Finite Group Databasebeta

← #21455765

Subgroups — #21455765

Order 7808.

410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14519753C211yesmaximal, characteristic
2#117×D61C211yesmaximal, characteristic
3#16840102C212yesmaximal, complemented
4#16840101C212yesmaximal, complemented
5#16840096C212yesmaximal, complemented
6#16840091C212yesmaximal, complemented
7#16839805C211yesmaximal, characteristic, complemented
8#16839804C211yesmaximal, characteristic, complemented
9#16839771C211yesmaximal, characteristic, complemented
10#16839725C211yesmaximal, characteristic
11C61×#419C211yesmaximal, characteristic, complemented
12C22×C4×D61C2211yescharacteristic
13C2×#11758194C2211yescharacteristic
14#14519753—21no—
15#14519753—21no—
16#14519753C2212yes—
17#14519753C2212yes—
18#14519736C2211yescharacteristic
19#14519735C2211yescharacteristic
20#14519735C2211yescharacteristic
21#14519734—21no—
22#14519733—21no—
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196—21no—
25C4⋊C4×D61C2211yescharacteristic
26C4⋊C4×D61C2211yescharacteristic
27C2×#11758198—21no—
28C22⋊C4×D61—21no—
29C42×D61—21no—
30#14519711C2212yescomplemented
31#14519710C2212yescomplemented
32#14519709C2212yescomplemented
33#14519708C2212yescomplemented
34#14519701C2212yescomplemented
35#14519701C2212yescomplemented
36#14519689C2212yes—
37#14519689C2212yes—
38C22×Q8×C61C2211yescharacteristic
39C2×M16×C61C2211yescharacteristic
40#117×C61C2211yescharacteristic
41#103×C61C2212yescomplemented
42#103×C61C2212yescomplemented
43C23×D61D411yescharacteristic
44C2×Q8×C61—21no—
45C2×Q8×C61—22no—
46C2×Q8×C61—22no—
47C2×Q8×C61C2312yes—
48C22×C4×C61—21no—
49C22×C4×C61C2311yescharacteristic
50C22×Dic61—21no—
51C22×Dic61D411yescharacteristic
52C2×C4×D61—22no—
53C2×C4×D61—22no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61D411yescharacteristic
57C2×C4×D61D411yescharacteristic
58C2×C4×D61C2311yescharacteristic
59C2×C4×D61C2311yescharacteristic
60M16×C61—22no—
61C2×C8×C61C2312yes—
62C4⋊C4×C61C2311yescharacteristic
63C4⋊C4×C61C2311yescharacteristic
64C22⋊C4×C61—21no—
65C42×C61—21no—
66C22⋊Dic61—21no—
67#11758198—21no—
68#11758198—21no—
69#11758198—22no—
70#11758198—22no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2311yescharacteristic
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2312yes—
75#11758196—21no—
76#11758196—21no—
77#11758196—22no—
78#11758196—22no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82#11758194—22no—
83C2×#92418C2312yes—
84C23×C61C2×D411yescharacteristic
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—41no—
88C22×D61C2×D411yescharacteristic
89C22×D61C2×D411yescharacteristic
90Q8×C61—22no—
91Q8×C61—22no—
92Q8×C61—42no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—42no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61#4112yes—
99C2×C4×C61#4112yes—
100C2×C4×C61C2411yescharacteristic
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61—42no—
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108C4×D61—22no—
109C4×D61—22no—
110C4×D61—21no—
111C4×D61—21no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—42no—
115C4×D61—42no—
116C8×C61—22no—
117#92418—22no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61#12312yes—
121C22×C61C22×D411yescharacteristic
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—21no—
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—44no—
128C2×D61#13712yes—
129C4×C61—42no—
130C4×C61—41no—
131C4×C61—41no—
132C4×C61#12312yes—
