Finite Group Databasebeta

← #23752891

Subgroups — #23752891

Order 9664.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#18012733C211yesmaximal, characteristic, complemented
3#18012725C211yesmaximal, characteristic, complemented
4#18012722C211yesmaximal, characteristic, complemented
5#18012721C211yesmaximal, characteristic, complemented
6#18012720C211yesmaximal, characteristic, complemented
7#18012718C211yesmaximal, characteristic, complemented
8#18012717C211yesmaximal, characteristic, complemented
9#18012707C211yesmaximal, characteristic
10C4×C22⋊D151C211yesmaximal, characteristic, complemented
11#18012696C211yesmaximal, characteristic, complemented
12#18012695C211yesmaximal, characteristic, complemented
13C2×(C2×D151)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D151C211yesmaximal, characteristic, complemented
15C4×D4×C151C211yesmaximal, characteristic, complemented
16C23×D151C2211yescharacteristic
17C2×Dic302C2211yescharacteristic, complemented
18C2×C22⋊D151C2211yescharacteristic
19C2×C22⋊D151C2211yescharacteristic
20C22×Dic151C2211yescharacteristic
21C2×C4×D151C2211yescharacteristic
22C2×C4×D151C2211yescharacteristic
23C4⋊Dic151C2211yescharacteristic, complemented
24Dic151⋊C4C2211yescharacteristic, complemented
25Dic151⋊C4C2211yescharacteristic, complemented
26Dic151⋊C4C2211yescharacteristic, complemented
27Dic151⋊C4C2211yescharacteristic, complemented
28Dic151⋊C4C2211yescharacteristic, complemented
29Dic151⋊C4C2211yescharacteristic, complemented
30C22⋊Dic151C2211yescharacteristic
31C22⋊Dic151C2211yescharacteristic
32C22⋊Dic151C2211yescharacteristic, complemented
33C22⋊Dic151C2211yescharacteristic, complemented
34(C2×D151)⋊C4C2211yescharacteristic
35(C2×D151)⋊C4C2211yescharacteristic
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
45C22×C4×C151C2211yescharacteristic
46C22×C4×C151C2211yescharacteristic, complemented
47C4⋊C4×C151C2211yescharacteristic, complemented
48C22⋊C4×C151C2211yescharacteristic
49C22⋊C4×C151C2211yescharacteristic, complemented
50C42×C151C2211yescharacteristic, complemented
51C22×D151—22no—
52C22×D151—22no—
53C22×D151—41no—
54C22×D151C2311yescharacteristic
55C22×D151C2311yescharacteristic
56Dic302—41no—
57C22⋊D151—22no—
58C22⋊D151—41no—
59C2×Dic151—22no—
60C2×Dic151C2311yescharacteristic
61C2×Dic151C2311yescharacteristic
62C2×Dic151C2311yescharacteristic
63C2×Dic151C2311yescharacteristic
64C2×Dic151C2311yescharacteristic
65C2×Dic151C2311yescharacteristic
66C4×D151—22no—
67C4×D151—41no—
68C23×C151C2311yescharacteristic
69C23×C151C2311yescharacteristic
70D4×C151—22no—
71C2×C4×C151—41no—
72C2×C4×C151—41no—
73C2×C4×C151C2311yescharacteristic
74C2×C4×C151C2311yescharacteristic
75C2×C4×C151C2311yescharacteristic
76C2×C4×C151C2311yescharacteristic
77C2×C4×C151C2311yescharacteristic
78C22×C151—21no—
79C22×C151—21no—
80C22×C151—21no—
81C22×C151—21no—
82C22×C151—21no—
83C22×C151#4112yes—
84C22×C151C2411yescharacteristic
85C2×D151—21no—
86C2×D151—21no—
87C2×D151—21no—
88C2×D151—21no—
89C2×D151—21no—
90C2×D151—44no—
91C2×D151#4112yes—
92C4×C151—21no—
93C4×C151—21no—
94C4×C151—21no—
95C4×C151—21no—
96C4×C151—21no—
97Dic151—21no—
98Dic151—21no—
99Dic151—21no—
100Dic151—21no—
101Dic151—21no—
102Dic151—21no—
103C2×C151—22no—
104C2×C151—41no—
105C2×C151C2×#4111yescharacteristic
106C2×C151C2×#4111yescharacteristic
107C2×C151H(5,𝔽2)11yescharacteristic
108D151—22no—
109D151—41no—
