Finite Group Databasebeta

← #20265852

Subgroups — #20265852

Order 6464.

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

normal subgroups only

This group has 248 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#15692248C211yesmaximal, characteristic, complemented
2#15692241C211yesmaximal, characteristic, complemented
3#15692240C211yesmaximal, characteristic, complemented
4#15692240C211yesmaximal, characteristic, complemented
5#15692237C211yesmaximal, characteristic, complemented
6#15692235C211yesmaximal, characteristic, complemented
7#15692233C211yesmaximal, characteristic, complemented
8#15692225C211yesmaximal, characteristic
9C4×D404C211yesmaximal, characteristic, complemented
10#15692217C211yesmaximal, characteristic, complemented
11#15692213C211yesmaximal, characteristic, complemented
12#15692212C211yesmaximal, characteristic, complemented
13C22⋊C4×D101C211yesmaximal, characteristic, complemented
14C22⋊C4×D101C211yesmaximal, characteristic, complemented
15#126×C101C211yesmaximal, characteristic, complemented
16C23×D101C2211yescharacteristic
17C2×Dic202C2211yescharacteristic, complemented
18C2×D404C2211yescharacteristic
19C2×D404C2211yescharacteristic
20C2×C22⋊D101C2211yescharacteristic
21C2×C4×D101C2211yescharacteristic
22C2×C4×D101C2211yescharacteristic
23C2×C4×D101C2211yescharacteristic
24C2×C4×D101C2211yescharacteristic
25C2×C4×D101C2211yescharacteristic, complemented
26C4⋊Dic101C2211yescharacteristic, complemented
27C4⋊Dic101C2211yescharacteristic, complemented
28#13108053C2211yescharacteristic, complemented
29#13108053C2211yescharacteristic, complemented
30#13108053C2211yescharacteristic, complemented
31C22⋊Dic101C2211yescharacteristic
32C22⋊Dic101C2211yescharacteristic
33#13108051C2211yescharacteristic
34#13108051C2211yescharacteristic
35#13108051C2211yescharacteristic
36#13108051C2211yescharacteristic
37#13108051C2211yescharacteristic
38#13108051C2211yescharacteristic
39#13108051C2211yescharacteristic, complemented
40#13108051C2211yescharacteristic, complemented
41#13108051C2211yescharacteristic, complemented
42C4×Dic101C2211yescharacteristic, complemented
43C4×Dic101C2211yescharacteristic, complemented
44C4⋊C4×C101C2211yescharacteristic, complemented
45C4⋊C4×C101C2211yescharacteristic, complemented
46C4⋊C4×C101C2211yescharacteristic, complemented
47C22⋊C4×C101C2211yescharacteristic
48C22⋊C4×C101C2211yescharacteristic
49C22⋊C4×C101C2211yescharacteristic
50C42×C101C2211yescharacteristic, complemented
51C23×C101C2311yescharacteristic
52C22×D101—22no—
53C22×D101—22no—
54C22×D101—41no—
55C22×D101C2311yescharacteristic
56C22×D101C2311yescharacteristic
57C22×D101C2311yescharacteristic
58C2×C4×C101C2311yescharacteristic
59C2×C4×C101C2311yescharacteristic
60C2×C4×C101C2311yescharacteristic
61C2×C4×C101C2311yescharacteristic
62C2×C4×C101C2311yescharacteristic
63C2×C4×C101C2311yescharacteristic
64C22⋊D101—41no—
65C2×Dic101C2311yescharacteristic
66C2×Dic101C2311yescharacteristic
67C2×Dic101C2311yescharacteristic
68C2×Dic101C2311yescharacteristic
69C2×Dic101C2311yescharacteristic
70D404—22no—
71D404—22no—
72C4×D101—22no—
73C4×D101—22no—
74C4×D101—41no—
75C4×D101—41no—
76C4×D101—41no—
77Dic202—41no—
78C22×C101—21no—
79C22×C101—21no—
80C22×C101—21no—
81C22×C101C2411yescharacteristic
82C2×D101—21no—
83C2×D101—21no—
84C2×D101—21no—
85C2×D101—21no—
86C2×D101—21no—
87C2×D101—21no—
88C2×D101—21no—
89C2×D101—44no—
90C2×D101#4112yes—
91C2×D101#4112yes—
92C4×C101—21no—
93C4×C101—21no—
94C4×C101—21no—
95C4×C101—21no—
96C4×C101—21no—
97C4×C101—21no—
98Dic101—21no—
