Finite Group Databasebeta

← D61⋊#328 #21461188

Subgroups — D61⋊#328 #21461188

Order 7808.

336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D61⋊(C22⋊C8)C211yesmaximal, characteristic
2C2×(C2×#6923)⋊C4C211yesmaximal, characteristic
3#16840616C212yesmaximal, complemented
4#16840615C212yesmaximal, complemented
5C22⋊Q8×D61C211yesmaximal, characteristic
6C23×#6923—21no—
7C2×D61⋊C8—21no—
8#14519834C2212yes—
9C22⋊#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12C2×Q8×D61C411yescharacteristic, complemented
13C22×C4×D61C2211yescharacteristic
14#14519757C2211yescharacteristic
15#14519756C411yescharacteristic, complemented
16#14519755—21no—
17#14519754—21no—
18#14519753C2211yescharacteristic
19C4⋊C4×D61—21no—
20C4⋊C4×D61C411yescharacteristic, complemented
21C22⋊C4×D61—21no—
22C22⋊Q8×C61C411yescharacteristic, complemented
23C23×D61D411yescharacteristic
24C22×#6923—24no—
25C22×#6923—22no—
26C22×#6923—42no—
27C22×#6923—42no—
28C2×Q8×C61C2×C411yescharacteristic, complemented
29C22×C4×C61C2×C411yescharacteristic
30C22×Dic61D411yescharacteristic
31Q8×D61—42no—
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61—42no—
35C2×C4×D61C2×C411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×C4×D61D411yescharacteristic
38C2×C4×D61C2311yescharacteristic
39C2×Dic122—21no—
40C2×Dic122C2×C411yescharacteristic, complemented
41C2×#92420—22no—
42D61⋊C8—42no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61C2×C411yescharacteristic, complemented
45C22⋊C4×C61—21no—
46C22⋊Dic61—21no—
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61C2×C411yescharacteristic, complemented
51#11758196—21no—
52#11758196—21no—
53#11758196—21no—
54C23×C61C22⋊C411yescharacteristic
55C22×D61—22no—
56C22×D61—22no—
57C22×D61C22⋊C411yescharacteristic
58C22×D61SD1612yes—
59C22×D61Q1612yes—
60C22×D61C2×D411yescharacteristic
61C2×#6923—24no—
62C2×#6923—42no—
63C2×#6923—48no—
64C2×#6923—42no—
65Q8×C61—41no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—41no—
69C2×C4×C61C22⋊C411yescharacteristic
70C2×C4×C61C22×C411yescharacteristic
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—41no—
74C2×Dic61C22⋊C411yescharacteristic
75C2×Dic61C2×D411yescharacteristic
76C4×D61—22no—
77C4×D61—22no—
78C4×D61—41no—
79C4×D61—41no—
80C4×D61—42no—
81C4×D61—42no—
82Dic122—42no—
83Dic122—41no—
84#92420—42no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61#10312yes—
88C22×C61C2×C22⋊C411yescharacteristic
89C2×D61—21no—
90C2×D61—21no—
91C2×D61—24no—
92C2×D61—24no—
93C2×D61#9912yes—
94C2×D61#10312yes—
95C2×D61#10412yes—
96C2×D61C2×SD1611yescharacteristic
97C2×D61C2×Q1611yescharacteristic
98#6923—44no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61—41no—
103Dic61—21no—
104Dic61—21no—
105Dic61—41no—
106Dic61—41no—
107C2×#328—611nomaximal, Sylow
108C2×C61—22no—
109C2×C61C2×#9911yescharacteristic
110C2×C61C2×#10311yescharacteristic
111C2×C61C2×#10411yescharacteristic
112D61—21no—
113D61—21no—
114D61#32814yescomplemented
115C2×C22⋊Q8—611no—
116C2×C22⋊C8—611no—
117C2×#95—611no—
118#328—612no—
119#328—612no—
120C61C2×#32811yescharacteristic, complemented, Sylow
121C22×Q8—611no—
122C23×C4—611no—
123C23×C4—1221no—
124C22×C8—1221no—
125C22⋊Q8—611no—
126C22⋊Q8—611no—
127C22⋊Q8—611no—
128C22⋊Q8—1221no—
129C22⋊Q8—1221no—
130C22⋊Q8#692311yescharacteristic, complemented
131C2×C4⋊C4—611no—
132C2×C4⋊C4—1221no—
133C2×C22⋊C4—1221no—
134C22⋊C8—612no—
135C22⋊C8—1221no—
136#95—612no—
137#95—1221no—
138C24—611no—
139C2×Q8—611no—
140C2×Q8—1221no—
141C2×Q8—2442no—
142C2×Q8C2×#692311yescharacteristic, complemented
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—611no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4—1222no—
151C22×C4—1224no—
152C22×C4—2442no—
153C22×C4—2442no—
154C22×C4—2442no—
155C22×C4C2×#692311yescharacteristic
156C2×C8—1222no—
157C2×C8—2442no—
158C4⋊C4—21no—
159C4⋊C4—611no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C4⋊C4C2×#692311yescharacteristic, complemented
165C22⋊C4—21no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C23—611no—
170C23—612no—
171C23—612no—
172C23—611no—
173C23—1222no—
174C23—1222no—
175C23C22⋊#692311yescharacteristic
176Q8—41no—
177Q8—2441no—
178Q8—2442no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—611no—
183C2×C4—611no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1224no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4—2441no—
194C2×C4—2442no—
195C2×C4—2448no—
196C2×C4—2442no—
197C2×C4C22⋊#692311yescharacteristic
198C2×C4C22×#692311yescharacteristic
199C8—2442no—
200C22—21no—
201C22—21no—
202C22—612no—
203C22—612no—
204C22—612no—
205C22—611no—
206C22—611no—
207C22—1224no—
208C22—1224no—
209C22—1221no—
210C22—1221no—
211C22#1451984012yes—
212C22C2×C22⋊#692311yescharacteristic
213C4—21no—
214C4—21no—
215C4—41no—
216C4—41no—
217C4—1221no—
218C4—1221no—
219C4—2444no—
220C4—2441no—
221C4—2441no—
222C2—22no—
223C2—614no—
224C2—1221no—
225C2—1221no—
226C2D61⋊#9911yescharacteristic
227C2C2×#1451984011yescharacteristic
228C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61C2×#328
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #16840616C2semidirect
4. #16840615C2semidirect
12. C2×Q8×D61C4semidirect
15. #14519756C4semidirect
20. C4⋊C4×D61C4semidirect
22. C22⋊Q8×C61C4semidirect
28. C2×Q8×C61C2×C4semidirect
40. C2×Dic122C2×C4semidirect
44. C4⋊C4×C61C2×C4semidirect
50. C4⋊Dic61C2×C4semidirect
114. D61#328semidirect
120. C61C2×#328semidirect
130. C22⋊Q8#6923semidirect
142. C2×Q8C2×#6923semidirect
164. C4⋊C4C2×#6923semidirect