110C151#55111yescharacteristic, complemented, Sylow
111#551—1511nomaximal, Sylow
112#126—1511no—
113#126—1511no—
114#124—1511no—
115#123—1511no—
116#123—1511no—
117#123—1511no—
118C22⋊Q8—1511no—
119C22⋊Q8—1511no—
120#120—1511no—
121C4×D4—1511no—
122C4×D4D15111yescharacteristic, complemented
123#117—1511no—
124#117—1511no—
125C2×C22⋊C4—1511no—
126C2×C22⋊C4—1511no—
127C24—1511no—
128C2×Q8—1511no—
129C2×D4—1511no—
130C2×D4—1511no—
131C2×D4C2×D15111yescharacteristic
132C22×C4—1511no—
133C22×C4—1511no—
134C22×C4—1511no—
135C22×C4C2×D15111yescharacteristic
136C22×C4C2×D15111yescharacteristic, complemented
137C4⋊C4—1511no—
138C4⋊C4—1511no—
139C4⋊C4—1511no—
140C4⋊C4—1511no—
141C4⋊C4—1511no—
142C4⋊C4—1511no—
143C4⋊C4—1511no—
144C4⋊C4C2×D15111yescharacteristic, complemented
145C22⋊C4—1511no—
146C22⋊C4—1511no—
147C22⋊C4—1511no—
148C22⋊C4—1511no—
149C22⋊C4—1511no—
150C22⋊C4—1511no—
151C22⋊C4—1511no—
152C22⋊C4—1511no—
153C22⋊C4—1511no—
154C22⋊C4—1511no—
155C22⋊C4—1511no—
156C22⋊C4—1511no—
157C22⋊C4C2×D15111yescharacteristic
158C22⋊C4C2×D15111yescharacteristic, complemented
159C42—1511no—
160C42—1511no—
161C42C2×D15111yescharacteristic, complemented
162C23—3022no—
163C23—3022no—
164C23—6041no—
165C23—1511no—
166C23—1511no—
167C23C22×D15111yescharacteristic
168C23C22×D15111yescharacteristic
169Q8—6041no—
170D4—22no—
171D4—3022no—
172D4—6041no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—3022no—
176C2×C4—3022no—
177C2×C4—6041no—
178C2×C4—1511no—
179C2×C4—1511no—
180C2×C4—1511no—
181C2×C4—1511no—
182C2×C4—1511no—
183C2×C4—1511no—
184C2×C4C22×D15111yescharacteristic
185C2×C4C22×D15111yescharacteristic
186C2×C4C22×D15111yescharacteristic
187C2×C4C22×D15111yescharacteristic
188C2×C4C22×D15111yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—3021no—
195C22—3021no—
196C22—3021no—
197C22—3021no—
198C22—3021no—
199C22—6044no—
200C22—1512no—
201C22#1455900412yes—
202C22C23×D15111yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—3021no—
209C4—3021no—
210C4—3021no—
211C4—3021no—
212C4—3021no—
213C4—3021no—
214C2—22no—
215C2—41no—
216C2—3022no—
217C2—6041no—
218C2#41×D15111yescharacteristic
219C2C2×#1455900411yescharacteristic
220C2#1801278411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D151
commutator, socle, cosocleC22×C151C24
FittingC4×D4×C151C2
prime radical#18012707C2
hypercenterC4×D4D151
hypocenterC151#551
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #18012734C2semidirect
2. #18012733C2semidirect
3. #18012725C2semidirect
4. #18012722C2semidirect
5. #18012721C2semidirect
6. #18012720C2semidirect
7. #18012718C2semidirect
8. #18012717C2semidirect
10. C4×C22⋊D151C2semidirect
11. #18012696C2semidirect
12. #18012695C2semidirect
13. C2×(C2×D151)⋊C4C2semidirect
14. C22⋊C4×D151C2semidirect
15. C4×D4×C151C2semidirect
17. C2×Dic302C22semidirect
23. C4⋊Dic151C22semidirect
24. Dic151⋊C4C22semidirect
25. Dic151⋊C4C22semidirect
26. Dic151⋊C4C22semidirect
27. Dic151⋊C4C22semidirect
28. Dic151⋊C4C22semidirect
29. Dic151⋊C4C22semidirect
32. C22⋊Dic151C22semidirect
33. C22⋊Dic151C22semidirect
42. C4×Dic151C22semidirect
43. C4×Dic151C22semidirect
46. C22×C4×C151C22semidirect
47. C4⋊C4×C151C22semidirect
49. C22⋊C4×C151C22semidirect
50. C42×C151C22semidirect
110. C151#551semidirect
122. C4×D4D151semidirect
136. C22×C4C2×D151semidirect
144. C4⋊C4C2×D151semidirect
158. C22⋊C4C2×D151semidirect
161. C42C2×D151semidirect