Finite Group Databasebeta

← #21461204

Subgroups — #21461204

Order 7808.

334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840733C211yesmaximal, characteristic, complemented
2C2×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
3#16840615C212yesmaximal, complemented
4#16840613C212yesmaximal, complemented
5#16840272C211yesmaximal, characteristic
6C23×#6923—21no—
7C2×#11758213—21no—
8#14519834C2212yes—
9C22⋊#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12C2×#11758224C411yescharacteristic, complemented
13C22×C4×D61C2211yescharacteristic
14#14519759—21no—
15#14519757C2211yescharacteristic
16#14519756C411yescharacteristic, complemented
17#14519748C2211yescharacteristic
18#14519745—21no—
19D4×Dic61—21no—
20#14519737—21no—
21#14519735C411yescharacteristic, complemented
22#121×C61C411yescharacteristic, complemented
23C23×D61D411yescharacteristic
24C22×#6923—24no—
25C22×#6923—22no—
26C22×#6923—42no—
27C22×#6923—42no—
28C2×D4×C61—21no—
29C2×D4×C61C2×C411yescharacteristic, complemented
30C22×C4×C61C2×C411yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C22×Dic61—21no—
34C22×Dic61D411yescharacteristic
35#11758224—42no—
36C2×C4×D61—42no—
37C2×C4×D61C2×C411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×C4×D61C2311yescharacteristic
41C2×Dic122C2×C411yescharacteristic, complemented
42C2×#92420—22no—
43#11758213—42no—
44C4⋊C4×C61C2×C411yescharacteristic, complemented
45C22⋊C4×C61—21no—
46C22⋊Dic61—21no—
47C22⋊Dic61—21no—
48#11758198—21no—
49#11758198—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61C2×C411yescharacteristic, complemented
52#11758196—21no—
53C4×Dic61—21no—
54C23×C61—21no—
55C23×C61C22⋊C411yescharacteristic
56C22×D61—22no—
57C22×D61—22no—
58C22×D61—21no—
59C22×D61—21no—
60C22×D61C22⋊C411yescharacteristic
61C22×D61C2×D411yescharacteristic
62C2×#6923—24no—
63C2×#6923—48no—
64C2×#6923—42no—
65C2×#6923—42no—
66D4×C61—41no—
67D4×C61—42no—
68C2×C4×C61—21no—
69C2×C4×C61—41no—
70C2×C4×C61C22⋊C411yescharacteristic
71C2×C4×C61C22×C411yescharacteristic
72C22⋊D61—42no—
73C22⋊D61—41no—
74C22⋊D61—41no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—41no—
78C2×Dic61—42no—
79C2×Dic61C22⋊C411yescharacteristic
80C2×Dic61C2×D411yescharacteristic
81C4×D61—22no—
82C4×D61—22no—
83C4×D61—41no—
84C4×D61—41no—
85Dic122—41no—
86#92420—42no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61#10412yes—
93C22×C61C2×C22⋊C411yescharacteristic
94C2×D61—24no—
95C2×D61—24no—
96C2×D61—21no—
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—21no—
100C2×D61#9912yes—
101C2×D61AGL(1,ℤ/8)11yescharacteristic
102C2×D61#13711yescharacteristic
103#6923—44no—
104C4×C61—21no—
105C4×C61—21no—
106C4×C61—41no—
107Dic61—21no—
108Dic61—21no—
109Dic61—41no—
110Dic61—41no—
111#1504—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—81no—
114C2×C61C2×#9911yescharacteristic
115C2×C61#41711yescharacteristic
116C2×C61C2×#10411yescharacteristic
117D61—21no—
118D61—22no—
119D61—21no—
120#525—611no—
121#407—611no—
122C2×#95—611no—
123#328—612no—
124#327—612no—
125C61#150411yescharacteristic, complemented, Sylow
126C2×#41—611no—
127C23×C4—611no—
128C23×C4—1221no—
129C2×M16—1221no—
130#123—1221no—
131C22⋊Q8—611no—
132C22⋊Q8—611no—
133#121—611no—
134#121#692311yescharacteristic, complemented
135#120—1221no—
136C4×D4—1221no—
137C4×D4—1221no—
138#117—611no—
139C22⋊C8—612no—
140C22⋊C8—1221no—
141#95—612no—
142#95—1221no—
143C24—611no—
144#41—2442no—
145C2×Q8—611no—
146C2×D4—21no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4C2×#692311yescharacteristic, complemented
150C22×C4—611no—
151C22×C4—611no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—1221no—
156C22×C4—1222no—
157C22×C4—1224no—
158C22×C4—2442no—
159C22×C4—2442no—
160C22×C4—2442no—
161C22×C4C2×#692311yescharacteristic
162M16—2442no—
163C2×C8—1222no—
164C4⋊C4—611no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4C2×#692311yescharacteristic, complemented
168C22⋊C4—21no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C42—1221no—
174C23—21no—
175C23—611no—
176C23—611no—
177C23—1222no—
178C23—1221no—
179C23—1221no—
180C23—1222no—
181C23C22⋊#692311yescharacteristic
182Q8—2441no—
183D4—41no—
184D4—42no—
185D4—2441no—
186D4—2441no—
187D4—2442no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1224no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4—2448no—
203C2×C4—2442no—
204C2×C4C22⋊#692311yescharacteristic
205C2×C4C22×#692311yescharacteristic
206C8—2442no—
207C22—21no—
208C22—21no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—612no—
213C22—611no—
214C22—611no—
215C22—1224no—
216C22—1224no—
217C22—1221no—
218C22—1221no—
219C22—1221no—
220C22—1221no—
221C22#1451984112yes—
222C22C2×C22⋊#692311yescharacteristic
223C4—21no—
224C4—21no—
225C4—41no—
226C4—1221no—
227C4—1221no—
228C4—2444no—
229C4—2441no—
230C4—2441no—
231C2—22no—
232C2—81no—
233C2—1221no—
234C2—1222no—
235C2—1221no—
236C2D61⋊#9911yescharacteristic
237C2#1684075311yescharacteristic
238C2C2×#1451984111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1504
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. #16840733C2semidirect
2. C2×(C2×#6923)⋊C4C2semidirect
3. #16840615C2semidirect
4. #16840613C2semidirect
12. C2×#11758224C4semidirect
16. #14519756C4semidirect
21. #14519735C4semidirect
22. #121×C61C4semidirect
29. C2×D4×C61C2×C4semidirect
41. C2×Dic122C2×C4semidirect
44. C4⋊C4×C61C2×C4semidirect
51. C4⋊Dic61C2×C4semidirect
125. C61#1504semidirect
134. #121#6923semidirect
149. C2×D4C2×#6923semidirect
167. C4⋊C4C2×#6923semidirect