Finite Group Databasebeta

← #21446270

Subgroups — #21446270

Order 7808.

598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#14519746C211yesmaximal, characteristic
2C22×C22⋊Dic61C211yesmaximal, characteristic, complemented
3C2×#14519691C212yesmaximal, complemented
4#16839528C212yesmaximal, complemented
5C61×#379C211yesmaximal, characteristic, complemented
6C22×C22⋊D61C412yescomplemented
7C22×C22⋊D61C2211yescharacteristic
8C23×Dic61—21no—
9#14519746—21no—
10#14519746—21no—
11#14519746—22no—
12C2×C22⋊Dic61—21no—
13C2×C22⋊Dic61—24no—
14C2×C22⋊Dic61C412yescomplemented
15C2×C22⋊Dic61C2211yescharacteristic
16C2×C22⋊Dic61C2212yes—
17#14519691—24no—
18C25×C61C2211yescharacteristic
19C2×C22⋊C4×C61—22no—
20C2×C22⋊C4×C61C2212yes—
21C24×C61—22no—
22C24×C61—22no—
23C24×C61—44no—
24C24×C61C2×C412yes—
25C24×C61D411yescharacteristic
26C24×C61D412yes—
27C24×C61D411yescharacteristic
28C24×C61C2311yescharacteristic
29C23×D61C2×C411yescharacteristic, complemented
30C22×C4×C61—22no—
31C2×C22⋊D61—22no—
32C2×C22⋊D61—22no—
33C2×C22⋊D61—22no—
34C2×C22⋊D61—21no—
35C2×C22⋊D61—21no—
36C2×C22⋊D61—22no—
37C2×C22⋊D61—44no—
38C22×Dic61—24no—
39C22×Dic61—22no—
40C22×Dic61—44no—
41C22×Dic61C2×C411yescharacteristic, complemented
42C22×Dic61C2×C412yescomplemented
43C22⋊C4×C61—22no—
44C22⋊C4×C61—22no—
45C22⋊C4×C61—44no—
46C22⋊Dic61—24no—
47C22⋊Dic61—22no—
48C22⋊Dic61—22no—
49C22⋊Dic61—22no—
50C22⋊Dic61—21no—
51C22⋊Dic61—21no—
52C22⋊Dic61D414yescomplemented
53C23×C61—24no—
54C23×C61—21no—
55C23×C61—21no—
56C23×C61—24no—
57C23×C61—24no—
58C23×C61—24no—
59C23×C61—21no—
60C23×C61—24no—
61C23×C61—21no—
62C23×C61—42no—
63C23×C61—42no—
64C23×C61—42no—
65C23×C61—42no—
66C23×C61—48no—
67C23×C61—48no—
68C23×C61C22⋊C412yes—
69C23×C61C22⋊C412yes—
70C23×C61C22×C411yescharacteristic
71C23×C61C2×D411yescharacteristic
72C23×C61C2×D411yescharacteristic
73C23×C61C2×D412yes—
74C23×C61#4112yes—
75C22×D61—21no—
76C22×D61—22no—
77C22×D61—42no—
78C2×C4×C61—44no—
79C2×C4×C61—42no—
80C22⋊D61—44no—
81C22⋊D61—44no—
82C22⋊D61—41no—
83C22⋊D61—42no—
84C22⋊D61—41no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—24no—
89C2×Dic61—48no—
90C2×Dic61—44no—
91C2×Dic61—42no—
92C22×C61—24no—
93C22×C61—24no—
94C22×C61—22no—
95C22×C61—22no—
96C22×C61—22no—
97C22×C61—22no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—22no—
101C22×C61—22no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—48no—
105C22×C61—48no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61#9914yescomplemented
109C22×C61C2×C22⋊C411yescharacteristic
110C22×C61C4×D412yes—
111C22×C61#12011yescharacteristic
112C22×C61#12112yes—
113C22×C61#12311yescharacteristic
114C2×D61—41no—
115C2×D61—42no—
116C2×D61—82no—
117C4×C61—82no—
118Dic61—44no—
119Dic61—41no—
120Dic61—42no—
121#1898—611nomaximal, Sylow
122C2×C61—21no—
123C2×C61—22no—
124C2×C61—22no—
125C2×C61—24no—
126C2×C61—21no—
127C2×C61—42no—
128C2×C61#38611yescharacteristic