99Dic101—21no—
100Dic101—21no—
101Dic101—21no—
102Dic101—21no—
103C2×C101—41no—
104C2×C101C2×#4111yescharacteristic
105C2×C101C2×#4111yescharacteristic
106C2×C101H(5,𝔽2)11yescharacteristic
107D101—22no—
108D101—22no—
109D101—41no—
110C101#55111yescharacteristic, complemented, Sylow
111#551—1011nomaximal, Sylow
112#126—1011no—
113#126D10111yescharacteristic, complemented
114#124—1011no—
115#123—1011no—
116#123—1011no—
117#123—1011no—
118C22⋊Q8—1011no—
119C22⋊Q8—1011no—
120#120—1011no—
121C4×D4—1011no—
122C4×D4—1011no—
123#117—1011no—
124#117—1011no—
125C2×C22⋊C4—1011no—
126C2×C22⋊C4—1011no—
127C24—1011no—
128C2×Q8—1011no—
129C2×D4—1011no—
130C2×D4—1011no—
131C2×D4—1011no—
132C22×C4—1011no—
133C22×C4—1011no—
134C22×C4—1011no—
135C22×C4—1011no—
136C22×C4—1011no—
137C4⋊C4—1011no—
138C4⋊C4—1011no—
139C4⋊C4—1011no—
140C4⋊C4—1011no—
141C4⋊C4—1011no—
142C4⋊C4C2×D10111yescharacteristic, complemented
143C4⋊C4C2×D10111yescharacteristic, complemented
144C4⋊C4C2×D10111yescharacteristic, complemented
145C22⋊C4—1011no—
146C22⋊C4—1011no—
147C22⋊C4—1011no—
148C22⋊C4—1011no—
149C22⋊C4—1011no—
150C22⋊C4—1011no—
151C22⋊C4—1011no—
152C22⋊C4—1011no—
153C22⋊C4—1011no—
154C22⋊C4—1011no—
155C22⋊C4—1011no—
156C22⋊C4C2×D10111yescharacteristic
157C22⋊C4C2×D10111yescharacteristic
158C22⋊C4C2×D10111yescharacteristic
159C42—1011no—
160C42—1011no—
161C42C2×D10111yescharacteristic, complemented
162C23—1011no—
163C23—1011no—
164C23—1011no—
165C23—4041no—
166C23—2022no—
167C23—2022no—
168C23C22×D10111yescharacteristic
169Q8—4041no—
170D4—4041no—
171D4—2022no—
172D4—2022no—
173C2×C4—1011no—
174C2×C4—1011no—
175C2×C4—1011no—
176C2×C4—1011no—
177C2×C4—1011no—
178C2×C4—4041no—
179C2×C4—4041no—
180C2×C4—4041no—
181C2×C4—2022no—
182C2×C4—2022no—
183C2×C4C22×D10111yescharacteristic
184C2×C4C22×D10111yescharacteristic
185C2×C4C22×D10111yescharacteristic
186C2×C4C22×D10111yescharacteristic
187C2×C4C22×D10111yescharacteristic
188C2×C4C22×D10111yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—1012no—
193C22—1012no—
194C22—4044no—
195C22—2021no—
196C22—2021no—
197C22—2021no—
198C22—2021no—
199C22—2021no—
200C22—2021no—
201C22—2021no—
202C22C23×D10111yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—2021no—
210C4—2021no—
211C4—2021no—
212C4—2021no—
213C4—2021no—
214C2—41no—
215C2—4041no—
216C2—2022no—
217C2—2022no—
218C2#41×D10111yescharacteristic
219C2#41×D10111yescharacteristic
220C2#1569230111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D101
commutator, socleC22×C101C24
Fitting#126×C101C2
hypercenter#126D101
hypocenterC101#551
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #15692248C2semidirect
2. #15692241C2semidirect
3. #15692240C2semidirect
4. #15692240C2semidirect
5. #15692237C2semidirect
6. #15692235C2semidirect
7. #15692233C2semidirect
9. C4×D404C2semidirect
10. #15692217C2semidirect
11. #15692213C2semidirect
12. #15692212C2semidirect
13. C22⋊C4×D101C2semidirect
14. C22⋊C4×D101C2semidirect
15. #126×C101C2semidirect
17. C2×Dic202C22semidirect
25. C2×C4×D101C22semidirect
26. C4⋊Dic101C22semidirect
27. C4⋊Dic101C22semidirect
28. #13108053C22semidirect
29. #13108053C22semidirect
30. #13108053C22semidirect
39. #13108051C22semidirect
40. #13108051C22semidirect
41. #13108051C22semidirect
42. C4×Dic101C22semidirect
43. C4×Dic101C22semidirect
44. C4⋊C4×C101C22semidirect
45. C4⋊C4×C101C22semidirect
46. C4⋊C4×C101C22semidirect
50. C42×C101C22semidirect
110. C101#551semidirect
113. #126D101semidirect
142. C4⋊C4C2×D101semidirect
143. C4⋊C4C2×D101semidirect
144. C4⋊C4C2×D101semidirect
161. C42C2×D101semidirect