Finite Group Databasebeta

← #23752794

Subgroups — #23752794

Order 9664.

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#18012734C211yesmaximal, characteristic, complemented
2#18012732C211yesmaximal, characteristic, complemented
3#18012726C211yesmaximal, characteristic, complemented
4#18012725C211yesmaximal, characteristic, complemented
5#18012722C211yesmaximal, characteristic, complemented
6#18012720C211yesmaximal, characteristic, complemented
7#18012717C211yesmaximal, characteristic, complemented
8#18012711C211yesmaximal, characteristic, complemented
9#18012710C211yesmaximal, characteristic, complemented
10#18012707C211yesmaximal, characteristic, complemented
11#18012707C211yesmaximal, characteristic, complemented
12C4×C22⋊D151C211yesmaximal, characteristic, complemented
13(C22⋊D151)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D151C211yesmaximal, characteristic, complemented
15#121×C151C211yesmaximal, characteristic, complemented
16C23×D151C2211yescharacteristic
17C2×Dic302C2211yescharacteristic, complemented
18C2×C22⋊D151C2211yescharacteristic
19C2×C22⋊D151C2211yescharacteristic
20C2×C22⋊D151C2211yescharacteristic
21C2×C22⋊D151C2211yescharacteristic
22C22×Dic151C2211yescharacteristic, complemented
23C2×C4×D151C2211yescharacteristic
24C2×C4×D151C2211yescharacteristic
25C4⋊Dic151C2211yescharacteristic, complemented
26Dic151⋊C4C2211yescharacteristic, complemented
27Dic151⋊C4C2211yescharacteristic, complemented
28Dic151⋊C4C2211yescharacteristic, complemented
29Dic151⋊C4C2211yescharacteristic, complemented
30C22⋊Dic151C2211yescharacteristic
31C22⋊Dic151C2211yescharacteristic
32C22⋊Dic151C2211yescharacteristic
33C22⋊Dic151C2211yescharacteristic, complemented
34C22⋊Dic151C2211yescharacteristic, complemented
35C22⋊Dic151C2211yescharacteristic, complemented
36(C2×D151)⋊C4C2211yescharacteristic
37(C2×D151)⋊C4C2211yescharacteristic
38(C2×D151)⋊C4C2211yescharacteristic
39(C2×D151)⋊C4C2211yescharacteristic
40(C2×D151)⋊C4C2211yescharacteristic
41(C2×D151)⋊C4C2211yescharacteristic
42C4×Dic151C2211yescharacteristic, complemented
43C4×Dic151C2211yescharacteristic, complemented
44C2×D4×C151C2211yescharacteristic
45C2×D4×C151C2211yescharacteristic
46C2×D4×C151C2211yescharacteristic, complemented
47C22×C4×C151C2211yescharacteristic, complemented
48C4⋊C4×C151C2211yescharacteristic, complemented
49C22⋊C4×C151C2211yescharacteristic
50C22⋊C4×C151C2211yescharacteristic, complemented
51C22×D151—22no—
52C22×D151—41no—
53C22×D151—41no—
54C22×D151C2311yescharacteristic
55C22×D151C2311yescharacteristic
56Dic302—41no—
57C22⋊D151—22no—
58C22⋊D151—22no—
59C22⋊D151—41no—
60C22⋊D151—41no—
61C2×Dic151—41no—
62C2×Dic151C2311yescharacteristic
63C2×Dic151C2311yescharacteristic
64C2×Dic151C2311yescharacteristic
65C2×Dic151C2311yescharacteristic
66C2×Dic151C2311yescharacteristic
67C2×Dic151C2311yescharacteristic
68C4×D151—41no—
69C4×D151—41no—
70C23×C151C2311yescharacteristic
71C23×C151C2311yescharacteristic
72C23×C151C2311yescharacteristic
73D4×C151—41no—
74D4×C151—41no—
75D4×C151—41no—
76C2×C4×C151—41no—
77C2×C4×C151C2311yescharacteristic
78C2×C4×C151C2311yescharacteristic
79C2×C4×C151C2311yescharacteristic
80C2×C4×C151C2311yescharacteristic
81C22×C151—21no—
82C22×C151—21no—
83C22×C151—21no—
84C22×C151—21no—
85C22×C151—21no—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151—21no—
89C22×C151—21no—
90C22×C151C2411yescharacteristic
91C2×D151—21no—
92C2×D151—21no—
93C2×D151—21no—
94C2×D151—21no—
95C2×D151—21no—
96C2×D151—44no—
97C2×D151#4112yes—
98C4×C151—21no—
99C4×C151—21no—
100C4×C151—21no—
101C4×C151—21no—
102Dic151—21no—
103Dic151—21no—
104Dic151—21no—
