Finite Group Databasebeta

← #20268380

Subgroups — #20268380

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#15693009C211yesmaximal, characteristic, complemented
3#15693007C211yesmaximal, characteristic, complemented
4#15693006C211yesmaximal, characteristic, complemented
5#15693003C211yesmaximal, characteristic, complemented
6#15692999C211yesmaximal, characteristic, complemented
7#15692996C211yesmaximal, characteristic, complemented
8#15692996C211yesmaximal, characteristic, complemented
9#15692994C211yesmaximal, characteristic, complemented
10#15692991C211yesmaximal, characteristic, complemented
11#15692991C211yesmaximal, characteristic, complemented
12C4×D412C211yesmaximal, characteristic, complemented
13#15692983C211yesmaximal, characteristic, complemented
14C22⋊C4×D103C211yesmaximal, characteristic, complemented
15#126×C103C211yesmaximal, characteristic, complemented
16C23×D103C2211yescharacteristic
17C2×Dic206C2211yescharacteristic, complemented
18C2×D412C2211yescharacteristic
19C2×D412C2211yescharacteristic
20C2×D412C2211yescharacteristic
21C2×D412C2211yescharacteristic
22C2×D412C2211yescharacteristic, complemented
23C2×C22⋊D103C2211yescharacteristic
24C2×C22⋊D103C2211yescharacteristic
25C2×C4×D103C2211yescharacteristic
26C2×C4×D103C2211yescharacteristic
27C2×C4×D103C2211yescharacteristic, complemented
28C2×C4×D103C2211yescharacteristic, complemented
29C4⋊Dic103C2211yescharacteristic, complemented
30Dic103⋊C4C2211yescharacteristic, complemented
31Dic103⋊C4C2211yescharacteristic, complemented
32C22⋊Dic103C2211yescharacteristic
33(C2×D103)⋊C4C2211yescharacteristic
34(C2×D103)⋊C4C2211yescharacteristic
35(C2×D103)⋊C4C2211yescharacteristic
36(C2×D103)⋊C4C2211yescharacteristic
37(C2×D103)⋊C4C2211yescharacteristic
38(C2×D103)⋊C4C2211yescharacteristic
39(C2×D103)⋊C4C2211yescharacteristic, complemented
40(C2×D103)⋊C4C2211yescharacteristic, complemented
41(C2×D103)⋊C4C2211yescharacteristic, complemented
42(C2×D103)⋊C4C2211yescharacteristic, complemented
43C4×Dic103C2211yescharacteristic, complemented
44C4⋊C4×C103C2211yescharacteristic, complemented
45C4⋊C4×C103C2211yescharacteristic, complemented
46C4⋊C4×C103C2211yescharacteristic, complemented
47C22⋊C4×C103C2211yescharacteristic
48C22⋊C4×C103C2211yescharacteristic
49C22⋊C4×C103C2211yescharacteristic
50C42×C103C2211yescharacteristic, complemented
51C23×C103C2311yescharacteristic
52C22×D103—22no—
53C22×D103—41no—
54C22×D103—41no—
55C22×D103C2311yescharacteristic
56C22×D103C2311yescharacteristic
57C22×D103C2311yescharacteristic
58C22×D103C2311yescharacteristic
59C2×C4×C103C2311yescharacteristic
60C2×C4×C103C2311yescharacteristic
61C2×C4×C103C2311yescharacteristic
62C2×C4×C103C2311yescharacteristic
63C2×C4×C103C2311yescharacteristic
64C2×C4×C103C2311yescharacteristic
65C22⋊D103—41no—
66C22⋊D103—41no—
67C2×Dic103C2311yescharacteristic
68C2×Dic103C2311yescharacteristic
69C2×Dic103C2311yescharacteristic
70C2×Dic103C2311yescharacteristic
71D412—22no—
72D412—22no—
73D412—41no—
74D412—41no—
75D412—41no—
76C4×D103—41no—
77C4×D103—41no—
78C4×D103—41no—
79C4×D103—41no—
80Dic206—41no—
81C22×C103—21no—
82C22×C103—21no—
83C22×C103—21no—
84C22×C103C2411yescharacteristic
85C2×D103—21no—
86C2×D103—21no—
87C2×D103—21no—
88C2×D103—21no—
89C2×D103—21no—
90C2×D103—21no—
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—
102C4×C103—21no—
