Finite Group Databasebeta

← #21455734

Subgroups — #21455734

Order 7808.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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
2C2×#14519736C211yesmaximal, characteristic, complemented
3#16840104C212yesmaximal, complemented
4#16840098C211yesmaximal, characteristic, complemented
5#16840093C211yesmaximal, characteristic, complemented
6#16840087C212yesmaximal, complemented
7#16840081C211yesmaximal, characteristic, complemented
8#16840076C211yesmaximal, characteristic, complemented
9#16839800C212yesmaximal, complemented
10#16839759C212yesmaximal, complemented
11C2×C22⋊C8×C61C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13#14519760—21no—
14#14519756C2211yescharacteristic
15#14519756C2211yescharacteristic
16#14519751C2211yescharacteristic
17#14519751C2211yescharacteristic
18#14519746—21no—
19C4×C22⋊D61—21no—
20C4×C22⋊D61—21no—
21#14519736—21no—
22#14519736—21no—
23#14519736C2212yes—
24#14519736C2212yes—
25#14519736C2211yescharacteristic
26C2×C4⋊Dic61C2211yescharacteristic
27C2×C4⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61—21no—
29C2×C4×Dic61—21no—
30#14519711C2212yescomplemented
31#14519711C2212yescomplemented
32#14519709C2212yescomplemented
33#14519709C2212yescomplemented
34#14519702C2212yescomplemented
35#14519702C2212yescomplemented
36#14519699C2212yescomplemented
37#14519699C2212yescomplemented
38C23×C4×C61C2211yescharacteristic
39C22×C8×C61C2212yes—
40C22⋊C8×C61C2211yescharacteristic
41C22⋊C8×C61C2211yescharacteristic
42C22⋊C8×C61C2212yes—
43C24×C61D411yescharacteristic
44C22×C4×C61—24no—
45C22×C4×C61D411yescharacteristic
46C22×C4×C61D411yescharacteristic
47C22×C4×C61D411yescharacteristic
48C22×C4×C61C2311yescharacteristic
49C22×C4×C61C2311yescharacteristic
50C22×C4×C61C2311yescharacteristic
51C2×C22⋊D61—21no—
52C2×C22⋊D61—21no—
53C2×C22⋊D61—21no—
54C22×Dic61—21no—
55C22×Dic61—21no—
56#11758222—24no—
57C2×D244C2311yescharacteristic
58C2×C4×D61—21no—
59C2×Dic122C2311yescharacteristic
60C2×C8×C61—24no—
61C2×C8×C61C2312yes—
62C2×C8×C61C2312yes—
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65C22⋊Dic61—21no—
66C22⋊Dic61—21no—
67C22⋊Dic61—21no—
68#11758198—21no—
69#11758198—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2312yes—
73C4⋊Dic61C2312yes—
74C4⋊Dic61C2311yescharacteristic
75C4⋊Dic61C2311yescharacteristic
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—22no—
79C4×Dic61—22no—
80C4×Dic61—21no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—41no—
84C23×C61C2×D411yescharacteristic
85C23×C61C2×D411yescharacteristic
86C23×C61C2×D411yescharacteristic
87C22×D61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61#4114yes—
97C2×C4×C61C2411yescharacteristic
98C22⋊D61—42no—
99C22⋊D61—42no—
100C22⋊D61—42no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108D244—22no—
109C4×D61—42no—
110Dic122—22no—
111C8×C61—22no—
112C8×C61—22no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—21no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61—44no—
121C22×C61#12312yes—
122C22×C61#13512yes—
123C22×C61C22×D411yescharacteristic
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—41no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61#12312yes—
130C4×C61C2×#4112yes—
131Dic61—41no—
132Dic61—42no—
133Dic61—41no—
134Dic61—42no—
135Dic61—41no—
136#3091—611nomaximal, Sylow
137C2×C61—22no—
138C2×C61—22no—
139C2×C61—41no—
