Finite Group Databasebeta

← D61⋊#327 #21461185

Subgroups — D61⋊#327 #21461185

Order 7808.

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

normal subgroups only

This group has 388 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, complemented
2C2×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
3#16840614C212yesmaximal, complemented
4#16840613C212yesmaximal, complemented
5#121×D61C211yesmaximal, characteristic
6C23×#6923—21no—
7C2×D61⋊C8—21no—
8#14519834C2212yescomplemented
9C22⋊#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yescomplemented
12C2×D4×D61—21no—
13C2×D4×D61C411yescharacteristic, complemented
14C22×C4×D61C2211yescharacteristic
15#14519752C2211yescharacteristic
16#14519751C411yescharacteristic, complemented
17#14519750—21no—
18#14519749—21no—
19#14519748C2211yescharacteristic
20C4⋊C4×D61C411yescharacteristic, complemented
21C22⋊C4×D61—21no—
22#121×C61C411yescharacteristic, complemented
23C23×D61—21no—
24C23×D61D411yescharacteristic
25C22×#6923—24no—
26C22×#6923—22no—
27C22×#6923—42no—
28C22×#6923—42no—
29C2×D4×C61—21no—
30C2×D4×C61C2×C411yescharacteristic, complemented
31C22×C4×C61C2×C411yescharacteristic
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C22×Dic61D411yescharacteristic
36D4×D61—42no—
37D4×D61—42no—
38D4×D61—42no—
39C2×D244—21no—
40C2×D244C2×C411yescharacteristic, complemented
41C2×C4×D61—21no—
42C2×C4×D61—42no—
43C2×C4×D61C2×C411yescharacteristic
44C2×C4×D61D411yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×C4×D61C2311yescharacteristic
47C2×#92420—22no—
48D61⋊C8—42no—
49C4⋊C4×C61C2×C411yescharacteristic, complemented
50C22⋊C4×C61—21no—
51C22⋊Dic61—21no—
52#11758198—21no—
53#11758198—21no—
54C4⋊Dic61C2×C411yescharacteristic, complemented
55#11758196—21no—
56C23×C61—21no—
57C23×C61C22⋊C411yescharacteristic
58C22×D61—22no—
59C22×D61—22no—
60C22×D61—21no—
61C22×D61—42no—
62C22×D61—42no—
63C22×D61—42no—
64C22×D61C22⋊C411yescharacteristic
65C22×D61D812yes—
66C22×D61SD1612yes—
67C22×D61C2×D411yescharacteristic
68C2×#6923—24no—
69C2×#6923—42no—
70C2×#6923—48no—
71C2×#6923—42no—
72D4×C61—41no—
73D4×C61—42no—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61C22⋊C411yescharacteristic
77C2×C4×C61C22×C411yescharacteristic
78C22⋊D61—42no—
79C22⋊D61—42no—
80C22⋊D61—41no—
81C22⋊D61—41no—
82C2×Dic61—21no—
83C2×Dic61—41no—
84C2×Dic61C22⋊C411yescharacteristic
85C2×Dic61C2×D411yescharacteristic
86D244—41no—
87D244—41no—
88D244—41no—
89C4×D61—22no—
90C4×D61—22no—
91C4×D61—41no—
92C4×D61—41no—
93C4×D61—42no—
94#92420—42no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61#10212yes—
101C22×C61C2×C22⋊C411yescharacteristic
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—24no—
105C2×D61—24no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—84no—
110C2×D61#9912yes—
111C2×D61#10212yes—
112C2×D61#10412yes—
113C2×D61C2×D811yescharacteristic
114C2×D61C2×SD1611yescharacteristic
115#6923—44no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—41no—
119Dic61—21no—
120Dic61—21no—
121Dic61—41no—
122C2×#327—611nomaximal, Sylow
123C2×C61—22no—
124C2×C61—81no—
