—1224no—
124C2×C4—1222no—
125C2×C4—1222no—
126C2×C4—2441no—
127C2×C4—2442no—
128C2×C4—2441no—
129C8—2444no—
130C22—28no—
131C22—21no—
132C22—21no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22#1451983512yes—
138C22#1451983812yes—
139C22C2×C22⋊#692311yescharacteristic
140C22D61⋊M1612yes—
141C4—42no—
142C4—1224no—
143C4—1222no—
144C4—1222no—
145C2—22no—
146C2—22no—
147C2—22no—
148C2#1684073411yescharacteristic
149C2C2×#1451983511yescharacteristic
150C2C2×#1451983811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC23×C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC23×C4#6923
hypocenterC61#1463
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #16840608C2semidirect
51. C2×Dic61M16semidirect
79. C61#1463semidirect