105Dic151—21no—
106Dic151—21no—
107Dic151—21no—
108C2×C151—41no—
109C2×C151—41no—
110C2×C151—41no—
111C2×C151C2×#4111yescharacteristic
112C2×C151H(5,𝔽2)11yescharacteristic
113C2×C151H(5,𝔽2)11yescharacteristic
114D151—22no—
115D151—41no—
116C151#53811yescharacteristic, complemented, Sylow
117#538—1511nomaximal, Sylow
118#126—1511no—
119#126—1511no—
120#124—1511no—
121#124—1511no—
122#123—1511no—
123#123—1511no—
124C22⋊Q8—1511no—
125#121—1511no—
126#121—1511no—
127#121D15111yescharacteristic, complemented
128#120—1511no—
129#120—1511no—
130C4×D4—1511no—
131C4×D4—1511no—
132C2×C22⋊C4—1511no—
133C24—1511no—
134C2×Q8—1511no—
135C2×D4—1511no—
136C2×D4—1511no—
137C2×D4—1511no—
138C2×D4—1511no—
139C2×D4C2×D15111yescharacteristic
140C2×D4C2×D15111yescharacteristic
141C2×D4C2×D15111yescharacteristic, complemented
142C22×C4—1511no—
143C22×C4—1511no—
144C22×C4—1511no—
145C22×C4C2×D15111yescharacteristic, complemented
146C4⋊C4—1511no—
147C4⋊C4—1511no—
148C4⋊C4—1511no—
149C4⋊C4—1511no—
150C4⋊C4—1511no—
151C4⋊C4C2×D15111yescharacteristic, complemented
152C22⋊C4—1511no—
153C22⋊C4—1511no—
154C22⋊C4—1511no—
155C22⋊C4—1511no—
156C22⋊C4—1511no—
157C22⋊C4—1511no—
158C22⋊C4—1511no—
159C22⋊C4—1511no—
160C22⋊C4—1511no—
161C22⋊C4—1511no—
162C22⋊C4—1511no—
163C22⋊C4—1511no—
164C22⋊C4C2×D15111yescharacteristic
165C22⋊C4C2×D15111yescharacteristic, complemented
166C42—1511no—
167C42—1511no—
168C23—3022no—
169C23—6041no—
170C23—6041no—
171C23—1511no—
172C23—1511no—
173C23C22×D15111yescharacteristic
174C23C22×D15111yescharacteristic
175C23C22×D15111yescharacteristic
176Q8—6041no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—3022no—
181D4—3022no—
182D4—6041no—
183D4—6041no—
184C2×C4—41no—
185C2×C4—6041no—
186C2×C4—6041no—
187C2×C4—6041no—
188C2×C4—1511no—
189C2×C4—1511no—
190C2×C4—1511no—
191C2×C4—1511no—
192C2×C4—1511no—
193C2×C4—1511no—
194C2×C4C22×D15111yescharacteristic
195C2×C4C22×D15111yescharacteristic
196C2×C4C22×D15111yescharacteristic
197C2×C4C22×D15111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—3021no—
208C22—3021no—
209C22—3021no—
210C22—3021no—
211C22—3021no—
212C22—6044no—
213C22—1512no—
214C22C23×D15111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—3021no—
220C4—3021no—
221C4—3021no—
222C4—3021no—
223C4—3021no—
224C4—3021no—
225C2—41no—
226C2—41no—
227C2—41no—
228C2—3022no—
229C2—6041no—
230C2#41×D15111yescharacteristic
231C2#1801278411yescharacteristic
232C2#1801278411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D151
commutator, socle, cosocleC22×C151C24
Fitting#121×C151C2
hypercenter#121D151
hypocenterC151#538
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #18012734C2semidirect
2. #18012732C2semidirect
3. #18012726C2semidirect
4. #18012725C2semidirect
5. #18012722C2semidirect
6. #18012720C2semidirect
7. #18012717C2semidirect
8. #18012711C2semidirect
9. #18012710C2semidirect
10. #18012707C2semidirect
11. #18012707C2semidirect
12. C4×C22⋊D151C2semidirect
13. (C22⋊D151)⋊C4C2semidirect
14. C22⋊C4×D151C2semidirect
15. #121×C151C2semidirect
17. C2×Dic302C22semidirect
22. C22×Dic151C22semidirect
25. C4⋊Dic151C22semidirect
26. Dic151⋊C4C22semidirect
27. Dic151⋊C4C22semidirect
28. Dic151⋊C4C22semidirect
29. Dic151⋊C4C22semidirect
33. C22⋊Dic151C22semidirect
34. C22⋊Dic151C22semidirect
35. C22⋊Dic151C22semidirect
42. C4×Dic151C22semidirect
43. C4×Dic151C22semidirect
46. C2×D4×C151C22semidirect
47. C22×C4×C151C22semidirect
48. C4⋊C4×C151C22semidirect
50. C22⋊C4×C151C22semidirect
116. C151#538semidirect
127. #121D151semidirect
141. C2×D4C2×D151semidirect
145. C22×C4C2×D151semidirect
151. C4⋊C4C2×D151semidirect
165. C22⋊C4C2×D151semidirect