Finite Group Databasebeta

← #21461155

Subgroups — #21461155

Order 7808.

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

normal subgroups only

This group has 266 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#16840766C211yesmaximal, characteristic, complemented
2C4×#11758213C211yesmaximal, characteristic, complemented
3#16840612C212yesmaximal, complemented
4D4⋊#92420C212yesmaximal, complemented
5C4×#11758224C211yesmaximal, characteristic
6C2×#11758213—21no—
7C2×#11758213—21no—
8C4⋊#92420—21no—
9C4⋊#92420C2212yes—
10#14519832—21no—
11C4×#92420C2212yes—
12C2×#11758224C411yescharacteristic
13C4×Dic122C411yescharacteristic
14#14519742C2211yescharacteristic
15D4×Dic61C2211yescharacteristic
16C4×C22⋊D61—21no—
17#14519737—21no—
18#14519735C411yescharacteristic
19#14519733—21no—
20C2×C4×Dic61—21no—
21C42×D61C2211yescharacteristic
22C4×D4×C61C411yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C22×C4×C61—21no—
25C2×C22⋊D61—21no—
26C22×Dic61—21no—
27C22×Dic61—21no—
28#11758224—22no—
29#11758224—22no—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×Dic122C2×C411yescharacteristic
34C2×#92420—22no—
35C2×#92420—22no—
36#11758213—24no—
37#11758213—42no—
38C4⋊C4×C61C2×C411yescharacteristic
39C22⋊C4×C61—21no—
40C42×C61C2×C411yescharacteristic
41C22⋊Dic61—21no—
42#11758198—21no—
43C4⋊Dic61C2×C411yescharacteristic
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C4×Dic61D411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61C2311yescharacteristic
52C23×C61—21no—
53C22×D61C22⋊C411yescharacteristic
54D4×C61—21no—
55D4×C61M1612yescomplemented
56C2×C4×C61—21no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22×C411yescharacteristic
61C22⋊D61—24no—
62C2×Dic61—24no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C2×D411yescharacteristic
69C2×Dic61C2×D411yescharacteristic
70C4×D61—22no—
71C4×D61—21no—
72C4×D61—21no—
73C4×D61—21no—
74C4×D61—21no—
75Dic122—21no—
76Dic122M1612yescomplemented
77#92420—24no—
78#92420—42no—
79C22×C61—22no—
80C22×C61—41no—
81C22×C61—41no—
82C22×C61C2×C22⋊C411yescharacteristic
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—21no—
86C4×C61—21no—
87C4×C61—41no—
88C4×C61#10412yes—
89C4×C61C2×M1611yescharacteristic
90C4×C61C2×M1611yescharacteristic
91Dic61—22no—
92Dic61—21no—
93Dic61—21no—
94Dic61—41no—
95Dic61AGL(1,ℤ/8)11yescharacteristic
96Dic61#13711yescharacteristic
97#1489—611nomaximal, Sylow
98C2×C61—42no—
99C2×C61#40711yescharacteristic
100C2×C61#41711yescharacteristic
101C2×C61C2×#10411yescharacteristic
102D61—41no—
103C4×#41—611no—
104#423—611no—
105C4×M16—611no—
106Q8⋊C8—612no—
107D4⋊C8—612no—
108C61#148911yescharacteristic, complemented, Sylow
109C2×#41—611no—
110C2×M16—1221no—
111C2×M16—1221no—
112C4×Q8—611no—
113C4×Q8—611no—
114C4×D4—611no—
115C4×D4—1221no—
116C4×D4—1221no—
117C4×D4#692311yescharacteristic
118#117—611no—
119#117—1221no—
120C2×C42—611no—
121C2×C42—1221no—
122C4⋊C8—612no—
123C4⋊C8—1221no—
124#97—1221no—
125C4×C8—612no—
126#41—1222no—
127#41—1222no—
128C2×Q8—611no—
129C2×D4—1221no—
130C2×D4C2×#692311yescharacteristic
131C22×C4—21no—
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—611no—
135C22×C4—1221no—
136C22×C4—1221no—
137M16—1224no—
138M16—2442no—
139C2×C8—1222no—
140C2×C8—1222no—
141C4⋊C4—611no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4C2×#692311yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C42—611no—
149C42—611no—
150C42—611no—
151C42—1221no—
152C42—1221no—
153C42—1221no—
154C42C2×#692311yescharacteristic
155C23—21no—
156C23—611no—
157Q8—612no—
158Q8—1221no—
159D4—21no—
160D4—1224no—
161D4#1175821312yescomplemented
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—611no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—1224no—
170C2×C4—1221no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4C22⋊#692311yescharacteristic
178C2×C4C22⋊#692311yescharacteristic
179C2×C4C22×#692311yescharacteristic
180C8—1224no—
181C8—2442no—
182C22—22no—
183C22—41no—
184C22—41no—
185C22—1221no—
186C22—1221no—
187C22—1221no—
188C22C2×C22⋊#692311yescharacteristic
189C4—21no—
190C4—41no—
191C4—611no—
192C4—611no—
193C4—1221no—
194C4—1222no—
195C4—1221no—
196C4—2441no—
197C4#1451984112yes—
198C4D61⋊M1611yescharacteristic
199C4C2×#1175821311yescharacteristic
200C2—42no—
201C2—2441no—
202C2#1684073311yescharacteristic
203C2#1684075311yescharacteristic
204C2C2×#1451984111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1489
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #16840766C2semidirect
2. C4×#11758213C2semidirect
3. #16840612C2semidirect
4. D4⋊#92420C2semidirect
55. D4×C61M16semidirect
76. Dic122M16semidirect
108. C61#1489semidirect
161. D4#11758213semidirect