Finite Group Databasebeta

← #20268373

Subgroups — #20268373

Order 6592.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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#15693016C211yesmaximal, characteristic, complemented
2#15693014C211yesmaximal, characteristic, complemented
3#15693008C211yesmaximal, characteristic, complemented
4#15693007C211yesmaximal, characteristic, complemented
5#15693004C211yesmaximal, characteristic, complemented
6#15693002C211yesmaximal, characteristic, complemented
7#15692999C211yesmaximal, characteristic, complemented
8#15692993C211yesmaximal, characteristic, complemented
9#15692992C211yesmaximal, characteristic, complemented
10#15692989C211yesmaximal, characteristic, complemented
11#15692989C211yesmaximal, characteristic, complemented
12C4×C22⋊D103C211yesmaximal, characteristic, complemented
13(C22⋊D103)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D103C211yesmaximal, characteristic, complemented
15#121×C103C211yesmaximal, characteristic, complemented
16C23×D103C2211yescharacteristic
17C2×Dic206C2211yescharacteristic, complemented
18C2×C22⋊D103C2211yescharacteristic
19C2×C22⋊D103C2211yescharacteristic
20C2×C22⋊D103C2211yescharacteristic
21C2×C22⋊D103C2211yescharacteristic
22C22×Dic103C2211yescharacteristic, complemented
23C2×C4×D103C2211yescharacteristic
24C2×C4×D103C2211yescharacteristic
25C4⋊Dic103C2211yescharacteristic, complemented
26Dic103⋊C4C2211yescharacteristic, complemented
27Dic103⋊C4C2211yescharacteristic, complemented
28Dic103⋊C4C2211yescharacteristic, complemented
29Dic103⋊C4C2211yescharacteristic, complemented
30C22⋊Dic103C2211yescharacteristic
31C22⋊Dic103C2211yescharacteristic
32C22⋊Dic103C2211yescharacteristic
33C22⋊Dic103C2211yescharacteristic, complemented
34C22⋊Dic103C2211yescharacteristic, complemented
35C22⋊Dic103C2211yescharacteristic, complemented
36(C2×D103)⋊C4C2211yescharacteristic
37(C2×D103)⋊C4C2211yescharacteristic
38(C2×D103)⋊C4C2211yescharacteristic
39(C2×D103)⋊C4C2211yescharacteristic
40(C2×D103)⋊C4C2211yescharacteristic
41(C2×D103)⋊C4C2211yescharacteristic
42C4×Dic103C2211yescharacteristic, complemented
43C4×Dic103C2211yescharacteristic, complemented
44C2×D4×C103C2211yescharacteristic
45C2×D4×C103C2211yescharacteristic
46C2×D4×C103C2211yescharacteristic, complemented
47C22×C4×C103C2211yescharacteristic, complemented
48C4⋊C4×C103C2211yescharacteristic, complemented
49C22⋊C4×C103C2211yescharacteristic
50C22⋊C4×C103C2211yescharacteristic, complemented
51C23×C103C2311yescharacteristic
52C23×C103C2311yescharacteristic
53C23×C103C2311yescharacteristic
54C22×D103—22no—
55C22×D103—41no—
56C22×D103—41no—
57C22×D103C2311yescharacteristic
58C22×D103C2311yescharacteristic
59D4×C103—41no—
60D4×C103—41no—
61D4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103C2311yescharacteristic
64C2×C4×C103C2311yescharacteristic
65C2×C4×C103C2311yescharacteristic
66C2×C4×C103C2311yescharacteristic
67C22⋊D103—22no—
68C22⋊D103—22no—
69C22⋊D103—41no—
70C22⋊D103—41no—
71C2×Dic103—41no—
72C2×Dic103C2311yescharacteristic
73C2×Dic103C2311yescharacteristic
74C2×Dic103C2311yescharacteristic
75C2×Dic103C2311yescharacteristic
76C2×Dic103C2311yescharacteristic
77C2×Dic103C2311yescharacteristic
78C4×D103—41no—
79C4×D103—41no—
80Dic206—41no—
81C22×C103—21no—
82C22×C103—21no—
83C22×C103—21no—
84C22×C103—21no—
85C22×C103—21no—
86C22×C103—21no—
87C22×C103—21no—
88C22×C103—21no—
89C22×C103—21no—
90C22×C103C2411yescharacteristic
91C2×D103—21no—
92C2×D103—21no—
93C2×D103—21no—
94C2×D103—21no—
95C2×D103—21no—
96C2×D103—44no—
97C2×D103#4112yes—
98C4×C103—21no—
99C4×C103—21no—
100C4×C103—21no—
101C4×C103—21no—
102Dic103—21no—
