Finite Group Databasebeta

← #21461145

Subgroups — #21461145

Order 7808.

312 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 76 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#16840781C211yesmaximal, characteristic, complemented
2#16840766C211yesmaximal, characteristic, complemented
3#16840610C212yesmaximal, complemented
4D4⋊#92420C212yesmaximal, complemented
5C4×D4×D61C211yesmaximal, characteristic
6C2×#11758213—21no—
7C4⋊#92420—21no—
8C4⋊#92420—21no—
9C4⋊#92420C2212yescomplemented
10#14519834—21no—
11C4×#92420C2212yescomplemented
12C2×D4×D61C411yescharacteristic
13C22×C4×D61—21no—
14C4×D244C411yescharacteristic
15D4×Dic61C2211yescharacteristic
16#14519739C2211yescharacteristic
17C4×C22⋊D61—21no—
18#14519737—21no—
19C4⋊C4×D61C411yescharacteristic
20C22⋊C4×D61—21no—
21C42×D61C2211yescharacteristic
22C4×D4×C61C411yescharacteristic
23C23×D61—21no—
24C2×D4×C61C2×C411yescharacteristic
25C22×C4×C61—21no—
26C2×C22⋊D61—21no—
27C22×Dic61—21no—
28D4×D61—22no—
29D4×D61—22no—
30C2×D244C2×C411yescharacteristic
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61—42no—
35C2×C4×D61—42no—
36C2×C4×D61C2×C411yescharacteristic
37C2×C4×D61D411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×#92420—22no—
40C2×#92420—22no—
41#11758213—42no—
42C4⋊C4×C61C2×C411yescharacteristic
43C22⋊C4×C61—21no—
44C42×C61C2×C411yescharacteristic
45C22⋊Dic61—21no—
46#11758198—21no—
47#11758198—21no—
48C4⋊Dic61C2×C411yescharacteristic
49#11758196—21no—
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C4×Dic61C2311yescharacteristic
53C23×C61—21no—
54C22×D61—24no—
55C22×D61—21no—
56C22×D61—42no—
57C22×D61—42no—
58C22×D61C22⋊C411yescharacteristic
59D4×C61—21no—
60D4×C61M1612yescomplemented
61C2×C4×C61—21no—
62C2×C4×C61—42no—
63C2×C4×C61C22⋊C411yescharacteristic
64C2×C4×C61C22⋊C411yescharacteristic
65C2×C4×C61C22×C411yescharacteristic
66C22⋊D61—24no—
67C2×Dic61—21no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C2×D411yescharacteristic
72C2×Dic61C2×D411yescharacteristic
73D244—21no—
74D244M1612yescomplemented
75C4×D61—21no—
76C4×D61—21no—
77C4×D61—41no—
78C4×D61—42no—
79C4×D61—42no—
80C4×D61—41no—
81C4×D61—41no—
82C4×D61D812yes—
83C4×D61SD1612yes—
84#92420—42no—
85#92420—42no—
86C22×C61—22no—
87C22×C61—41no—
88C22×C61—41no—
89C22×C61C2×C22⋊C411yescharacteristic
90C2×D61—21no—
91C2×D61—21no—
92C2×D61—22no—
93C2×D61—48no—
94C2×D61—41no—
95C2×D61—41no—
96C2×D61#10212yes—
97C4×C61—21no—
98C4×C61—41no—
99C4×C61#10212yes—
100C4×C61C2×M1611yescharacteristic
101C4×C61C2×M1611yescharacteristic
102Dic61—21no—
103Dic61—21no—
104Dic61—41no—
105Dic61C2×D811yescharacteristic
106Dic61C2×SD1611yescharacteristic
107#1486—611nomaximal, Sylow
108C2×C61—42no—
109C2×C61#40711yescharacteristic
110C2×C61C2×#10211yescharacteristic
111C2×C61#42111yescharacteristic
112D61—22no—
113D61—42no—
114C2×C4×D4—611no—
115#431—611no—
116#423—611no—
117D4⋊C8—612no—
118D4⋊C8—612no—
119C61#148611yescharacteristic, complemented, Sylow
120C22×D4—611no—
121C23×C4—1221no—
122C2×M16—1221no—
123C4×D4—611no—
124C4×D4—611no—
125C4×D4—611no—
126C4×D4—1221no—
127C4×D4—1221no—
128C4×D4#692311yescharacteristic
129C2×C4⋊C4—611no—
130C2×C22⋊C4—1221no—
131C2×C42—611no—
132C4⋊C8—612no—
133C4⋊C8—1221no—
134C4⋊C8—1221no—
135C22⋊C8—1221no—
136C4×C8—612no—
137C24—1221no—
138C2×D4—611no—
139C2×D4—1221no—
140C2×D4—1222no—
141C2×D4—1222no—
142C2×D4C2×#692311yescharacteristic
143C22×C4—21no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4—1221no—
151C22×C4—2442no—
152C22×C4—2442no—
153M16—2442no—
154C2×C8—1222no—
155C2×C8—1222no—
156C4⋊C4—611no—
157C4⋊C4—1221no—
158C4⋊C4C2×#692311yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C42—611no—
164C42—611no—
165C42—611no—
166C42C2×#692311yescharacteristic
167C23—21no—
168C23—611no—
169C23—1224no—
170C23—1221no—
171C23—2442no—
172C23—2442no—
173D4—21no—
174D4—612no—
175D4—1224no—
176D4—1221no—
177D4#1175821312yescomplemented
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—611no—
181C2×C4—612no—
182C2×C4—612no—
183C2×C4—611no—
184C2×C4—611no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4—2442no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4—2442no—
195C2×C4C22⋊#692311yescharacteristic
196C2×C4C22⋊#692311yescharacteristic
197C2×C4C22×#692311yescharacteristic
198C8—2442no—
199C8—2442no—
200C22—22no—
201C22—41no—
202C22—41no—
203C22—612no—
204C22—1221no—
205C22—1221no—
206C22—1222no—
207C22—2448no—
208C22—2441no—
209C22—2441no—
210C22C2×C22⋊#692311yescharacteristic
211C4—21no—
212C4—41no—
213C4—611no—
214C4—611no—
215C4—1221no—
216C4—1221no—
217C4—2441no—
218C4#1451983912yes—
219C4D61⋊M1611yescharacteristic
220C4C2×#1175821311yescharacteristic
221C2—42no—
222C2—1222no—
223C2—2442no—
224C2#1684073311yescharacteristic
225C2C2×#1451983911yescharacteristic
226C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1486
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. #16840781C2semidirect
2. #16840766C2semidirect
3. #16840610C2semidirect
4. D4⋊#92420C2semidirect
9. C4⋊#92420C22semidirect
11. C4×#92420C22semidirect
60. D4×C61M16semidirect
74. D244M16semidirect
119. C61#1486semidirect
177. D4#11758213semidirect