Finite Group Databasebeta

← #21455756

Subgroups — #21455756

Order 7808.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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#121×D61C211yesmaximal, characteristic
2C2×#14519735C211yesmaximal, characteristic, complemented
3#16840088C212yesmaximal, complemented
4#16840084C212yesmaximal, complemented
5#16840080C211yesmaximal, characteristic, complemented
6#16840076C211yesmaximal, characteristic, complemented
7#16840073C211yesmaximal, characteristic, complemented
8#16839801C212yesmaximal, complemented
9#16839765C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#481C211yesmaximal, characteristic, complemented
12C2×D4×D61—21no—
13C2×D4×D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C2×#11758189C2212yes—
16#14519752C2211yescharacteristic
17#14519751C2211yescharacteristic
18#14519750—21no—
19#14519749—21no—
20#14519748C2211yescharacteristic
21#14519735—21no—
22#14519735—21no—
23#14519735C2212yes—
24#14519735C2212yescomplemented
25C2×C4⋊Dic61C2211yescharacteristic, complemented
26C4⋊C4×D61C2211yescharacteristic
27C2×#11758198—21no—
28C22⋊C4×D61—21no—
29C2×C4×Dic61—21no—
30#14519711C2212yescomplemented
31#14519710C2212yescomplemented
32#14519708C2212yescomplemented
33#14519699C2212yescomplemented
34#14519698C2212yescomplemented
35#14519697C2212yescomplemented
36C22⋊#92418C2211yescharacteristic, complemented
37#14519689C2212yescomplemented
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic, complemented
40#106×C61C2212yescomplemented
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic, complemented
43C23×D61—21no—
44C23×D61D411yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—21no—
50C2×C22⋊D61—21no—
51C2×C22⋊D61—21no—
52C22×Dic61—21no—
53C22×Dic61D411yescharacteristic
54D4×D61—24no—
55D4×D61—44no—
56C2×D244—21no—
57C2×D244C2311yescharacteristic
58C2×C4×D61—24no—
59C2×C4×D61—21no—
60C2×C4×D61D411yescharacteristic
61C2×C4×D61D411yescharacteristic
62C2×C4×D61C2311yescharacteristic
63C2×C4×D61C2311yescharacteristic
64C2×C8×C61C2312yes—
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2312yes—
67C4⋊C4×C61C2311yescharacteristic
68C22⋊C4×C61—21no—
69C22⋊Dic61—21no—
70#11758198—22no—
71#11758198—22no—
72#11758198—21no—
73#11758198—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2312yes—
76C4⋊Dic61C2311yescharacteristic
77#11758196—21no—
78C4×Dic61—22no—
79C4×Dic61—22no—
80C2×#92418C2312yes—
81#11758189—24no—
82C23×C61—21no—
83C23×C61C2×D411yescharacteristic
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—21no—
87C22×D61—41no—
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61C2×D411yescharacteristic
92C22×D61C2×D411yescharacteristic
93D4×C61—22no—
94D4×C61—42no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—42no—
99C2×C4×C61C2×D411yescharacteristic
100C2×C4×C61C2411yescharacteristic
101C22⋊D61—42no—
102C22⋊D61—42no—
103C22⋊D61—42no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—21no—
107C2×Dic61—42no—
108C2×Dic61C2×D411yescharacteristic
109C2×Dic61C2×D411yescharacteristic
110D244—22no—
111D244—42no—
112C4×D61—22no—
113C4×D61—22no—
114C4×D61—22no—
115C4×D61—42no—
116C4×D61#4114yes—
117C8×C61—22no—
118#92418—22no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61AGL(1,ℤ/8)12yes—
125C22×C61C22×D411yescharacteristic
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—44no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—84no—
136C2×D61#12312yes—
137C4×C61—21no—
138C4×C61—41no—
139C4×C61—42no—
140C4×C61C2×#4112yes—
141Dic61—21no—
142Dic61—41no—
143Dic61—42no—
144Dic61#12312yes—
145#3094—611nomaximal, Sylow
146C2×C61—22no—
147C2×C61—81no—
148C2×C61C2×#12311yescharacteristic