133C4×C61C2×#4111yescharacteristic
134C4×C61C2×#4111yescharacteristic
135Dic61—21no—
136Dic61—21no—
137Dic61—41no—
138Dic61—41no—
139Dic61—42no—
140#3095—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61C2×#12311yescharacteristic
143C2×C61C2×#13711yescharacteristic
144C2×C61#57511yescharacteristic
145D61—22no—
146D61—41no—
147C2×C22⋊Q8—611no—
148C2×#117—611no—
149#485—612no—
150#485—612no—
151#484—612no—
152#483—612no—
153#428—611no—
154#428—611no—
155#419—611no—
156#419D6111yescharacteristic, complemented
157#407—611no—
158C61#309511yescharacteristic, complemented, Sylow
159C22×Q8C2×D6111yescharacteristic
160C23×C4—611no—
161C2×M16—611no—
162C2×M16C2×D6111yescharacteristic
163C22⋊Q8—612no—
164C22⋊Q8—612no—
165C22⋊Q8—1221no—
166C22⋊Q8—1221no—
167#117—611no—
168#117—611no—
169#117—611no—
170#117—1221no—
171#117—1221no—
172#117C2×D6111yescharacteristic
173C2×C4⋊C4—611no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—1221no—
177C2×C22⋊C4—1221no—
178C2×C22⋊C4—1221no—
179C2×C42—1221no—
180#107—612no—
181#107—612no—
182#106—612no—
183#106—612no—
184#103—612no—
185#103—612no—
186#103C2×D6112yescomplemented
187#103C2×D6112yescomplemented
188C22⋊C8—612no—
189C22⋊C8—612no—
190C24—611no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8C22×D6112yes—
195C22×C4—21no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4—1222no—
204C22×C4—1222no—
205C22×C4—1221no—
206C22×C4C22×D6111yescharacteristic
207M16—22no—
208M16—1222no—
209C2×C8—612no—
210C2×C8C22×D6112yes—
211C4⋊C4—611no—
212C4⋊C4—611no—
213C4⋊C4—612no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4—1222no—
217C4⋊C4—1222no—
218C4⋊C4—1221no—
219C4⋊C4C22×D6111yescharacteristic
220C4⋊C4C22×D6111yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—1221no—
223C22⋊C4—1221no—
224C22⋊C4—1222no—
225C22⋊C4—1222no—
226C22⋊C4—1221no—
227C42—21no—
228C42—1221no—
229C42—1221no—
230C42—1221no—
231C23—611no—
232C23—611no—
233C23—1222no—
234C23—1222no—
235C23—2441no—
236C23D4×D6111yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—42no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1222no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4#1175822212yes—
260C2×C4D4×D6111yescharacteristic
261C2×C4#1175822412yes—
262C2×C4C23×D6111yescharacteristic
263C8—22no—
264C8—1222no—
265C22—21no—
266C22—21no—
267C22—612no—
268C22—1221no—
269C22—1221no—
270C22—1221no—
271C22—1221no—
272C22—1221no—
273C22—2444no—
274C22#1451975912yes—
275C22C2×D4×D6111yescharacteristic
276C4—42no—
277C4—41no—
278C4—41no—
279C4—1221no—
280C4—1221no—
281C4—2441no—
282C4—2441no—
283C4—2442no—
284C4#1451975912yes—
285C4C2×#1175822411yescharacteristic
286C4C2×#1175822211yescharacteristic
287C2—22no—
288C2—1222no—
289C2—2441no—
290C2C2×#1451975911yescharacteristic
291C2#137×D6111yescharacteristic
292C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#419C2
socleC22×C61C22×D4
hypercenter#419D61
hypocenterC61#3095
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #16840102C2semidirect
4. #16840101C2semidirect
5. #16840096C2semidirect
6. #16840091C2semidirect
7. #16839805C2semidirect
8. #16839804C2semidirect
9. #16839771C2semidirect
11. C61×#419C2semidirect
30. #14519711C22semidirect
31. #14519710C22semidirect
32. #14519709C22semidirect
33. #14519708C22semidirect
34. #14519701C22semidirect
35. #14519701C22semidirect
41. #103×C61C22semidirect
42. #103×C61C22semidirect
156. #419D61semidirect
158. C61#3095semidirect
186. #103C2×D61semidirect
187. #103C2×D61semidirect