125C2×C61C2×#9911yescharacteristic
126C2×C61C2×#10211yescharacteristic
127C2×C61C2×#10411yescharacteristic
128D61—21no—
129D61—21no—
130D61—81no—
131D61#32714yescomplemented
132C2×#121—611no—
133C2×C22⋊C8—611no—
134C2×#95—611no—
135#327—612no—
136#327—612no—
137C61C2×#32711yescharacteristic, complemented, Sylow
138C22×D4—611no—
139C22×D4—1221no—
140C23×C4—611no—
141C23×C4—1221no—
142C22×C8—1221no—
143#121—611no—
144#121—611no—
145#121—611no—
146#121—1221no—
147#121—1221no—
148#121#692311yescharacteristic, complemented
149C2×C4⋊C4—611no—
150C2×C22⋊C4—1221no—
151C22⋊C8—612no—
152C22⋊C8—1221no—
153#95—612no—
154#95—1221no—
155C24—611no—
156C24—1221no—
157C2×D4—21no—
158C2×D4—611no—
159C2×D4—1221no—
160C2×D4—1221no—
161C2×D4—1221no—
162C2×D4—1221no—
163C2×D4—2442no—
164C2×D4—2442no—
165C2×D4—2442no—
166C2×D4C2×#692311yescharacteristic, complemented
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—1221no—
173C22×C4—1222no—
174C22×C4—1224no—
175C22×C4—2442no—
176C22×C4—2442no—
177C22×C4—2442no—
178C22×C4C2×#692311yescharacteristic
179C2×C8—1222no—
180C2×C8—2442no—
181C4⋊C4—611no—
182C4⋊C4—1221no—
183C4⋊C4C2×#692311yescharacteristic, complemented
184C22⋊C4—21no—
185C22⋊C4—1221no—
186C22⋊C4—1221no—
187C22⋊C4—1221no—
188C23—21no—
189C23—611no—
190C23—612no—
191C23—612no—
192C23—611no—
193C23—1222no—
194C23—1222no—
195C23—1221no—
196C23—2442no—
197C23—2442no—
198C23—2442no—
199C23C22⋊#692311yescharacteristic
200D4—41no—
201D4—42no—
202D4—2441no—
203D4—2441no—
204D4—2441no—
205D4—2442no—
206D4—2441no—
207D4—2441no—
208D4—2442no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—611no—
212C2×C4—611no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1224no—
216C2×C4—1221no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2442no—
220C2×C4—2441no—
221C2×C4—2442no—
222C2×C4—2448no—
223C2×C4—2442no—
224C2×C4C22⋊#692311yescharacteristic
225C2×C4C22×#692311yescharacteristic
226C8—2442no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—612no—
233C22—612no—
234C22—612no—
235C22—611no—
236C22—611no—
237C22—1224no—
238C22—1224no—
239C22—1221no—
240C22—1221no—
241C22—4884no—
242C22—2441no—
243C22—2441no—
244C22—2441no—
245C22#1451983912yes—
246C22C2×C22⋊#692311yescharacteristic
247C4—21no—
248C4—21no—
249C4—41no—
250C4—1221no—
251C4—1221no—
252C4—2444no—
253C4—2441no—
254C2—22no—
255C2—81no—
256C2—614no—
257C2—1221no—
258C2—1221no—
259C2—4881no—
260C2D61⋊#9911yescharacteristic
261C2C2×#1451983911yescharacteristic
262C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61C2×#327
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. D61⋊(C22⋊C8)C2semidirect
2. C2×(C2×#6923)⋊C4C2semidirect
3. #16840614C2semidirect
4. #16840613C2semidirect
8. #14519834C22semidirect
11. (C2×#6923)⋊C4C22semidirect
13. C2×D4×D61C4semidirect
16. #14519751C4semidirect
20. C4⋊C4×D61C4semidirect
22. #121×C61C4semidirect
30. C2×D4×C61C2×C4semidirect
40. C2×D244C2×C4semidirect
49. C4⋊C4×C61C2×C4semidirect
54. C4⋊Dic61C2×C4semidirect
131. D61#327semidirect
137. C61C2×#327semidirect
148. #121#6923semidirect
166. C2×D4C2×#6923semidirect
183. C4⋊C4C2×#6923semidirect