149C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C61#57511yescharacteristic
151D61—22no—
152D61—41no—
153D61—81no—
154C2×#121—611no—
155C2×#117—611no—
156#482—612no—
157#482—612no—
158#481—611no—
159#481D6111yescharacteristic, complemented
160#480—611no—
161#480—611no—
162#428—612no—
163#418—612no—
164#407—611no—
165C61#309411yescharacteristic, complemented, Sylow
166C22×D4—611no—
167C22×D4—1221no—
168C23×C4—611no—
169C2×M16—612no—
170#121—611no—
171#121—611no—
172#121—611no—
173#121—1221no—
174#121—1221no—
175#121C2×D6111yescharacteristic
176#117—612no—
177#117—612no—
178#117—1221no—
179#117—1221no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4C2×D6111yescharacteristic, complemented
183C2×C22⋊C4—1221no—
184C2×C22⋊C4—1221no—
185C2×C42—1221no—
186#107—612no—
187#107—612no—
188#106—612no—
189#106C2×D6112yescomplemented
190#102—612no—
191#102—612no—
192#102—612no—
193#102C2×D6112yescomplemented
194C22⋊C8—611no—
195C22⋊C8—612no—
196C22⋊C8C2×D6111yescharacteristic, complemented
197C24—611no—
198C24—1221no—
199C2×D4—21no—
200C2×D4—611no—
201C2×D4—1221no—
202C2×D4—1224no—
203C2×D4—1221no—
204C2×D4—1221no—
205C2×D4—1221no—
206C2×D4—2444no—
207C2×D4C22×D6111yescharacteristic
208C22×C4—21no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—1224no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4C22×D6111yescharacteristic
218M16—1224no—
219C2×C8—612no—
220C2×C8C22×D6112yes—
221C4⋊C4—21no—
222C4⋊C4—612no—
223C4⋊C4—611no—
224C4⋊C4—1221no—
225C4⋊C4—1221no—
226C4⋊C4C22×D6112yes—
227C4⋊C4C22×D6111yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—1221no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C22⋊C4—1221no—
233C22⋊C4—1221no—
234C42—1222no—
235C42—1222no—
236C23—21no—
237C23—611no—
238C23—611no—
239C23—1222no—
240C23—1222no—
241C23—1221no—
242C23—2441no—
243C23—2442no—
244C23—2442no—
245C23—2442no—
246C23D4×D6111yescharacteristic
247D4—22no—
248D4—42no—
249D4—1222no—
250D4—2442no—
251D4—2442no—
252D4—2442no—
253D4—2442no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—611no—
259C2×C4—614no—
260C2×C4—611no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—2442no—
268C2×C4—2442no—
269C2×C4D4×D6111yescharacteristic
270C2×C4C23×D6111yescharacteristic
271C8—22no—
272C8—1222no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—612no—
279C22—1221no—
280C22—1221no—
281C22—1221no—
282C22—1221no—
283C22—1221no—
284C22—4884no—
285C22—2444no—
286C22—2441no—
287C22—2441no—
288C22—2441no—
289C22#1451980412yes—
290C22C2×D4×D6111yescharacteristic
291C4—21no—
292C4—41no—
293C4—42no—
294C4—612no—
295C4—1221no—
296C4—2442no—
297C4—2441no—
298C4#41×D6112yes—
299C2—22no—
300C2—81no—
301C2—1222no—
302C2—4881no—
303C2—2441no—
304C2#123×D6111yescharacteristic
305C2C2×#1451980411yescharacteristic
306C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#481C2
socleC22×C61C22×D4
hypercenter#481D61
hypocenterC61#3094
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#14519735C2semidirect
3. #16840088C2semidirect
4. #16840084C2semidirect
5. #16840080C2semidirect
6. #16840076C2semidirect
7. #16840073C2semidirect
8. #16839801C2semidirect
9. #16839765C2semidirect
10. #16839724C2semidirect
11. C61×#481C2semidirect
24. #14519735C22semidirect
25. C2×C4⋊Dic61C22semidirect
30. #14519711C22semidirect
31. #14519710C22semidirect
32. #14519708C22semidirect
33. #14519699C22semidirect
34. #14519698C22semidirect
35. #14519697C22semidirect
36. C22⋊#92418C22semidirect
37. #14519689C22semidirect
39. C2×C4⋊C4×C61C22semidirect
40. #106×C61C22semidirect
41. #102×C61C22semidirect
42. C22⋊C8×C61C22semidirect
159. #481D61semidirect
165. C61#3094semidirect
182. C2×C4⋊C4C2×D61semidirect
189. #106C2×D61semidirect
193. #102C2×D61semidirect
196. C22⋊C8C2×D61semidirect