Finite Group Databasebeta

← #14521787

Subgroups — #14521787

Order 1984.

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
1C31×#121C211yesmaximal, characteristic, complemented
2#11758517C211yesmaximal, characteristic, complemented
3#11758516C211yesmaximal, characteristic, complemented
4#11758516C211yesmaximal, characteristic, complemented
5#11758515C211yesmaximal, characteristic, complemented
6#11758514C211yesmaximal, characteristic, complemented
7#11758514C211yesmaximal, characteristic, complemented
8#11758507C211yesmaximal, characteristic, complemented
9#11758506C211yesmaximal, characteristic, complemented
10#11758475C211yesmaximal, characteristic, complemented
11#11758471C211yesmaximal, characteristic, complemented
12#11758463C211yesmaximal, characteristic, complemented
13#11758461C211yesmaximal, characteristic, complemented
14#11758459C211yesmaximal, characteristic, complemented
15#11758456C211yesmaximal, characteristic, complemented
16C23×D31C2211yescharacteristic
17C2×D4×C31C2211yescharacteristic
18C2×D4×C31C2211yescharacteristic
19C2×D4×C31C2211yescharacteristic, complemented
20C22×C4×C31C2211yescharacteristic, complemented
21C2×C22⋊D31C2211yescharacteristic
22C2×C22⋊D31C2211yescharacteristic
23C2×C22⋊D31C2211yescharacteristic
24C2×C22⋊D31C2211yescharacteristic
25C2×C22⋊D31C2211yescharacteristic
26C2×C22⋊D31C2211yescharacteristic, complemented
27C2×C22⋊D31C2211yescharacteristic, complemented
28C22×Dic31C2211yescharacteristic, complemented
29C2×D124C2211yescharacteristic
30C2×D124C2211yescharacteristic
31C2×C4×D31C2211yescharacteristic, complemented
32C4⋊C4×C31C2211yescharacteristic, complemented
33C22⋊C4×C31C2211yescharacteristic
34C22⋊C4×C31C2211yescharacteristic, complemented
35C22⋊Dic31C2211yescharacteristic
36C22⋊Dic31C2211yescharacteristic
37C22⋊Dic31C2211yescharacteristic, complemented
38(C2×D31)⋊C4C2211yescharacteristic
39(C2×D31)⋊C4C2211yescharacteristic
40(C2×D31)⋊C4C2211yescharacteristic
41(C2×D31)⋊C4C2211yescharacteristic
42(C2×D31)⋊C4C2211yescharacteristic
43(C2×D31)⋊C4C2211yescharacteristic
44(C2×D31)⋊C4C2211yescharacteristic, complemented
45C4⋊Dic31C2211yescharacteristic, complemented
46C4⋊Dic31C2211yescharacteristic, complemented
47Dic31⋊C4C2211yescharacteristic, complemented
48Dic31⋊C4C2211yescharacteristic, complemented
49Dic31⋊C4C2211yescharacteristic, complemented
50C4×Dic31C2211yescharacteristic, complemented
51C23×C31C2311yescharacteristic
52C23×C31C2311yescharacteristic
53C23×C31C2311yescharacteristic
54C22×D31—41no—
55C22×D31—41no—
56C22×D31—41no—
57C22×D31C2311yescharacteristic
58C22×D31C2311yescharacteristic
59C22×D31C2311yescharacteristic
60D4×C31—41no—
61D4×C31—41no—
62D4×C31—41no—
63C2×C4×C31—41no—
64C2×C4×C31C2311yescharacteristic
65C2×C4×C31C2311yescharacteristic
66C2×C4×C31C2311yescharacteristic
67C2×C4×C31C2311yescharacteristic
68C22⋊D31—41no—
69C22⋊D31—41no—
70C22⋊D31—41no—
71C22⋊D31—41no—
72C22⋊D31—41no—
73C22⋊D31—41no—
74C22⋊D31—41no—
75C2×Dic31—41no—
76C2×Dic31C2311yescharacteristic
77C2×Dic31C2311yescharacteristic
78C2×Dic31C2311yescharacteristic
79C2×Dic31C2311yescharacteristic
80C2×Dic31C2311yescharacteristic
81D124—41no—
82D124—41no—
83C4×D31—41no—
84C22×C31—21no—
85C22×C31—21no—
86C22×C31—21no—
87C22×C31—21no—
88C22×C31—21no—
89C22×C31—21no—
90C22×C31—21no—
91C22×C31—21no—
92C22×C31—21no—
93C22×C31C2411yescharacteristic
94C2×D31—21no—
95C2×D31—21no—
96C2×D31—21no—
97C2×D31—21no—
98C2×D31—21no—
99C2×D31—21no—
100C2×D31—21no—
101C2×D31—21no—
102C2×D31—21no—
103C2×D31—44no—
104C4×C31—21no—
105C4×C31—21no—
106C4×C31—21no—
107C4×C31—21no—
108Dic31—21no—
109Dic31—21no—
110Dic31—21no—
111Dic31—21no—
112Dic31—21no—
113#560—311nomaximal, Sylow
114C2×C31—41no—
