Finite Group Databasebeta

← #20265760

Subgroups — #20265760

Order 6464.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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#15692250C211yesmaximal, characteristic, complemented
2#15692249C211yesmaximal, characteristic, complemented
3#15692243C211yesmaximal, characteristic, complemented
4#15692241C211yesmaximal, characteristic, complemented
5#15692240C211yesmaximal, characteristic, complemented
6#15692238C211yesmaximal, characteristic, complemented
7#15692232C211yesmaximal, characteristic, complemented
8#15692229C211yesmaximal, characteristic, complemented
9#15692228C211yesmaximal, characteristic, complemented
10#15692227C211yesmaximal, characteristic, complemented
11#15692225C211yesmaximal, characteristic, complemented
12#15692223C211yesmaximal, characteristic, complemented
13C4×C22⋊D101C211yesmaximal, characteristic, complemented
14C2×#13108051C211yesmaximal, characteristic, complemented
15C4×D4×C101C211yesmaximal, characteristic, complemented
16C23×D101C2211yescharacteristic
17C2×Dic202C2211yescharacteristic, complemented
18C2×D404C2211yescharacteristic
19C2×D404C2211yescharacteristic
20C2×C22⋊D101C2211yescharacteristic
21C2×C22⋊D101C2211yescharacteristic
22C2×C22⋊D101C2211yescharacteristic
23C2×C22⋊D101C2211yescharacteristic, complemented
24C22×Dic101C2211yescharacteristic
25C2×C4×D101C2211yescharacteristic, complemented
26C4⋊Dic101C2211yescharacteristic, complemented
27#13108053C2211yescharacteristic, complemented
28#13108053C2211yescharacteristic, complemented
29#13108053C2211yescharacteristic, complemented
30#13108053C2211yescharacteristic, complemented
31C22⋊Dic101C2211yescharacteristic
32C22⋊Dic101C2211yescharacteristic, complemented
33#13108051C2211yescharacteristic
34#13108051C2211yescharacteristic
35#13108051C2211yescharacteristic
36#13108051C2211yescharacteristic
37#13108051C2211yescharacteristic
38#13108051C2211yescharacteristic
39#13108051C2211yescharacteristic
40#13108051C2211yescharacteristic
41#13108051C2211yescharacteristic, complemented
42#13108051C2211yescharacteristic, complemented
43C4×Dic101C2211yescharacteristic, complemented
44C2×D4×C101C2211yescharacteristic
45C22×C4×C101C2211yescharacteristic
46C22×C4×C101C2211yescharacteristic, complemented
47C4⋊C4×C101C2211yescharacteristic, complemented
48C22⋊C4×C101C2211yescharacteristic
49C22⋊C4×C101C2211yescharacteristic, complemented
50C42×C101C2211yescharacteristic, complemented
51C23×C101C2311yescharacteristic
52C23×C101C2311yescharacteristic
53C22×D101—22no—
54C22×D101—41no—
55C22×D101—41no—
56C22×D101C2311yescharacteristic
57C22×D101C2311yescharacteristic
58C22×D101C2311yescharacteristic
59D4×C101—22no—
60C2×C4×C101—41no—
61C2×C4×C101—41no—
62C2×C4×C101C2311yescharacteristic
63C2×C4×C101C2311yescharacteristic
64C2×C4×C101C2311yescharacteristic
65C2×C4×C101C2311yescharacteristic
66C2×C4×C101C2311yescharacteristic
67C22⋊D101—22no—
68C22⋊D101—41no—
69C22⋊D101—41no—
70C22⋊D101—41no—
71C2×Dic101—41no—
72C2×Dic101C2311yescharacteristic
73C2×Dic101C2311yescharacteristic
74C2×Dic101C2311yescharacteristic
75C2×Dic101C2311yescharacteristic
76C2×Dic101C2311yescharacteristic
77D404—41no—
78D404—41no—
79C4×D101—41no—
80Dic202—41no—
81C22×C101—21no—
82C22×C101—21no—
83C22×C101—21no—
84C22×C101—21no—
85C22×C101—21no—
86C22×C101#4112yes—
87C22×C101C2411yescharacteristic
88C2×D101—21no—
89C2×D101—21no—
90C2×D101—21no—
91C2×D101—21no—
92C2×D101—21no—
93C2×D101—21no—
94C2×D101—21no—
95C2×D101—21no—
96C2×D101—21no—
97C2×D101—44no—
98C4×C101—21no—
99C4×C101—21no—
100C4×C101—21no—
101C4×C101—21no—
102C4×C101—21no—
103Dic101—21no—
104Dic101—21no—
105Dic101—21no—