103C4×C103—21no—
104Dic103—21no—
105Dic103—21no—
106Dic103—21no—
107Dic103—21no—
108C2×C103—41no—
109C2×C103C2×#4111yescharacteristic
110C2×C103H(5,𝔽2)11yescharacteristic
111C2×C103H(5,𝔽2)11yescharacteristic
112D103—22no—
113D103—41no—
114D103—41no—
115D103—41no—
116C103#53811yescharacteristic, complemented, Sylow
117#538—1031nomaximal, Sylow
118#126—1031no—
119#126D10311yescharacteristic, complemented
120#124—1031no—
121#124—1031no—
122#123—1031no—
123#123—1031no—
124C22⋊Q8—1031no—
125#121—1031no—
126#121—1031no—
127#121—1031no—
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×D4—1031no—
140C2×D4—1031no—
141C2×D4—1031no—
142C22×C4—1031no—
143C22×C4—1031no—
144C22×C4—1031no—
145C22×C4—1031no—
146C4⋊C4—1031no—
147C4⋊C4—1031no—
148C4⋊C4—1031no—
149C4⋊C4C2×D10311yescharacteristic, complemented
150C4⋊C4C2×D10311yescharacteristic, complemented
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⋊C4C2×D10311yescharacteristic
164C22⋊C4C2×D10311yescharacteristic
165C22⋊C4C2×D10311yescharacteristic
166C42—1031no—
167C42C2×D10311yescharacteristic, complemented
168C23—1031no—
169C23—1031no—
170C23—1031no—
171C23—1031no—
172C23—4121no—
173C23—4121no—
174C23—2062no—
175C23C22×D10311yescharacteristic
176Q8—4121no—
177D4—4121no—
178D4—4121no—
179D4—4121no—
180D4—4121no—
181D4—4121no—
182D4—2062no—
183D4—2062no—
184C2×C4—1031no—
185C2×C4—1031no—
186C2×C4—1031no—
187C2×C4—1031no—
188C2×C4—4121no—
189C2×C4—4121no—
190C2×C4—4121no—
191C2×C4—4121no—
192C2×C4C22×D10311yescharacteristic
193C2×C4C22×D10311yescharacteristic
194C2×C4C22×D10311yescharacteristic
195C2×C4C22×D10311yescharacteristic
196C2×C4C22×D10311yescharacteristic
197C2×C4C22×D10311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—1032no—
202C22—4124no—
203C22—2061no—
204C22—2061no—
205C22—2061no—
206C22—2061no—
207C22—2061no—
208C22—2061no—
209C22—2061no—
210C22—2061no—
211C22—2061no—
212C22—2061no—
213C22—2061no—
214C22C23×D10311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—2061no—
222C4—2061no—
223C4—2061no—
224C4—2061no—
225C2—41no—
226C2—4121no—
227C2—4121no—
228C2—4121no—
229C2—2062no—
230C2#41×D10311yescharacteristic
231C2#1569306711yescharacteristic
232C2#1569306711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D103
commutator, socleC22×C103C24
Fitting#126×C103C2
hypercenter#126D103
hypocenterC103#538
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #15693016C2semidirect
2. #15693009C2semidirect
3. #15693007C2semidirect
4. #15693006C2semidirect
5. #15693003C2semidirect
6. #15692999C2semidirect
7. #15692996C2semidirect
8. #15692996C2semidirect
9. #15692994C2semidirect
10. #15692991C2semidirect
11. #15692991C2semidirect
12. C4×D412C2semidirect
13. #15692983C2semidirect
14. C22⋊C4×D103C2semidirect
15. #126×C103C2semidirect
17. C2×Dic206C22semidirect
22. C2×D412C22semidirect
27. C2×C4×D103C22semidirect
28. C2×C4×D103C22semidirect
29. C4⋊Dic103C22semidirect
30. Dic103⋊C4C22semidirect
31. Dic103⋊C4C22semidirect
39. (C2×D103)⋊C4C22semidirect
40. (C2×D103)⋊C4C22semidirect
41. (C2×D103)⋊C4C22semidirect
42. (C2×D103)⋊C4C22semidirect
43. C4×Dic103C22semidirect
44. C4⋊C4×C103C22semidirect
45. C4⋊C4×C103C22semidirect
46. C4⋊C4×C103C22semidirect
50. C42×C103C22semidirect
116. C103#538semidirect
119. #126D103semidirect
149. C4⋊C4C2×D103semidirect
150. C4⋊C4C2×D103semidirect
151. C4⋊C4C2×D103semidirect
167. C42C2×D103semidirect