Finite Group Databasebeta

← #21460797

Subgroups — #21460797

Order 7808.

222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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#16840640C211yesmaximal, characteristic, complemented
2#16840606C211yesmaximal, characteristic, complemented
3#16839670C211yesmaximal, characteristic
4C2×C22⋊#6923—21no—
5C22⋊#92420—21no—
6C22×C22⋊D61—21no—
7C2×C22⋊Dic61—21no—
8C2×#11758198C2211yescharacteristic
9#14519684C411yescharacteristic, complemented
10C22×D4×C61C411yescharacteristic, complemented
11C24×C61—21no—
12C23×D61D411yescharacteristic
13C22×#6923—41no—
14C2×D4×C61—41no—
15C2×D4×C61—42no—
16C22×C4×C61C2×C411yescharacteristic
17C2×C22⋊D61—42no—
18C2×C22⋊D61—42no—
19C2×C22⋊D61—41no—
20C2×C22⋊D61—41no—
21C22×Dic61—21no—
22C22×Dic61D411yescharacteristic
23C22⋊#6923—22no—
24C22⋊#6923—41no—
25C2×#92420—41no—
26C22⋊Dic61—42no—
27#11758198—41no—
28C23×C61—22no—
29C23×C61—41no—
30C23×C61—41no—
31C23×C61—41no—
32C23×C61—41no—
33C23×C61—41no—
34C23×C61—41no—
35C23×C61C22⋊C411yescharacteristic
36C22×D61—21no—
37C22×D61—21no—
38C22×D61—41no—
39C22×D61—41no—
40C22×D61D811yescharacteristic
41C22×D61SD1611yescharacteristic
42C2×#6923—42no—
43C2×#6923—81no—
44C2×#6923—81no—
45D4×C61—42no—
46D4×C61—42no—
47C2×C4×C61—21no—
48C2×C4×C61—41no—
49C22⋊D61—44no—
50C22⋊D61—44no—
51C2×Dic61—22no—
52C2×Dic61—21no—
53C2×Dic61—41no—
54C2×Dic61—41no—
55C2×Dic61—41no—
56#92420—81no—
57C22×C61—21no—
58C22×C61—21no—
59C22×C61—42no—
60C22×C61—42no—
61C22×C61—42no—
62C22×C61—81no—
63C22×C61—81no—
64C22×C61—81no—
65C22×C61—81no—
66C22×C61#9911yescharacteristic
67C22×C61#10211yescharacteristic
68C22×C61#10411yescharacteristic
69C2×D61—21no—
70C2×D61—21no—
71C2×D61—41no—
72C2×D61—41no—
73C2×D61—41no—
74C2×D61—41no—
75C2×D61—81no—
76#6923—82no—
77C4×C61—41no—
78Dic61—42no—
79Dic61—41no—
80#1343—611nomaximal, Sylow
81C2×C61—21no—
82C2×C61—21no—
83C2×C61—82no—
84C2×C61#32711yescharacteristic
85C2×C61AΣL(1,𝔽16)11yescharacteristic
86C2×C61#35311yescharacteristic
87D61—41no—
88D61—41no—
89#392—611no—
90#342—611no—
91#323—611no—
92C61#134311yescharacteristic, complemented, Sylow
93C22×D4—1221no—
94C22×D4#692311yescharacteristic, complemented
95C2×C22⋊C4—611no—
96C2×C22⋊C4—1221no—
97C2×C22⋊C4—1221no—
98C22⋊C8—1221no—
99#95—611no—
100C24—21no—
101C24—611no—
102C2×D4—41no—
103C2×D4—42no—
104C2×D4—2442no—
105C2×D4—2442no—
106C2×D4—2441no—
107C2×D4—2441no—
108C22×C4—611no—
109C22×C4—1221no—
110C22×C4—2441no—
111C22×C4C2×#692311yescharacteristic
112C2×C8—2441no—
113C22⋊C4—1222no—
114C22⋊C4—2441no—
115C22⋊C4—2442no—
116C22⋊C4—2441no—
117C23—22no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—611no—
125C23—611no—
126C23—1221no—
127C23—1221no—
128C23—2441no—
129C23—2441no—
130C23C22⋊#692311yescharacteristic
131D4—42no—
132D4—42no—
133D4—2444no—
134D4—2444no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—1222no—
138C2×C4—1221no—
139C2×C4—4881no—
140C2×C4—4881no—
141C2×C4—2442no—
142C2×C4—2441no—
143C2×C4—2441no—
144C2×C4—2441no—
145C8—4881no—
146C22—21no—
147C22—21no—
148C22—42no—
149C22—42no—
150C22—42no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—1221no—
156C22—1221no—
157C22—4881no—
158C22—2441no—
159C22—2441no—
160C22—2441no—
161C22—2441no—
162C22#1451983511yescharacteristic
163C22#1451983911yescharacteristic
164C22#1451984111yescharacteristic
165C4—41no—
166C4—4882no—
167C4—2442no—
168C4—2441no—
169C2—21no—
170C2—21no—
171C2—82no—
172C2—2441no—
173C2—2441no—
174C2#1684061311yescharacteristic
175C2#1684066211yescharacteristic
176C2#1684066611yescharacteristic
subgroupG/H
centerC22#14519835
commutatorC22×C4×C61C2×C4
FrattiniC22×C4C2×#6923
FittingC22×D4×C61C4
socleC22×C61#99
hypercenterC22×D4#6923
hypocenterC61#1343
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #16840640C2semidirect
2. #16840606C2semidirect
9. #14519684C4semidirect
10. C22×D4×C61C4semidirect
92. C61#1343semidirect
94. C22×D4#6923semidirect