Finite Group Databasebeta

← #20265816

Subgroups — #20265816

Order 6464.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#13108073C211yesmaximal, characteristic, complemented
2C2×D4×D101C211yesmaximal, characteristic, complemented
3#15692241C211yesmaximal, characteristic, complemented
4#15692240C211yesmaximal, characteristic, complemented
5#15692236C211yesmaximal, characteristic, complemented
6#15692233C211yesmaximal, characteristic, complemented
7#15692228C211yesmaximal, characteristic, complemented
8#15692227C211yesmaximal, characteristic, complemented
9#15692223C211yesmaximal, characteristic, complemented
10#15692223C211yesmaximal, characteristic, complemented
11C4×C22⋊D101C211yesmaximal, characteristic, complemented
12#15692215C211yesmaximal, characteristic, complemented
13C2×#13108051C211yesmaximal, characteristic, complemented
14C22⋊C4×D101C211yesmaximal, characteristic, complemented
15#121×C101C211yesmaximal, characteristic, complemented
16C23×D101C2211yescharacteristic
17C23×D101C2211yescharacteristic
18#13108073—24no—
19C2×Dic202C2211yescharacteristic, complemented
20C2×D404C2211yescharacteristic
21C2×C22⋊D101C2211yescharacteristic
22C2×C22⋊D101C2211yescharacteristic
23C2×C22⋊D101C2211yescharacteristic
24C2×C22⋊D101C2211yescharacteristic, complemented
25C2×C22⋊D101C2211yescharacteristic, complemented
26D4×D101—24no—
27C22×Dic101C2211yescharacteristic, complemented
28C22×Dic101C2211yescharacteristic, complemented
29C2×C4×D101C2211yescharacteristic
30C2×C4×D101C2211yescharacteristic, complemented
31C2×C4×D101C2211yescharacteristic, complemented
32#13108053C2211yescharacteristic, complemented
33#13108053C2211yescharacteristic, complemented
34#13108053C2211yescharacteristic, complemented
35C22⋊Dic101C2211yescharacteristic, complemented
36C22⋊Dic101C2211yescharacteristic, complemented
37C22⋊Dic101C2211yescharacteristic, complemented
38#13108051C2211yescharacteristic
39#13108051C2211yescharacteristic
40#13108051C2211yescharacteristic
41#13108051C2211yescharacteristic, complemented
42#13108051C2211yescharacteristic, complemented
43#13108051C2211yescharacteristic, complemented
44#13108051C2211yescharacteristic, complemented
45C4×Dic101C2211yescharacteristic, complemented
46C2×D4×C101C2211yescharacteristic
47C2×D4×C101C2211yescharacteristic, complemented
48C2×D4×C101C2211yescharacteristic, complemented
49C22×C4×C101C2211yescharacteristic, complemented
50C4⋊C4×C101C2211yescharacteristic, complemented
51C22⋊C4×C101C2211yescharacteristic, complemented
52C22⋊C4×C101C2211yescharacteristic, complemented
53C23×C101C2311yescharacteristic
54C23×C101C2311yescharacteristic
55C23×C101C2311yescharacteristic
56C22×D101—22no—
57C22×D101—22no—
58C22×D101—22no—
59C22×D101—22no—
60C22×D101—41no—
61C22×D101—41no—
62C22×D101C2311yescharacteristic
63C22×D101C2311yescharacteristic
64C22×D101C2311yescharacteristic
65D4×C101—22no—
66D4×C101—22no—
67D4×C101—41no—
68C2×C4×C101—41no—
69C2×C4×C101C2311yescharacteristic
70C2×C4×C101C2311yescharacteristic
71C2×C4×C101C2311yescharacteristic
72C2×C4×C101C2311yescharacteristic
73C22⋊D101—22no—
74C22⋊D101—22no—
75C22⋊D101—22no—
76C22⋊D101—41no—
77C22⋊D101D414yescomplemented
78C2×Dic101—22no—
79C2×Dic101—22no—
80C2×Dic101C2311yescharacteristic
81C2×Dic101C2311yescharacteristic
82C2×Dic101C2311yescharacteristic
83C2×Dic101C2311yescharacteristic
84C2×Dic101C2311yescharacteristic
85D404—22no—
86C4×D101—22no—
87C4×D101—22no—
88C4×D101—41no—
89Dic202—22no—
90C22×C101—21no—
91C22×C101—21no—
92C22×C101—21no—
93C22×C101—21no—
94C22×C101—21no—
95C22×C101—21no—
96C22×C101—21no—
97C22×C101—21no—
98C22×C101C2×D412yes—
99C22×C101C2411yescharacteristic
100C2×D101—21no—
101C2×D101—21no—
102C2×D101—21no—
103C2×D101—21no—
104C2×D101—21no—
105C2×D101—21no—
106C2×D101—21no—
107C2×D101—44no—
108C2×D101—44no—
109C2×D101C2×D412yes—
110C2×D101#4112yescomplemented
111C4×C101—21no—
112C4×C101—21no—
113C4×C101—21no—
114C4×C101—21no—
115Dic101—21no—
116Dic101—21no—
117Dic101—21no—
118Dic101—21no—
119Dic101C2×D412yes—
120C2×C101—22no—
121C2×C101—41no—
122C2×C101—41no—
123C2×C101C22×D411yescharacteristic