115C2×C31—41no—
116C2×C31—41no—
117C2×C31H(5,𝔽2)11yescharacteristic
118C2×C31H(5,𝔽2)11yescharacteristic
119C2×C31H(5,𝔽2)11yescharacteristic
120D31—41no—
121D31—41no—
122D31—41no—
123#127—311no—
124#126—311no—
125#126—311no—
126#123—311no—
127#123—311no—
128#123—311no—
129#121—311no—
130#121—311no—
131#121—311no—
132#121—311no—
133#121—311no—
134#121D3111yescharacteristic, complemented
135#120—311no—
136#120—311no—
137#120—311no—
138C31#56011yescharacteristic, complemented, Sylow
139C24—311no—
140C2×D4—311no—
141C2×D4—311no—
142C2×D4—311no—
143C2×D4—311no—
144C2×D4—311no—
145C2×D4—311no—
146C2×D4—311no—
147C2×D4—311no—
148C2×D4—311no—
149C2×D4C2×D3111yescharacteristic
150C2×D4C2×D3111yescharacteristic
151C2×D4C2×D3111yescharacteristic, complemented
152C22×C4—311no—
153C22×C4—311no—
154C22×C4C2×D3111yescharacteristic, complemented
155C4⋊C4—311no—
156C4⋊C4—311no—
157C4⋊C4—311no—
158C4⋊C4—311no—
159C4⋊C4—311no—
160C4⋊C4C2×D3111yescharacteristic, complemented
161C22⋊C4—311no—
162C22⋊C4—311no—
163C22⋊C4—311no—
164C22⋊C4—311no—
165C22⋊C4—311no—
166C22⋊C4—311no—
167C22⋊C4—311no—
168C22⋊C4—311no—
169C22⋊C4—311no—
170C22⋊C4—311no—
171C22⋊C4C2×D3111yescharacteristic
172C22⋊C4C2×D3111yescharacteristic, complemented
173C42—311no—
174C23—311no—
175C23—311no—
176C23—311no—
177C23—1241no—
178C23—1241no—
179C23—1241no—
180C23C22×D3111yescharacteristic
181C23C22×D3111yescharacteristic
182C23C22×D3111yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—1241no—
187D4—1241no—
188D4—1241no—
189D4—1241no—
190D4—1241no—
191D4—1241no—
192D4—1241no—
193D4—1241no—
194D4—1241no—
195C2×C4—41no—
196C2×C4—311no—
197C2×C4—311no—
198C2×C4—311no—
199C2×C4—311no—
200C2×C4—311no—
201C2×C4—1241no—
202C2×C4—1241no—
203C2×C4C22×D3111yescharacteristic
204C2×C4C22×D3111yescharacteristic
205C2×C4C22×D3111yescharacteristic
206C2×C4C22×D3111yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—621no—
217C22—621no—
218C22—621no—
219C22—621no—
220C22—621no—
221C22—621no—
222C22—621no—
223C22—621no—
224C22—621no—
225C22—1244no—
226C22C23×D3111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—621no—
232C4—621no—
233C4—621no—
234C4—621no—
235C4—621no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—1241no—
240C2—1241no—
241C2—1241no—
242C2#1175856111yescharacteristic
243C2#1175856111yescharacteristic
244C2#1175856611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC31×#121C2
hypercenter#121D31
hypocenterC31#560
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C31×#121C2semidirect
2. #11758517C2semidirect
3. #11758516C2semidirect
4. #11758516C2semidirect
5. #11758515C2semidirect
6. #11758514C2semidirect
7. #11758514C2semidirect
8. #11758507C2semidirect
9. #11758506C2semidirect
10. #11758475C2semidirect
11. #11758471C2semidirect
12. #11758463C2semidirect
13. #11758461C2semidirect
14. #11758459C2semidirect
15. #11758456C2semidirect
19. C2×D4×C31C22semidirect
20. C22×C4×C31C22semidirect
26. C2×C22⋊D31C22semidirect
27. C2×C22⋊D31C22semidirect
28. C22×Dic31C22semidirect
31. C2×C4×D31C22semidirect
32. C4⋊C4×C31C22semidirect
34. C22⋊C4×C31C22semidirect
37. C22⋊Dic31C22semidirect
44. (C2×D31)⋊C4C22semidirect
45. C4⋊Dic31C22semidirect
46. C4⋊Dic31C22semidirect
47. Dic31⋊C4C22semidirect
48. Dic31⋊C4C22semidirect
49. Dic31⋊C4C22semidirect
50. C4×Dic31C22semidirect
134. #121D31semidirect
138. C31#560semidirect
151. C2×D4C2×D31semidirect
154. C22×C4C2×D31semidirect
160. C4⋊C4C2×D31semidirect
172. C22⋊C4C2×D31semidirect

Maximal subgroups

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

subgroupindex
C31×#1212
#117585172
#117585162
#117585152
#117585142
#117585072
#117585062
#117584752
#117584712
#117584632
#117584612
#117584592
#117584562
#56031