Finite Group Databasebeta

← #21455744

Subgroups — #21455744

Order 7808.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
2C22×C4⋊Dic61C211yesmaximal, characteristic, complemented
3#16840098C212yesmaximal, complemented
4#16840093C212yesmaximal, complemented
5#16840081C212yesmaximal, complemented
6#16840076C212yesmaximal, complemented
7#16839804C212yesmaximal, complemented
8#16839764C212yesmaximal, complemented
9C61×#407C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C23×Dic61—21no—
12#14519760—21no—
13#14519756C2211yescharacteristic
14#14519756C2211yescharacteristic
15#14519751C2211yescharacteristic
16#14519751C2211yescharacteristic
17#14519746—21no—
18C4×C22⋊D61—21no—
19C4×C22⋊D61—21no—
20#14519736C2211yescharacteristic
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61C2212yes—
25C2×C4⋊Dic61C2212yes—
26C2×C4⋊Dic61C2212yes—
27#14519711C2214yescomplemented
28#14519709C2214yescomplemented
29#14519702C2214yescomplemented
30#14519699C2214yescomplemented
31C23×C4×C61C2211yescharacteristic
32C2×M16×C61C2212yes—
33C22⋊C8×C61C2212yes—
34C22⋊C8×C61C2212yes—
35C24×C61D411yescharacteristic
36C22×C4×C61—24no—
37C22×C4×C61D411yescharacteristic
38C22×C4×C61D411yescharacteristic
39C22×C4×C61D411yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—21no—
44C2×C22⋊D61—21no—
45C2×C22⋊D61—21no—
46C22×Dic61—22no—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61—44no—
50#11758222—24no—
51C2×D244C2311yescharacteristic
52C2×C4×D61—21no—
53C2×Dic122C2311yescharacteristic
54M16×C61—24no—
55C2×C8×C61C2314yes—
56C22⋊Dic61—21no—
57C22⋊Dic61—21no—
58C22⋊Dic61—21no—
59#11758198—21no—
60#11758198—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63C4⋊Dic61—22no—
64C4⋊Dic61C2314yes—
65C4⋊Dic61C2311yescharacteristic
66C4⋊Dic61C2311yescharacteristic
67#11758196—21no—
68#11758196—21no—
69C4×Dic61—21no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61C2×D411yescharacteristic
74C23×C61C2×D411yescharacteristic
75C23×C61C2×D411yescharacteristic
76C22×D61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61#4114yes—
86C2×C4×C61C2411yescharacteristic
87C22⋊D61—42no—
88C22⋊D61—42no—
89C22⋊D61—42no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—24no—
94C2×Dic61—44no—
95C2×Dic61—44no—
96C2×Dic61—44no—
97D244—22no—
98C4×D61—42no—
99Dic122—22no—
100C8×C61—24no—
101C22×C61—28no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—21no—
108C22×C61#12312yes—
109C22×C61AGL(1,ℤ/8)12yes—
110C22×C61#13712yes—
111C22×C61C22×D411yescharacteristic
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—41no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61#12312yes—
118C4×C61C2×#4112yes—
119Dic61—41no—
120Dic61—44no—
121Dic61—41no—
122Dic61—41no—
123#3092—611nomaximal, Sylow
124C2×C61—22no—
125C2×C61—22no—
126C2×C61—22no—
127C2×C61C2×#12311yescharacteristic
128C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C61C2×#13711yescharacteristic
130D61—81no—
131#525—611no—
132C22×C4⋊C4—611no—
133#484—612no—
134#483—612no—
135#481—612no—
136#480—612no—
137#428—612no—
138#417—612no—
139#407D6111yescharacteristic, complemented
140C61#309211yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C23×C4—1221no—
143C23×C4C2×D6111yescharacteristic
144C2×M16C2×D6112yes—
145#123—1221no—
146C22⋊Q8—611no—
147C22⋊Q8—611no—
148#121—611no—
149#121—611no—
150#120—1221no—
151C4×D4—1221no—
152C4×D4—1221no—
153#117—611no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—1221no—
159C2×C4⋊C4—1221no—
160#107—614no—
161#106—614no—
162#103—614no—
163#102—614no—
164C22⋊C8C2×D6112yes—
165C22⋊C8C2×D6112yes—
166C24D24411yescharacteristic
167#41—1224no—
168C2×Q8—611no—
169C2×D4—611no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—1221no—
173C22×C4—24no—
174C22×C4—1222no—
175C22×C4—1222no—
176C22×C4—1222no—
177C22×C4—1221no—
178C22×C4—2444no—
179C22×C4D24411yescharacteristic
180C22×C4D24411yescharacteristic
181C22×C4D24411yescharacteristic
182C22×C4C22×D6111yescharacteristic
183C22×C4C22×D6111yescharacteristic
184C22×C4C22×D6111yescharacteristic
185M16—24no—
186C2×C8C22×D6114yes—
187C4⋊C4—614no—
188C4⋊C4—611no—
189C4⋊C4—611no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C22⋊C4—1221no—
200C42—1221no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—1221no—
205C23C2×D24411yescharacteristic
206C23C2×D24411yescharacteristic
207C23C2×D24411yescharacteristic
208Q8—1222no—
209D4—1222no—
210D4—2442no—
211D4—2442no—
212D4—2442no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1224no—
222C2×C4—2444no—
223C2×C4—2444no—
224C2×C4—2444no—
225C2×C4—2442no—
226C2×C4C2×D24411yescharacteristic
227C2×C4C2×D24411yescharacteristic
228C2×C4C2×D24411yescharacteristic
229C2×C4#1175822414yes—
230C2×C4C23×D6111yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—2441no—
240C22—2441no—
241C22—2441no—
242C22#1451976112yes—
243C22#1451980512yes—
244C22#1451981012yes—
245C22C22×D24411yescharacteristic
246C4—21no—
247C4—21no—
248C4—2441no—
249C4—2444no—
250C4—2441no—
251C4—2441no—
252C4#1451976112yes—
253C4C2×#1175822412yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—4881no—
258C2C2×#1451976111yescharacteristic
259C2C2×#1451980511yescharacteristic
260C2C2×#1451981011yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#407C2
socleC22×C61C22×D4
hypercenter#407D61
hypocenterC61#3092
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic61C2semidirect
3. #16840098C2semidirect
4. #16840093C2semidirect
5. #16840081C2semidirect
6. #16840076C2semidirect
7. #16839804C2semidirect
8. #16839764C2semidirect
9. C61×#407C2semidirect
27. #14519711C22semidirect
28. #14519709C22semidirect
29. #14519702C22semidirect
30. #14519699C22semidirect
139. #407D61semidirect
140. C61#3092semidirect