124C2×C101C2×#4111yescharacteristic
125C2×C101H(5,𝔽2)11yescharacteristic
126D101—22no—
127D101—22no—
128D101—41no—
129C101#54611yescharacteristic, complemented, Sylow
130#546—1011nomaximal, Sylow
131C2×#41—1011no—
132C22×D4—1011no—
133#124—1011no—
134#123—1011no—
135#123—1011no—
136C22⋊Q8—1011no—
137#121—1011no—
138#121—1011no—
139#121D10111yescharacteristic, complemented
140#120—1011no—
141#120—1011no—
142C4×D4—1011no—
143C4×D4—1011no—
144C2×C22⋊C4—1011no—
145C2×C22⋊C4—1011no—
146C24—1011no—
147C24—1011no—
148#41—2024no—
149C2×Q8—1011no—
150C2×D4—1011no—
151C2×D4—1011no—
152C2×D4—1011no—
153C2×D4—1011no—
154C2×D4—1011no—
155C2×D4—1011no—
156C2×D4—2024no—
157C2×D4C2×D10111yescharacteristic
158C2×D4C2×D10111yescharacteristic, complemented
159C2×D4C2×D10111yescharacteristic, complemented
160C22×C4—1011no—
161C22×C4—1011no—
162C22×C4—1011no—
163C22×C4—1011no—
164C22×C4—1011no—
165C22×C4C2×D10111yescharacteristic, complemented
166C4⋊C4—1011no—
167C4⋊C4—1011no—
168C4⋊C4—1011no—
169C4⋊C4C2×D10111yescharacteristic, complemented
170C22⋊C4—1011no—
171C22⋊C4—1011no—
172C22⋊C4—1011no—
173C22⋊C4—1011no—
174C22⋊C4—1011no—
175C22⋊C4—1011no—
176C22⋊C4—1011no—
177C22⋊C4—1011no—
178C22⋊C4—1011no—
179C22⋊C4—1011no—
180C22⋊C4C2×D10111yescharacteristic, complemented
181C22⋊C4C2×D10111yescharacteristic, complemented
182C42—1011no—
183C23—1011no—
184C23—1011no—
185C23—1011no—
186C23—4041no—
187C23—4041no—
188C23—2022no—
189C23—2022no—
190C23—2022no—
191C23—2022no—
192C23C22×D10111yescharacteristic
193C23C22×D10111yescharacteristic
194C23C22×D10111yescharacteristic
195Q8—2022no—
196D4—22no—
197D4—22no—
198D4—41no—
199D4—1014no—
200D4—4041no—
201D4—2022no—
202D4—2022no—
203D4—2022no—
204D4—2022no—
205C2×C4—41no—
206C2×C4—1011no—
207C2×C4—1011no—
208C2×C4—1011no—
209C2×C4—1011no—
210C2×C4—1011no—
211C2×C4—4041no—
212C2×C4—2022no—
213C2×C4—2022no—
214C2×C4—2022no—
215C2×C4—2022no—
216C2×C4C22×D10111yescharacteristic
217C2×C4C22×D10111yescharacteristic
218C2×C4C22×D10111yescharacteristic
219C2×C4C22×D10111yescharacteristic
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—1012no—
229C22—1012no—
230C22—4044no—
231C22—4044no—
232C22—2021no—
233C22—2021no—
234C22—2021no—
235C22—2021no—
236C22—2021no—
237C22—2021no—
238C22—2021no—
239C22D4×D10112yes—
240C22C23×D10111yescharacteristic
241C4—21no—
242C4—21no—
243C4—21no—
244C4—21no—
245C4—1012no—
246C4—2021no—
247C4—2021no—
248C4—2021no—
249C4—2021no—
250C2—22no—
251C2—41no—
252C2—41no—
253C2—4041no—
254C2—2022no—
255C2—2022no—
256C2C2×D4×D10111yescharacteristic
257C2#41×D10111yescharacteristic
258C2#1569230011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D101
commutator, socleC22×C101C24
Fitting#121×C101C2
hypercenter#121D101
hypocenterC101#546
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#13108073C2semidirect
2. C2×D4×D101C2semidirect
3. #15692241C2semidirect
4. #15692240C2semidirect
5. #15692236C2semidirect
6. #15692233C2semidirect
7. #15692228C2semidirect
8. #15692227C2semidirect
9. #15692223C2semidirect
10. #15692223C2semidirect
11. C4×C22⋊D101C2semidirect
12. #15692215C2semidirect
13. C2×#13108051C2semidirect
14. C22⋊C4×D101C2semidirect
15. #121×C101C2semidirect
19. C2×Dic202C22semidirect
24. C2×C22⋊D101C22semidirect
25. C2×C22⋊D101C22semidirect
27. C22×Dic101C22semidirect
28. C22×Dic101C22semidirect
30. C2×C4×D101C22semidirect
31. C2×C4×D101C22semidirect
32. #13108053C22semidirect
33. #13108053C22semidirect
34. #13108053C22semidirect
35. C22⋊Dic101C22semidirect
36. C22⋊Dic101C22semidirect
37. C22⋊Dic101C22semidirect
41. #13108051C22semidirect
42. #13108051C22semidirect
43. #13108051C22semidirect
44. #13108051C22semidirect
45. C4×Dic101C22semidirect
47. C2×D4×C101C22semidirect
48. C2×D4×C101C22semidirect
49. C22×C4×C101C22semidirect
50. C4⋊C4×C101C22semidirect
51. C22⋊C4×C101C22semidirect
52. C22⋊C4×C101C22semidirect
77. C22⋊D101D4semidirect
110. C2×D101#41semidirect
129. C101#546semidirect
139. #121D101semidirect
158. C2×D4C2×D101semidirect
159. C2×D4C2×D101semidirect
165. C22×C4C2×D101semidirect
169. C4⋊C4C2×D101semidirect
180. C22⋊C4C2×D101semidirect
181. C22⋊C4C2×D101semidirect