Finite Group Databasebeta

← #44529788

Subgroups — #44529788

Order 31168.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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#29510211C211yesmaximal, characteristic, complemented
2#29510210C211yesmaximal, characteristic, complemented
3#29510208C211yesmaximal, characteristic, complemented
4#29510200C211yesmaximal, characteristic, complemented
5#29510199C211yesmaximal, characteristic, complemented
6#29510198C211yesmaximal, characteristic, complemented
7#29510189C211yesmaximal, characteristic, complemented
8#29510188C211yesmaximal, characteristic, complemented
9#29510187C211yesmaximal, characteristic, complemented
10#29510187C211yesmaximal, characteristic, complemented
11#29510186C211yesmaximal, characteristic, complemented
12#29510185C211yesmaximal, characteristic, complemented
13#29510183C211yesmaximal, characteristic, complemented
14#29510183C211yesmaximal, characteristic, complemented
15#121×C487C211yesmaximal, characteristic, complemented
16C23×D487C2211yescharacteristic
17C2×D1948C2211yescharacteristic
18C2×D1948C2211yescharacteristic
19C2×C22⋊D487C2211yescharacteristic
20C2×C22⋊D487C2211yescharacteristic
21C2×C22⋊D487C2211yescharacteristic
22C2×C22⋊D487C2211yescharacteristic
23C2×C22⋊D487C2211yescharacteristic
24C2×C22⋊D487C2211yescharacteristic, complemented
25C2×C22⋊D487C2211yescharacteristic, complemented
26C22×Dic487C2211yescharacteristic, complemented
27C2×C4×D487C2211yescharacteristic, complemented
28C4⋊Dic487C2211yescharacteristic, complemented
29C4⋊Dic487C2211yescharacteristic, complemented
30Dic487⋊C4C2211yescharacteristic, complemented
31Dic487⋊C4C2211yescharacteristic, complemented
32Dic487⋊C4C2211yescharacteristic, complemented
33C22⋊Dic487C2211yescharacteristic
34C22⋊Dic487C2211yescharacteristic
35C22⋊Dic487C2211yescharacteristic, complemented
36(C2×D487)⋊C4C2211yescharacteristic
37(C2×D487)⋊C4C2211yescharacteristic
38(C2×D487)⋊C4C2211yescharacteristic
39(C2×D487)⋊C4C2211yescharacteristic
40(C2×D487)⋊C4C2211yescharacteristic
41(C2×D487)⋊C4C2211yescharacteristic
42(C2×D487)⋊C4C2211yescharacteristic, complemented
43C4×Dic487C2211yescharacteristic, complemented
44C2×D4×C487C2211yescharacteristic
45C2×D4×C487C2211yescharacteristic
46C2×D4×C487C2211yescharacteristic, complemented
47C22×C4×C487C2211yescharacteristic, complemented
48C4⋊C4×C487C2211yescharacteristic, complemented
49C22⋊C4×C487C2211yescharacteristic
50C22⋊C4×C487C2211yescharacteristic, complemented
51C22×D487—41no—
52C22×D487—41no—
53C22×D487—41no—
54C22×D487C2311yescharacteristic
55C22×D487C2311yescharacteristic
56C22×D487C2311yescharacteristic
57D1948—41no—
58D1948—41no—
59C22⋊D487—41no—
60C22⋊D487—41no—
61C22⋊D487—41no—
62C22⋊D487—41no—
63C22⋊D487—41no—
64C22⋊D487—41no—
65C22⋊D487—41no—
66C2×Dic487—41no—
67C2×Dic487C2311yescharacteristic
68C2×Dic487C2311yescharacteristic
69C2×Dic487C2311yescharacteristic
70C2×Dic487C2311yescharacteristic
71C2×Dic487C2311yescharacteristic
72C4×D487—41no—
73C23×C487C2311yescharacteristic
74C23×C487C2311yescharacteristic
75C23×C487C2311yescharacteristic
76D4×C487—41no—
77D4×C487—41no—
78D4×C487—41no—
79C2×C4×C487—41no—
80C2×C4×C487C2311yescharacteristic
81C2×C4×C487C2311yescharacteristic
82C2×C4×C487C2311yescharacteristic
83C2×C4×C487C2311yescharacteristic
84C22×C487—21no—
85C22×C487—21no—
86C22×C487—21no—
87C22×C487—21no—
88C22×C487—21no—
89C22×C487—21no—
90C22×C487—21no—
91C22×C487—21no—
92C22×C487—21no—
93C22×C487C2411yescharacteristic
94C2×D487—21no—
95C2×D487—21no—
96C2×D487—21no—
97C2×D487—21no—
98C2×D487—21no—
99C2×D487—21no—
100C2×D487—21no—
101C2×D487—21no—
102C2×D487—21no—
103C2×D487—44no—
104C4×C487—21no—
105C4×C487—21no—
106C4×C487—21no—
107C4×C487—21no—
108Dic487—21no—
109Dic487—21no—
110Dic487—21no—
111Dic487—21no—
112Dic487—21no—
113C2×C487—41no—
114C2×C487—41no—
115C2×C487—41no—