106Dic101—21no—
107Dic101—21no—
108C2×C101—22no—
109C2×C101—41no—
110C2×C101C2×#4111yescharacteristic
111C2×C101H(5,𝔽2)11yescharacteristic
112C2×C101H(5,𝔽2)11yescharacteristic
113D101—41no—
114D101—41no—
115D101—41no—
116C101#53811yescharacteristic, complemented, Sylow
117#538—1011nomaximal, Sylow
118#126—1011no—
119#126—1011no—
120#124—1011no—
121#124—1011no—
122#123—1011no—
123#123—1011no—
124C22⋊Q8—1011no—
125#121—1011no—
126#121—1011no—
127#121—1011no—
128#120—1011no—
129#120—1011no—
130C4×D4—1011no—
131C4×D4D10111yescharacteristic, complemented
132C2×C22⋊C4—1011no—
133C24—1011no—
134C2×Q8—1011no—
135C2×D4—1011no—
136C2×D4—1011no—
137C2×D4—1011no—
138C2×D4—1011no—
139C2×D4—1011no—
140C2×D4—1011no—
141C2×D4C2×D10111yescharacteristic
142C22×C4—1011no—
143C22×C4—1011no—
144C22×C4C2×D10111yescharacteristic
145C22×C4C2×D10111yescharacteristic, complemented
146C4⋊C4—1011no—
147C4⋊C4—1011no—
148C4⋊C4—1011no—
149C4⋊C4—1011no—
150C4⋊C4—1011no—
151C4⋊C4C2×D10111yescharacteristic, complemented
152C22⋊C4—1011no—
153C22⋊C4—1011no—
154C22⋊C4—1011no—
155C22⋊C4—1011no—
156C22⋊C4—1011no—
157C22⋊C4—1011no—
158C22⋊C4—1011no—
159C22⋊C4—1011no—
160C22⋊C4—1011no—
161C22⋊C4—1011no—
162C22⋊C4—1011no—
163C22⋊C4—1011no—
164C22⋊C4C2×D10111yescharacteristic
165C22⋊C4C2×D10111yescharacteristic, complemented
166C42—1011no—
167C42C2×D10111yescharacteristic, complemented
168C23—1011no—
169C23—1011no—
170C23—1011no—
171C23—4041no—
172C23—4041no—
173C23—2022no—
174C23C22×D10111yescharacteristic
175C23C22×D10111yescharacteristic
176Q8—4041no—
177D4—22no—
178D4—4041no—
179D4—4041no—
180D4—4041no—
181D4—4041no—
182D4—4041no—
183D4—2022no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1011no—
187C2×C4—1011no—
188C2×C4—1011no—
189C2×C4—1011no—
190C2×C4—1011no—
191C2×C4—4041no—
192C2×C4—4041no—
193C2×C4C22×D10111yescharacteristic
194C2×C4C22×D10111yescharacteristic
195C2×C4C22×D10111yescharacteristic
196C2×C4C22×D10111yescharacteristic
197C2×C4C22×D10111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—4044no—
204C22—2021no—
205C22—2021no—
206C22—2021no—
207C22—2021no—
208C22—2021no—
209C22—2021no—
210C22—2021no—
211C22—2021no—
212C22—2021no—
213C22#1310807412yes—
214C22C23×D10111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—2021no—
221C4—2021no—
222C4—2021no—
223C4—2021no—
224C4—2021no—
225C2—22no—
226C2—41no—
227C2—4041no—
228C2—4041no—
229C2—4041no—
230C2C2×#1310807411yescharacteristic
231C2#1569230011yescharacteristic
232C2#1569230111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D101
commutator, socleC22×C101C24
FittingC4×D4×C101C2
hypercenterC4×D4D101
hypocenterC101#538
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #15692250C2semidirect
2. #15692249C2semidirect
3. #15692243C2semidirect
4. #15692241C2semidirect
5. #15692240C2semidirect
6. #15692238C2semidirect
7. #15692232C2semidirect
8. #15692229C2semidirect
9. #15692228C2semidirect
10. #15692227C2semidirect
11. #15692225C2semidirect
12. #15692223C2semidirect
13. C4×C22⋊D101C2semidirect
14. C2×#13108051C2semidirect
15. C4×D4×C101C2semidirect
17. C2×Dic202C22semidirect
23. C2×C22⋊D101C22semidirect
25. C2×C4×D101C22semidirect
26. C4⋊Dic101C22semidirect
27. #13108053C22semidirect
28. #13108053C22semidirect
29. #13108053C22semidirect
30. #13108053C22semidirect
32. C22⋊Dic101C22semidirect
41. #13108051C22semidirect
42. #13108051C22semidirect
43. C4×Dic101C22semidirect
46. C22×C4×C101C22semidirect
47. C4⋊C4×C101C22semidirect
49. C22⋊C4×C101C22semidirect
50. C42×C101C22semidirect
116. C101#538semidirect
131. C4×D4D101semidirect
145. C22×C4C2×D101semidirect
151. C4⋊C4C2×D101semidirect
165. C22⋊C4C2×D101semidirect
167. C42C2×D101semidirect