Finite Group Databasebeta

← #21444321

Subgroups — #21444321

Order 7808.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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#16840273C211yesmaximal, characteristic
2#16839726C211yesmaximal, characteristic, complemented
3#16839498C212yesmaximal, complemented
4#16839495C212yesmaximal, complemented
5C2×#95×C61C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic, complemented
7C2×#11758194—21no—
8#14519760—21no—
9#14519756C411yescharacteristic, complemented
10#14519756C2211yescharacteristic
11#14519751C411yescharacteristic, complemented
12#14519751C2211yescharacteristic
13#14519746—21no—
14C4×C22⋊D61—21no—
15C4×C22⋊D61—21no—
16#14519736C411yescharacteristic, complemented
17C22⋊#92418—21no—
18C22⋊#92418C2212yes—
19C23×C4×C61—21no—
20C23×C4×C61C2211yescharacteristic
21#95×C61—21no—
22#95×C61C2212yes—
23C24×C61D411yescharacteristic
24C22×C4×C61—24no—
25C22×C4×C61—22no—
26C22×C4×C61—42no—
27C22×C4×C61—42no—
28C22×C4×C61—42no—
29C22×C4×C61C2×C411yescharacteristic
30C22×C4×C61C2×C411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61D411yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C2×C22⋊D61—21no—
37C2×C22⋊D61—21no—
38#11758222—42no—
39C2×D244C2×C411yescharacteristic, complemented
40C2×C4×D61—21no—
41C2×Dic122C2×C411yescharacteristic, complemented
42C22⋊Dic61—21no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45#11758198—21no—
46#11758198—21no—
47C4⋊Dic61C2×C411yescharacteristic, complemented
48C4⋊Dic61C2×C411yescharacteristic, complemented
49#11758196—21no—
50#11758196—21no—
51C4×Dic61—21no—
52#11758194—42no—
53C2×#92418—22no—
54C23×C61—22no—
55C23×C61—22no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61C22⋊C411yescharacteristic
59C23×C61C22⋊C411yescharacteristic
60C23×C61C2×D411yescharacteristic
61C22×D61—21no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—24no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—48no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61C22⋊C411yescharacteristic
73C2×C4×C61C22⋊C411yescharacteristic
74C2×C4×C61C22×C411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C22⋊D61—42no—
77C22⋊D61—42no—
78C22⋊D61—41no—
79C22⋊D61—41no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83D244—41no—
84C4×D61—42no—
85Dic122—41no—
86#92418—42no—
87C22×C61—24no—
88C22×C61—24no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61#9912yes—
96C22×C61#10412yes—
97C22×C61C2×C22⋊C411yescharacteristic
98C22×C61AGL(1,ℤ/8)11yescharacteristic
99C22×C61#13711yescharacteristic
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—41no—
103C4×C61—21no—
104C4×C61—21no—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—44no—
108Dic61—41no—
109Dic61—41no—
110Dic61—41no—
111#1504—611nomaximal, Sylow
112C2×C61—21no—
113C2×C61—22no—
114C2×C61—22no—
115C2×C61—21no—
116C2×C61C2×#9911yescharacteristic
117C2×C61#41711yescharacteristic
118C2×C61C2×#10411yescharacteristic
119D61—81no—
120#525—611no—
121#407—611no—
122C2×#95D6111yescharacteristic, complemented
123#328—612no—
124#327—612no—
125C61#150411yescharacteristic, complemented, Sylow
126C2×#41—611no—
127C23×C4—21no—
128C23×C4C2×D6111yescharacteristic
129C2×M16—1221no—
130#123—1221no—
131C22⋊Q8—611no—
132C22⋊Q8—611no—
133#121—611no—
134#121—611no—
135#120—1221no—
136C4×D4—1221no—
137C4×D4—1221no—
138#117—611no—
139C22⋊C8—612no—
140C22⋊C8—1221no—
141#95—21no—
142#95C2×D6112yes—
143C24C22⋊D6111yescharacteristic
144#41—2442no—
145C2×Q8—611no—
146C2×D4—611no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4—1221no—
150C22×C4—24no—
151C22×C4—22no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—1221no—
156C22×C4C4×D6111yescharacteristic
157C22×C4C4×D6111yescharacteristic
158C22×C4D24411yescharacteristic
159C22×C4D24411yescharacteristic
160C22×C4C22⋊D6111yescharacteristic
161C22×C4C22×D6111yescharacteristic
162M16—2442no—
163C2×C8—1222no—
164C4⋊C4—611no—
165C4⋊C4—611no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C42—1221no—
174C23—21no—
175C23—22no—
176C23—22no—
177C23—21no—
178C23—1221no—
179C23#1175819811yescharacteristic
180C23#1175819811yescharacteristic
181C23C2×C22⋊D6111yescharacteristic
182Q8—2441no—
183D4—2441no—
184D4—2441no—
185D4—2442no—
186D4—2442no—
187D4—2441no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—48no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—2442no—
202C2×C4#1175819811yescharacteristic
203C2×C4#1175819811yescharacteristic
204C2×C4C2×C4×D6111yescharacteristic
205C2×C4C2×D24411yescharacteristic
206C8—2442no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—2441no—
216C22—2441no—
217C22—2441no—
218C22#1451969112yes—
219C22#1451970512yes—
220C22C2×#1175819811yescharacteristic
221C22#1451980311yescharacteristic
222C22#1451980811yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—44no—
228C4—2441no—
229C4—2441no—
230C4—2441no—
231C2—21no—
232C2—21no—
233C2—22no—
234C2—22no—
235C2—4881no—
236C2C2×#1451969111yescharacteristic
237C2#1683976111yescharacteristic
238C2C2×#1451970511yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#95×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#95D61
hypocenterC61#1504
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. #16839726C2semidirect
3. #16839498C2semidirect
4. #16839495C2semidirect
5. C2×#95×C61C2semidirect
6. C2×#11758222C4semidirect
9. #14519756C4semidirect
11. #14519751C4semidirect
16. #14519736C4semidirect
39. C2×D244C2×C4semidirect
41. C2×Dic122C2×C4semidirect
47. C4⋊Dic61C2×C4semidirect
48. C4⋊Dic61C2×C4semidirect
122. C2×#95D61semidirect
125. C61#1504semidirect