116C2×C487H(5,𝔽2)11yescharacteristic
117C2×C487H(5,𝔽2)11yescharacteristic
118C2×C487H(5,𝔽2)11yescharacteristic
119D487—41no—
120D487—41no—
121D487—41no—
122C487#56011yescharacteristic, complemented, Sylow
123#560—4871nomaximal, Sylow
124#127—4871no—
125#126—4871no—
126#126—4871no—
127#123—4871no—
128#123—4871no—
129#123—4871no—
130#121—4871no—
131#121—4871no—
132#121—4871no—
133#121—4871no—
134#121—4871no—
135#121D48711yescharacteristic, complemented
136#120—4871no—
137#120—4871no—
138#120—4871no—
139C24—4871no—
140C2×D4—4871no—
141C2×D4—4871no—
142C2×D4—4871no—
143C2×D4—4871no—
144C2×D4—4871no—
145C2×D4—4871no—
146C2×D4—4871no—
147C2×D4—4871no—
148C2×D4—4871no—
149C2×D4C2×D48711yescharacteristic
150C2×D4C2×D48711yescharacteristic
151C2×D4C2×D48711yescharacteristic, complemented
152C22×C4—4871no—
153C22×C4—4871no—
154C22×C4C2×D48711yescharacteristic, complemented
155C4⋊C4—4871no—
156C4⋊C4—4871no—
157C4⋊C4—4871no—
158C4⋊C4—4871no—
159C4⋊C4—4871no—
160C4⋊C4C2×D48711yescharacteristic, complemented
161C22⋊C4—4871no—
162C22⋊C4—4871no—
163C22⋊C4—4871no—
164C22⋊C4—4871no—
165C22⋊C4—4871no—
166C22⋊C4—4871no—
167C22⋊C4—4871no—
168C22⋊C4—4871no—
169C22⋊C4—4871no—
170C22⋊C4—4871no—
171C22⋊C4C2×D48711yescharacteristic
172C22⋊C4C2×D48711yescharacteristic, complemented
173C42—4871no—
174C23—19481no—
175C23—19481no—
176C23—19481no—
177C23—4871no—
178C23—4871no—
179C23—4871no—
180C23C22×D48711yescharacteristic
181C23C22×D48711yescharacteristic
182C23C22×D48711yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—19481no—
187D4—19481no—
188D4—19481no—
189D4—19481no—
190D4—19481no—
191D4—19481no—
192D4—19481no—
193D4—19481no—
194D4—19481no—
195C2×C4—41no—
196C2×C4—19481no—
197C2×C4—19481no—
198C2×C4—4871no—
199C2×C4—4871no—
200C2×C4—4871no—
201C2×C4—4871no—
202C2×C4—4871no—
203C2×C4C22×D48711yescharacteristic
204C2×C4C22×D48711yescharacteristic
205C2×C4C22×D48711yescharacteristic
206C2×C4C22×D48711yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—19484no—
217C22—9741no—
218C22—9741no—
219C22—9741no—
220C22—9741no—
221C22—9741no—
222C22—9741no—
223C22—9741no—
224C22—9741no—
225C22—9741no—
226C22C23×D48711yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—9741no—
232C4—9741no—
233C4—9741no—
234C4—9741no—
235C4—9741no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—19481no—
240C2—19481no—
241C2—19481no—
242C2#2951026011yescharacteristic
243C2#2951026011yescharacteristic
244C2#2951026111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D487
commutator, socle, cosocleC22×C487C24
Fitting#121×C487C2
hypercenter#121D487
hypocenterC487#560
LCSG ▷ C22×C487 ▷ C487
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #29510211C2semidirect
2. #29510210C2semidirect
3. #29510208C2semidirect
4. #29510200C2semidirect
5. #29510199C2semidirect
6. #29510198C2semidirect
7. #29510189C2semidirect
8. #29510188C2semidirect
9. #29510187C2semidirect
10. #29510187C2semidirect
11. #29510186C2semidirect
12. #29510185C2semidirect
13. #29510183C2semidirect
14. #29510183C2semidirect
15. #121×C487C2semidirect
24. C2×C22⋊D487C22semidirect
25. C2×C22⋊D487C22semidirect
26. C22×Dic487C22semidirect
27. C2×C4×D487C22semidirect
28. C4⋊Dic487C22semidirect
29. C4⋊Dic487C22semidirect
30. Dic487⋊C4C22semidirect
31. Dic487⋊C4C22semidirect
32. Dic487⋊C4C22semidirect
35. C22⋊Dic487C22semidirect
42. (C2×D487)⋊C4C22semidirect
43. C4×Dic487C22semidirect
46. C2×D4×C487C22semidirect
47. C22×C4×C487C22semidirect
48. C4⋊C4×C487C22semidirect
50. C22⋊C4×C487C22semidirect
122. C487#560semidirect
135. #121D487semidirect
151. C2×D4C2×D487semidirect
154. C22×C4C2×D487semidirect
160. C4⋊C4C2×D487semidirect
172. C22⋊C4C2×D487semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#295102112
#295102102
#295102082
#295102002
#295101992
#295101982
#295101892
#295101882
#295101872
#295101862
#295101852
#295101832
#121×C4872
#560487