Finite Group Databasebeta

← #37560160

Subgroups — #37560160

Order 23872.

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#26045788C211yesmaximal, characteristic, complemented
2#26045787C211yesmaximal, characteristic, complemented
3#26045785C211yesmaximal, characteristic, complemented
4#26045777C211yesmaximal, characteristic, complemented
5#26045776C211yesmaximal, characteristic, complemented
6#26045775C211yesmaximal, characteristic, complemented
7#26045766C211yesmaximal, characteristic, complemented
8#26045765C211yesmaximal, characteristic, complemented
9#26045764C211yesmaximal, characteristic, complemented
10#26045764C211yesmaximal, characteristic, complemented
11#26045763C211yesmaximal, characteristic, complemented
12#26045762C211yesmaximal, characteristic, complemented
13#26045760C211yesmaximal, characteristic, complemented
14#26045760C211yesmaximal, characteristic, complemented
15#121×C373C211yesmaximal, characteristic, complemented
16C23×D373C2211yescharacteristic
17C2×D1492C2211yescharacteristic
18C2×D1492C2211yescharacteristic
19C2×C22⋊D373C2211yescharacteristic
20C2×C22⋊D373C2211yescharacteristic
21C2×C22⋊D373C2211yescharacteristic
22C2×C22⋊D373C2211yescharacteristic
23C2×C22⋊D373C2211yescharacteristic
24C2×C22⋊D373C2211yescharacteristic, complemented
25C2×C22⋊D373C2211yescharacteristic, complemented
26C22×Dic373C2211yescharacteristic, complemented
27C2×C4×D373C2211yescharacteristic, complemented
28C4⋊Dic373C2211yescharacteristic, complemented
29C4⋊Dic373C2211yescharacteristic, complemented
30#20238589C2211yescharacteristic, complemented
31#20238589C2211yescharacteristic, complemented
32#20238589C2211yescharacteristic, complemented
33C22⋊Dic373C2211yescharacteristic
34C22⋊Dic373C2211yescharacteristic
35C22⋊Dic373C2211yescharacteristic, complemented
36#20238587C2211yescharacteristic
37#20238587C2211yescharacteristic
38#20238587C2211yescharacteristic
39#20238587C2211yescharacteristic
40#20238587C2211yescharacteristic
41#20238587C2211yescharacteristic
42#20238587C2211yescharacteristic, complemented
43C4×Dic373C2211yescharacteristic, complemented
44C2×D4×C373C2211yescharacteristic
45C2×D4×C373C2211yescharacteristic
46C2×D4×C373C2211yescharacteristic, complemented
47C22×C4×C373C2211yescharacteristic, complemented
48C4⋊C4×C373C2211yescharacteristic, complemented
49C22⋊C4×C373C2211yescharacteristic
50C22⋊C4×C373C2211yescharacteristic, complemented
51C22×D373—41no—
52C22×D373—41no—
53C22×D373—41no—
54C22×D373C2311yescharacteristic
55C22×D373C2311yescharacteristic
56C22×D373C2311yescharacteristic
57D1492—41no—
58D1492—41no—
59C22⋊D373—41no—
60C22⋊D373—41no—
61C22⋊D373—41no—
62C22⋊D373—41no—
63C22⋊D373—41no—
64C22⋊D373—41no—
65C22⋊D373—41no—
66C2×Dic373—41no—
67C2×Dic373C2311yescharacteristic
68C2×Dic373C2311yescharacteristic
69C2×Dic373C2311yescharacteristic
70C2×Dic373C2311yescharacteristic
71C2×Dic373C2311yescharacteristic
72C4×D373—41no—
73C23×C373C2311yescharacteristic
74C23×C373C2311yescharacteristic
75C23×C373C2311yescharacteristic
76D4×C373—41no—
77D4×C373—41no—
78D4×C373—41no—
79C2×C4×C373—41no—
80C2×C4×C373C2311yescharacteristic
81C2×C4×C373C2311yescharacteristic
82C2×C4×C373C2311yescharacteristic
83C2×C4×C373C2311yescharacteristic
84C22×C373—21no—
85C22×C373—21no—
86C22×C373—21no—
87C22×C373—21no—
88C22×C373—21no—
89C22×C373—21no—
90C22×C373—21no—
91C22×C373—21no—
92C22×C373—21no—
93C22×C373C2411yescharacteristic
94C2×D373—21no—
95C2×D373—21no—
96C2×D373—21no—
97C2×D373—21no—
98C2×D373—21no—
99C2×D373—21no—
100C2×D373—21no—
101C2×D373—21no—
102C2×D373—21no—
103C2×D373—44no—
104C4×C373—21no—
105C4×C373—21no—
106C4×C373—21no—
107C4×C373—21no—
108Dic373—21no—
109Dic373—21no—
110Dic373—21no—
111Dic373—21no—
112Dic373—21no—
113C2×C373—41no—
114C2×C373—41no—
115C2×C373—41no—
116C2×C373H(5,𝔽2)11yescharacteristic
117C2×C373H(5,𝔽2)11yescharacteristic
