Finite Group Databasebeta

← #21458063

Subgroups — #21458063

Order 7808.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840477C211yesmaximal, characteristic, complemented
2D4×D244C211yesmaximal, characteristic, complemented
3#16840109C211yesmaximal, characteristic, complemented
4#16840089C212yesmaximal, complemented
5#16840052C211yesmaximal, characteristic, complemented
6#16840014C212yesmaximal, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839894C212yesmaximal, complemented
9#16839841C211yesmaximal, characteristic, complemented
10#16839765C212yesmaximal, complemented
11C4×D8×C61C211yesmaximal, characteristic, complemented
12C22×D244—21no—
13C2×D4×D61C2212yes—
14C2×#11758199C2212yescomplemented
15C2×#11758189C2212yescomplemented
16#14519777C2211yescharacteristic, complemented
17#14519774C2211yescharacteristic
18#14519763—22no—
19#14519752C2212yes—
20#14519751—21no—
21#14519751—21no—
22#14519748C2212yescomplemented
23#14519747—22no—
24C4×D244C2211yescharacteristic
25#14519736—21no—
26#14519735C2212yescomplemented
27#14519708C2212yescomplemented
28C4⋊#92418C2211yescharacteristic, complemented
29#14519699C2212yescomplemented
30#14519699C2212yescomplemented
31#14519698C2212yes—
32#14519697C2212yescomplemented
33#14519689C2212yescomplemented
34C2×D8×C61C2211yescharacteristic
35C4×D4×C61C2211yescharacteristic
36C4×D4×C61C2211yescharacteristic, complemented
37#107×C61C2211yescharacteristic, complemented
38#102×C61C2211yescharacteristic
39#102×C61C2211yescharacteristic, complemented
40C4×C8×C61C2211yescharacteristic, complemented
41C23×D61—22no—
42C2×D4×C61C2311yescharacteristic
43C2×D4×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48D4×D61—24no—
49D4×D61—42no—
50C2×D244—22no—
51C2×D244—21no—
52C2×D244—21no—
53C2×D244—44no—
54C2×D244D411yescharacteristic
55C2×D244C2312yes—
56C2×C4×D61C2312yes—
57C2×Dic122—21no—
58D8×C61—22no—
59C2×C8×C61C2311yescharacteristic
60C2×C8×C61C2311yescharacteristic
61C4⋊C4×C61C2311yescharacteristic
62C4⋊C4×C61C2311yescharacteristic
63C22⋊C4×C61—21no—
64C22⋊C4×C61—21no—
65C42×C61C2311yescharacteristic
66C22⋊Dic61—22no—
67#11758199—42no—
68#11758198—22no—
69#11758198—22no—
70#11758198D412yes—
71C4⋊Dic61—21no—
72C4⋊Dic61D411yescharacteristic
73C4⋊Dic61C2312yes—
74C4×Dic61—22no—
75C2×#92418C2312yes—
76#11758189—42no—
77C23×C61—21no—
78C23×C61—21no—
79C22×D61—22no—
80C22×D61—44no—
81C22×D61—44no—
82C22×D61—82no—
83C22×D61C2×D412yes—
84D4×C61—21no—
85D4×C61—21no—
86D4×C61—21no—
87D4×C61#4112yes—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C22⋊D61—44no—
96C22⋊D61—82no—
97C2×Dic61—22no—
98C2×Dic61C2×D412yes—
99D244—22no—
100D244—22no—
101D244—22no—
102D244—44no—
103D244—42no—
104D244—81no—
105C4×D61—22no—
106C4×D61—22no—
107Dic122—81no—
108C8×C61—21no—
109C8×C61—21no—
110#92418—22no—
111C22×C61—22no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61C22×D411yescharacteristic
118C2×D61—22no—
119C2×D61—22no—
120C2×D61—22no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—88no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61AGL(1,ℤ/8)12yes—
129C4×C61C2×#4111yescharacteristic
130C4×C61H(5,𝔽2)11yescharacteristic
131Dic61—22no—
132Dic61—42no—
133#3325—611nomaximal, Sylow
134C2×C61—42no—
135C2×C61—81no—
136C2×C61#54611yescharacteristic
137C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C61#57611yescharacteristic
139D61—42no—
140D61—82no—
141#555—611no—
142D42—611no—
143#486—611no—
144#482—612no—
145#476—611no—
146#469—612no—
147#459—611no—
148#447—612no—