140C2×C61C2×#12311yescharacteristic
141C2×C61C2×#13511yescharacteristic
142C2×C61#57511yescharacteristic
143D61—81no—
144#525—611no—
145C2×#117—611no—
146#485—612no—
147#484—611no—
148#483—611no—
149#482—612no—
150#481—611no—
151#480—611no—
152#427—612no—
153#416—612no—
154C2×C22⋊C8D6111yescharacteristic, complemented
155C61#309111yescharacteristic, complemented, Sylow
156C2×#41—611no—
157C23×C4C2×D6111yescharacteristic
158C22×C8C2×D6112yes—
159#123—1221no—
160C22⋊Q8—611no—
161C22⋊Q8—611no—
162#121—611no—
163#121—611no—
164#120—1221no—
165C4×D4—1221no—
166C4×D4—1221no—
167#117—612no—
168#117—612no—
169#117—611no—
170#117—1221no—
171#117—1221no—
172C2×C4⋊C4—611no—
173C2×C4⋊C4—611no—
174C2×C22⋊C4—1221no—
175C2×C42—1221no—
176#107—612no—
177#107—612no—
178#106—612no—
179#106—612no—
180#103—612no—
181#103—612no—
182#102—612no—
183#102—612no—
184C22⋊C8C2×D6111yescharacteristic
185C22⋊C8C2×D6111yescharacteristic
186C22⋊C8C2×D6112yes—
187C24D24411yescharacteristic
188#41—1224no—
189C2×Q8—611no—
190C2×D4—611no—
191C2×D4—1221no—
192C2×D4—1221no—
193C2×D4—1221no—
194C22×C4—24no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4D24411yescharacteristic
199C22×C4D24411yescharacteristic
200C22×C4D24411yescharacteristic
201C22×C4C22×D6111yescharacteristic
202C22×C4C22×D6111yescharacteristic
203C22×C4C22×D6111yescharacteristic
204C2×C8—24no—
205C2×C8C22×D6112yes—
206C2×C8C22×D6112yes—
207C4⋊C4—612no—
208C4⋊C4—612no—
209C4⋊C4—611no—
210C4⋊C4—611no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—1221no—
215C22⋊C4—1222no—
216C22⋊C4—1222no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C22⋊C4—1221no—
220C22⋊C4—1221no—
221C22⋊C4—1221no—
222C42—1222no—
223C42—1222no—
224C42—1221no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—1221no—
229C23C2×D24411yescharacteristic
230C23C2×D24411yescharacteristic
231C23C2×D24411yescharacteristic
232Q8—1222no—
233D4—1222no—
234D4—2442no—
235D4—2442no—
236D4—2442no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—2442no—
248C2×C4—2442no—
249C2×C4—2442no—
250C2×C4C2×D24411yescharacteristic
251C2×C4C2×D24411yescharacteristic
252C2×C4C2×D24411yescharacteristic
253C2×C4#1175822414yes—
254C2×C4C23×D6111yescharacteristic
255C8—22no—
256C8—22no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—2441no—
266C22—2441no—
267C22—2441no—
268C22#1451976112yes—
269C22#1451979912yes—
270C22C22×D24411yescharacteristic
271C4—21no—
272C4—21no—
273C4—2441no—
274C4—2442no—
275C4—2441no—
276C4—2442no—
277C4—2441no—
278C4#1451976112yes—
279C4C2×#1175822412yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—4881no—
284C2C2×#1451976111yescharacteristic
285C2C2×#1451979911yescharacteristic
286C2#1684056211yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C22⋊C8×C61C2
socleC22×C61C22×D4
hypercenterC2×C22⋊C8D61
hypocenterC61#3091
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14519736C2semidirect
3. #16840104C2semidirect
4. #16840098C2semidirect
5. #16840093C2semidirect
6. #16840087C2semidirect
7. #16840081C2semidirect
8. #16840076C2semidirect
9. #16839800C2semidirect
10. #16839759C2semidirect
11. C2×C22⋊C8×C61C2semidirect
30. #14519711C22semidirect
31. #14519711C22semidirect
32. #14519709C22semidirect
33. #14519709C22semidirect
34. #14519702C22semidirect
35. #14519702C22semidirect
36. #14519699C22semidirect
37. #14519699C22semidirect
154. C2×C22⋊C8D61semidirect
155. C61#3091semidirect