118C2×C373H(5,𝔽2)11yescharacteristic
119D373—41no—
120D373—41no—
121D373—41no—
122C373#56011yescharacteristic, complemented, Sylow
123#560—3731nomaximal, Sylow
124#127—3731no—
125#126—3731no—
126#126—3731no—
127#123—3731no—
128#123—3731no—
129#123—3731no—
130#121—3731no—
131#121—3731no—
132#121—3731no—
133#121—3731no—
134#121—3731no—
135#121D37311yescharacteristic, complemented
136#120—3731no—
137#120—3731no—
138#120—3731no—
139C24—3731no—
140C2×D4—3731no—
141C2×D4—3731no—
142C2×D4—3731no—
143C2×D4—3731no—
144C2×D4—3731no—
145C2×D4—3731no—
146C2×D4—3731no—
147C2×D4—3731no—
148C2×D4—3731no—
149C2×D4C2×D37311yescharacteristic
150C2×D4C2×D37311yescharacteristic
151C2×D4C2×D37311yescharacteristic, complemented
152C22×C4—3731no—
153C22×C4—3731no—
154C22×C4C2×D37311yescharacteristic, complemented
155C4⋊C4—3731no—
156C4⋊C4—3731no—
157C4⋊C4—3731no—
158C4⋊C4—3731no—
159C4⋊C4—3731no—
160C4⋊C4C2×D37311yescharacteristic, complemented
161C22⋊C4—3731no—
162C22⋊C4—3731no—
163C22⋊C4—3731no—
164C22⋊C4—3731no—
165C22⋊C4—3731no—
166C22⋊C4—3731no—
167C22⋊C4—3731no—
168C22⋊C4—3731no—
169C22⋊C4—3731no—
170C22⋊C4—3731no—
171C22⋊C4C2×D37311yescharacteristic
172C22⋊C4C2×D37311yescharacteristic, complemented
173C42—3731no—
174C23—3731no—
175C23—3731no—
176C23—3731no—
177C23—14921no—
178C23—14921no—
179C23—14921no—
180C23C22×D37311yescharacteristic
181C23C22×D37311yescharacteristic
182C23C22×D37311yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—14921no—
187D4—14921no—
188D4—14921no—
189D4—14921no—
190D4—14921no—
191D4—14921no—
192D4—14921no—
193D4—14921no—
194D4—14921no—
195C2×C4—41no—
196C2×C4—3731no—
197C2×C4—3731no—
198C2×C4—3731no—
199C2×C4—3731no—
200C2×C4—3731no—
201C2×C4—14921no—
202C2×C4—14921no—
203C2×C4C22×D37311yescharacteristic
204C2×C4C22×D37311yescharacteristic
205C2×C4C22×D37311yescharacteristic
206C2×C4C22×D37311yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—14924no—
217C22—7461no—
218C22—7461no—
219C22—7461no—
220C22—7461no—
221C22—7461no—
222C22—7461no—
223C22—7461no—
224C22—7461no—
225C22—7461no—
226C22C23×D37311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—7461no—
232C4—7461no—
233C4—7461no—
234C4—7461no—
235C4—7461no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—14921no—
240C2—14921no—
241C2—14921no—
242C2#2604583711yescharacteristic
243C2#2604583711yescharacteristic
244C2#2604583811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D373
commutator, socle, cosocleC22×C373C24
Fitting#121×C373C2
hypercenter#121D373
hypocenterC373#560
LCSG ▷ C22×C373 ▷ C373
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #26045788C2semidirect
2. #26045787C2semidirect
3. #26045785C2semidirect
4. #26045777C2semidirect
5. #26045776C2semidirect
6. #26045775C2semidirect
7. #26045766C2semidirect
8. #26045765C2semidirect
9. #26045764C2semidirect
10. #26045764C2semidirect
11. #26045763C2semidirect
12. #26045762C2semidirect
13. #26045760C2semidirect
14. #26045760C2semidirect
15. #121×C373C2semidirect
24. C2×C22⋊D373C22semidirect
25. C2×C22⋊D373C22semidirect
26. C22×Dic373C22semidirect
27. C2×C4×D373C22semidirect
28. C4⋊Dic373C22semidirect
29. C4⋊Dic373C22semidirect
30. #20238589C22semidirect
31. #20238589C22semidirect
32. #20238589C22semidirect
35. C22⋊Dic373C22semidirect
42. #20238587C22semidirect
43. C4×Dic373C22semidirect
46. C2×D4×C373C22semidirect
47. C22×C4×C373C22semidirect
48. C4⋊C4×C373C22semidirect
50. C22⋊C4×C373C22semidirect
122. C373#560semidirect
135. #121D373semidirect
151. C2×D4C2×D373semidirect
154. C22×C4C2×D373semidirect
160. C4⋊C4C2×D373semidirect
172. C22⋊C4C2×D373semidirect

Maximal subgroups

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

subgroupindex
#260457882
#260457872
#260457852
#260457772
#260457762
#260457752
#260457662
#260457652
#260457642
#260457632
#260457622
#260457602
#121×C3732
#560373