129C2×C61C2×#9912yes—
130D61—81no—
131C2×#120—611no—
132C22×C22⋊C4—611no—
133C2×#99—612no—
134#379D6111yescharacteristic, complemented
135#342—612no—
136C61#189811yescharacteristic, complemented, Sylow
137C25C2×D6111yescharacteristic
138C22×D4—611no—
139C22×D4—612no—
140C23×C4—1221no—
141#120—1221no—
142#120—1221no—
143#120—1222no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—612no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—611no—
148C2×C22⋊C4—1224no—
149C2×C22⋊C4—1221no—
150C2×C22⋊C4C2×D6112yes—
151#99—1224no—
152C24—22no—
153C24—22no—
154C24—44no—
155C24—611no—
156C24C4×D6112yes—
157C24D24411yescharacteristic
158C24D24411yescharacteristic
159C24C22⋊D6112yes—
160C24C22×D6111yescharacteristic
161C2×D4—1222no—
162C2×D4—1222no—
163C2×D4—1221no—
164C2×D4—1222no—
165C2×D4—1222no—
166C2×D4—1221no—
167C2×D4—2444no—
168C22×C4—22no—
169C22×C4—611no—
170C22×C4—612no—
171C22×C4—1224no—
172C22×C4—1222no—
173C22×C4—2444no—
174C22⋊C4—22no—
175C22⋊C4—22no—
176C22⋊C4—44no—
177C22⋊C4—614no—
178C22⋊C4—1224no—
179C22⋊C4—1222no—
180C22⋊C4—1222no—
181C22⋊C4—1221no—
182C22⋊C4—1222no—
183C22⋊C4—1221no—
184C23—24no—
185C23—21no—
186C23—21no—
187C23—24no—
188C23—24no—
189C23—24no—
190C23—21no—
191C23—24no—
192C23—21no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—48no—
198C23—48no—
199C23—1222no—
200C23—1221no—
201C23—2442no—
202C23#1175819812yes—
203C23#1175819812yes—
204C23C2×C4×D6111yescharacteristic
205C23C2×D24411yescharacteristic
206C23D4×D6112yes—
207C23#1175822412yes—
208C23C2×C22⋊D6111yescharacteristic
209D4—2444no—
210D4—2444no—
211D4—2441no—
212D4—2442no—
213D4—2441no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—1222no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1224no—
220C2×C4—2448no—
221C2×C4—2444no—
222C2×C4—2442no—
223C22—24no—
224C22—24no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—48no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—4882no—
240C22—2442no—
241C22—2441no—
242C22#1451969114yescomplemented
243C22C2×#1175819811yescharacteristic
244C22#1451973712yes—
245C22#1451974711yescharacteristic
246C22#1451974912yes—
247C22#1451976111yescharacteristic
248C4—82no—
249C4—2444no—
250C4—2442no—
251C4—2441no—
252C2—22no—
253C2—21no—
254C2—24no—
255C2—21no—
256C2—22no—
257C2—42no—
258C2—4881no—
259C2#1683963911yescharacteristic
260C2C2×#1451969112yes—
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC61×#379C2
socleC22×C61C2×C22⋊C4
hypercenter#379D61
hypocenterC61#1898
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊Dic61C2semidirect
3. C2×#14519691C2semidirect
4. #16839528C2semidirect
5. C61×#379C2semidirect
6. C22×C22⋊D61C4semidirect
14. C2×C22⋊Dic61C4semidirect
29. C23×D61C2×C4semidirect
41. C22×Dic61C2×C4semidirect
42. C22×Dic61C2×C4semidirect
52. C22⋊Dic61D4semidirect
108. C22×C61#99semidirect
134. #379D61semidirect
136. C61#1898semidirect
242. C22#14519691semidirect