103Dic103—21no—
104Dic103—21no—
105Dic103—21no—
106Dic103—21no—
107Dic103—21no—
108C2×C103—41no—
109C2×C103—41no—
110C2×C103—41no—
111C2×C103C2×#4111yescharacteristic
112C2×C103H(5,𝔽2)11yescharacteristic
113C2×C103H(5,𝔽2)11yescharacteristic
114D103—22no—
115D103—41no—
116C103#53811yescharacteristic, complemented, Sylow
117#538—1031nomaximal, Sylow
118#126—1031no—
119#126—1031no—
120#124—1031no—
121#124—1031no—
122#123—1031no—
123#123—1031no—
124C22⋊Q8—1031no—
125#121—1031no—
126#121—1031no—
127#121D10311yescharacteristic, complemented
128#120—1031no—
129#120—1031no—
130C4×D4—1031no—
131C4×D4—1031no—
132C2×C22⋊C4—1031no—
133C24—1031no—
134C2×Q8—1031no—
135C2×D4—1031no—
136C2×D4—1031no—
137C2×D4—1031no—
138C2×D4—1031no—
139C2×D4C2×D10311yescharacteristic
140C2×D4C2×D10311yescharacteristic
141C2×D4C2×D10311yescharacteristic, complemented
142C22×C4—1031no—
143C22×C4—1031no—
144C22×C4—1031no—
145C22×C4C2×D10311yescharacteristic, complemented
146C4⋊C4—1031no—
147C4⋊C4—1031no—
148C4⋊C4—1031no—
149C4⋊C4—1031no—
150C4⋊C4—1031no—
151C4⋊C4C2×D10311yescharacteristic, complemented
152C22⋊C4—1031no—
153C22⋊C4—1031no—
154C22⋊C4—1031no—
155C22⋊C4—1031no—
156C22⋊C4—1031no—
157C22⋊C4—1031no—
158C22⋊C4—1031no—
159C22⋊C4—1031no—
160C22⋊C4—1031no—
161C22⋊C4—1031no—
162C22⋊C4—1031no—
163C22⋊C4—1031no—
164C22⋊C4C2×D10311yescharacteristic
165C22⋊C4C2×D10311yescharacteristic, complemented
166C42—1031no—
167C42—1031no—
168C23—1031no—
169C23—1031no—
170C23—4121no—
171C23—4121no—
172C23—2062no—
173C23C22×D10311yescharacteristic
174C23C22×D10311yescharacteristic
175C23C22×D10311yescharacteristic
176Q8—4121no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—4121no—
181D4—4121no—
182D4—2062no—
183D4—2062no—
184C2×C4—41no—
185C2×C4—1031no—
186C2×C4—1031no—
187C2×C4—1031no—
188C2×C4—1031no—
189C2×C4—1031no—
190C2×C4—1031no—
191C2×C4—4121no—
192C2×C4—4121no—
193C2×C4—4121no—
194C2×C4C22×D10311yescharacteristic
195C2×C4C22×D10311yescharacteristic
196C2×C4C22×D10311yescharacteristic
197C2×C4C22×D10311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—1032no—
208C22—4124no—
209C22—2061no—
210C22—2061no—
211C22—2061no—
212C22—2061no—
213C22—2061no—
214C22C23×D10311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—2061no—
220C4—2061no—
221C4—2061no—
222C4—2061no—
223C4—2061no—
224C4—2061no—
225C2—41no—
226C2—41no—
227C2—41no—
228C2—4121no—
229C2—2062no—
230C2#41×D10311yescharacteristic
231C2#1569306611yescharacteristic
232C2#1569306611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D103
commutator, socleC22×C103C24
Fitting#121×C103C2
hypercenter#121D103
hypocenterC103#538
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #15693016C2semidirect
2. #15693014C2semidirect
3. #15693008C2semidirect
4. #15693007C2semidirect
5. #15693004C2semidirect
6. #15693002C2semidirect
7. #15692999C2semidirect
8. #15692993C2semidirect
9. #15692992C2semidirect
10. #15692989C2semidirect
11. #15692989C2semidirect
12. C4×C22⋊D103C2semidirect
13. (C22⋊D103)⋊C4C2semidirect
14. C22⋊C4×D103C2semidirect
15. #121×C103C2semidirect
17. C2×Dic206C22semidirect
22. C22×Dic103C22semidirect
25. C4⋊Dic103C22semidirect
26. Dic103⋊C4C22semidirect
27. Dic103⋊C4C22semidirect
28. Dic103⋊C4C22semidirect
29. Dic103⋊C4C22semidirect
33. C22⋊Dic103C22semidirect
34. C22⋊Dic103C22semidirect
35. C22⋊Dic103C22semidirect
42. C4×Dic103C22semidirect
43. C4×Dic103C22semidirect
46. C2×D4×C103C22semidirect
47. C22×C4×C103C22semidirect
48. C4⋊C4×C103C22semidirect
50. C22⋊C4×C103C22semidirect
116. C103#538semidirect
127. #121D103semidirect
141. C2×D4C2×D103semidirect
145. C22×C4C2×D103semidirect
151. C4⋊C4C2×D103semidirect
165. C22⋊C4C2×D103semidirect