Finite Group Databasebeta

← #21461278

Subgroups — #21461278

Order 7808.

264 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840783C211yesmaximal, characteristic, complemented
2C4×#11758217C211yesmaximal, characteristic, complemented
3#16840617C214yesmaximal, complemented
4C2×#14519764C211yesmaximal, characteristic
5C2×#11758217—21no—
6C4⋊#92420—21no—
7C22⋊#92420—21no—
8#14519832C2212yescomplemented
9#14519832C2212yescomplemented
10C4×#92420—21no—
11C22×Dic122C411yescharacteristic
12#14519764—21no—
13#14519764—21no—
14#14519764C412yes—
15#14519764C2212yes—
16C2×C22⋊Dic61—21no—
17C2×C22⋊Dic61—21no—
18C2×C4×Dic61C2211yescharacteristic
19C22×D4×C61C411yescharacteristic
20C24×C61—21no—
21C2×D4×C61—21no—
22C2×D4×C61—42no—
23C2×D4×C61C2×C412yes—
24C22×C4×C61C2×C411yescharacteristic
25C22×Dic61—21no—
26C22×Dic61D411yescharacteristic
27C22×Dic61D411yescharacteristic
28C2×Dic122—21no—
29C2×Dic122—42no—
30C2×Dic122C2×C412yes—
31#11758217—24no—
32C2×#92420—22no—
33C2×#92420—22no—
34C22⋊Dic61—22no—
35C22⋊Dic61—22no—
36C22⋊Dic61—22no—
37C22⋊Dic61—22no—
38C4×Dic61C2×C411yescharacteristic
39C4×Dic61D411yescharacteristic
40C4×Dic61D411yescharacteristic
41C4×Dic61C2311yescharacteristic
42C23×C61—22no—
43C23×C61—42no—
44C23×C61—42no—
45C23×C61—42no—
46C23×C61C22⋊C411yescharacteristic
47D4×C61—42no—
48D4×C61—42no—
49C2×C4×C61—22no—
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22×C411yescharacteristic
52C2×Dic61—22no—
53C2×Dic61—22no—
54C2×Dic61—41no—
55C2×Dic61—42no—
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59C2×Dic61C2×D411yescharacteristic
60Dic122—42no—
61Dic122—42no—
62#92420—24no—
63#92420—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61—42no—
67C22×C61—42no—
68C22×C61—42no—
69C22×C61—84no—
70C22×C61#10412yes—
71C22×C61C2×C22⋊C411yescharacteristic
72C4×C61—21no—
73C4×C61#10012yes—
74Dic61—21no—
75Dic61—21no—
76Dic61—21no—
77Dic61—21no—
78Dic61—42no—
79#1527—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61—82no—
82C2×C61C2×#10011yescharacteristic
83C2×C61C2×#10411yescharacteristic
84C2×C61#42111yescharacteristic
85C2×#124—611no—
86#432—611no—
87C4×M16—611no—
88#329—614no—
89C61#152711yescharacteristic, complemented, Sylow
90C22×Q8—611no—
91C22×D4#692311yescharacteristic
92C2×M16—1221no—
93#124—612no—
94#124—612no—
95#124—1221no—
96#124—1221no—
97C2×C22⋊C4—1221no—
98C2×C22⋊C4—1221no—
99C2×C42—611no—
100C4⋊C8—1221no—
101C22⋊C8—1221no—
102#97—612no—
103#97—612no—
104C4×C8—1221no—
105C24—21no—
106C2×Q8—612no—
107C2×Q8—1221no—
108C2×Q8—2442no—
109C2×D4—21no—
110C2×D4—42no—
111C2×D4C2×#692312yes—
112C22×C4—611no—
113C22×C4—611no—
114C22×C4—1221no—
115C22×C4C2×#692311yescharacteristic
116M16—1224no—
117C2×C8—1222no—
118C2×C8—1222no—
119C22⋊C4—1222no—
120C22⋊C4—1222no—
121C22⋊C4—1222no—
122C22⋊C4—1222no—
123C42—611no—
124C42—611no—
125C42—611no—
126C42—611no—
127C23—22no—
128C23—42no—
129C23—42no—
130C23—42no—
131C23C22⋊#692311yescharacteristic
132Q8—2442no—
133Q8—2442no—
134D4—42no—
135D4—42no—
136C2×C4—22no—
137C2×C4—611no—
138C2×C4—611no—
139C2×C4—611no—
140C2×C4—611no—
141C2×C4—1222no—
142C2×C4—1222no—
143C2×C4—2441no—
144C2×C4—2442no—
145C2×C4C22⋊#692311yescharacteristic
146C2×C4C22×#692311yescharacteristic
147C8—1224no—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22—84no—
155C22#1451984112yes—
156C22C2×C22⋊#692311yescharacteristic
157C4—21no—
158C4—1221no—
159C4—1221no—
160C4—1221no—
161C4—1221no—
162C4—2442no—
163C4#1451983712yes—
164C2—22no—
165C2—82no—
166C2C2×#1451983711yescharacteristic
167C2C2×#1451984111yescharacteristic
168C2#1684076011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22×D4#6923
hypocenterC61#1527
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #16840783C2semidirect
2. C4×#11758217C2semidirect
3. #16840617C2semidirect
8. #14519832C22semidirect
9. #14519832C22semidirect
89. C61#1527semidirect