149C4×D8D6111yescharacteristic, complemented
150#436—611no—
151#418—612no—
152C61#332511yescharacteristic, complemented, Sylow
153C22×D4—612no—
154C22×D4—1221no—
155C2×D8—612no—
156C2×D8C2×D6111yescharacteristic
157C2×M16—612no—
158C4⋊Q8—611no—
159#127—611no—
160#124—1222no—
161#121—612no—
162#121—612no—
163#121—1221no—
164#121—1221no—
165#120—1222no—
166C4×D4—611no—
167C4×D4C2×D6111yescharacteristic
168C4×D4C2×D6111yescharacteristic, complemented
169#117—612no—
170#117—1221no—
171#107C2×D6111yescharacteristic, complemented
172#106—612no—
173C4⋊C8—611no—
174#102—612no—
175#102—612no—
176#102—612no—
177#102—612no—
178#102C2×D6111yescharacteristic
179#102C2×D6111yescharacteristic, complemented
180C22⋊C8—612no—
181C4×C8C2×D6111yescharacteristic, complemented
182C24—1222no—
183C2×Q8—1221no—
184C2×D4—611no—
185C2×D4—612no—
186C2×D4—1222no—
187C2×D4—1222no—
188C2×D4—1224no—
189C2×D4—1222no—
190C2×D4—1221no—
191C2×D4—1221no—
192C2×D4—2444no—
193C2×D4—2442no—
194C2×D4C22×D6111yescharacteristic
195C2×D4C22×D6111yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—612no—
199D8—22no—
200D8—2442no—
201M16—2442no—
202C2×C8—612no—
203C2×C8C22×D6111yescharacteristic
204C2×C8C22×D6111yescharacteristic
205C4⋊C4—611no—
206C4⋊C4—612no—
207C4⋊C4—1221no—
208C4⋊C4C22×D6111yescharacteristic
209C4⋊C4C22×D6111yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—21no—
212C22⋊C4—612no—
213C22⋊C4—1222no—
214C22⋊C4—1222no—
215C22⋊C4—1222no—
216C42—1222no—
217C42C22×D6111yescharacteristic
218C23—21no—
219C23—21no—
220C23—612no—
221C23—1222no—
222C23—4882no—
223C23—2444no—
224C23—2444no—
225Q8—4881no—
226D4—21no—
227D4—21no—
228D4—21no—
229D4—1222no—
230D4—1222no—
231D4—1222no—
232D4—4881no—
233D4—4882no—
234D4—2444no—
235D4—2444no—
236D4—2442no—
237D4#1175822212yes—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—612no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4D4×D6111yescharacteristic
247C2×C4D4×D6111yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—21no—
250C8—21no—
251C8—1222no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—1222no—
259C22—1222no—
260C22—1222no—
261C22—4888no—
262C22—2442no—
263C22—2442no—
264C22—2442no—
265C22C2×D4×D6111yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—1222no—
270C4—2442no—
271C4#1451980112yes—
272C4C2×#1175822211yescharacteristic
273C4#1451982311yescharacteristic
274C2—42no—
275C2—81no—
276C2—4882no—
277C2—2442no—
278C2#1684040811yescharacteristic
279C2C2×#1451980111yescharacteristic
280C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×D8×C61C2
socleC22×C61C22×D4
hypercenterC4×D8D61
hypocenterC61#3325
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #16840477C2semidirect
2. D4×D244C2semidirect
3. #16840109C2semidirect
4. #16840089C2semidirect
5. #16840052C2semidirect
6. #16840014C2semidirect
7. #16839957C2semidirect
8. #16839894C2semidirect
9. #16839841C2semidirect
10. #16839765C2semidirect
11. C4×D8×C61C2semidirect
14. C2×#11758199C22semidirect
15. C2×#11758189C22semidirect
16. #14519777C22semidirect
22. #14519748C22semidirect
26. #14519735C22semidirect
27. #14519708C22semidirect
28. C4⋊#92418C22semidirect
29. #14519699C22semidirect
30. #14519699C22semidirect
32. #14519697C22semidirect
33. #14519689C22semidirect
36. C4×D4×C61C22semidirect
37. #107×C61C22semidirect
39. #102×C61C22semidirect
40. C4×C8×C61C22semidirect
149. C4×D8D61semidirect
152. C61#3325semidirect
168. C4×D4C2×D61semidirect
171. #107C2×D61semidirect
179. #102C2×D61semidirect
181. C4×C8C2×D61semidirect