Finite Group Databasebeta

← #14521634

Subgroups — #14521634

Order 1984.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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×#120C211yesmaximal, characteristic, complemented
2#11758530C211yesmaximal, characteristic, complemented
3C2×C22⋊Dic31C211yesmaximal, characteristic, complemented
4#11758516C211yesmaximal, characteristic, complemented
5#11758516C211yesmaximal, characteristic, complemented
6#11758515C211yesmaximal, characteristic, complemented
7#11758513C211yesmaximal, characteristic, complemented
8#11758512C211yesmaximal, characteristic, complemented
9D4×Dic31C211yesmaximal, characteristic, complemented
10#11758462C211yesmaximal, characteristic, complemented
11#11758460C211yesmaximal, characteristic, complemented
12(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
13#11758456C211yesmaximal, characteristic, complemented
14#11758456C211yesmaximal, characteristic, complemented
15#11758455C211yesmaximal, characteristic, complemented
16C24×C31C2211yescharacteristic
17C2×D4×C31C2211yescharacteristic
18C2×D4×C31C2211yescharacteristic
19C2×D4×C31C2211yescharacteristic
20C2×C22⋊D31C2211yescharacteristic
21C2×C22⋊D31C2211yescharacteristic
22C2×C22⋊D31C2211yescharacteristic
23C2×C22⋊D31C2211yescharacteristic, complemented
24C22×Dic31C2211yescharacteristic
25C22×Dic31C2211yescharacteristic
26C22×Dic31C2211yescharacteristic, complemented
27C2×C4×D31C2211yescharacteristic, complemented
28C2×Dic62C2211yescharacteristic, complemented
29C22⋊C4×C31C2211yescharacteristic
30C22⋊C4×C31C2211yescharacteristic
31C22⋊C4×C31C2211yescharacteristic
32C22⋊Dic31C2211yescharacteristic
33C22⋊Dic31C2211yescharacteristic
34C22⋊Dic31C2211yescharacteristic
35C22⋊Dic31C2211yescharacteristic
36C22⋊Dic31C2211yescharacteristic
37C22⋊Dic31C2211yescharacteristic
38C22⋊Dic31C2211yescharacteristic
39C22⋊Dic31C2211yescharacteristic, complemented
40C22⋊Dic31C2211yescharacteristic, complemented
41(C2×D31)⋊C4C2211yescharacteristic, complemented
42(C2×D31)⋊C4C2211yescharacteristic, complemented
43C4⋊Dic31C2211yescharacteristic, complemented
44C4⋊Dic31C2211yescharacteristic, complemented
45Dic31⋊C4C2211yescharacteristic, complemented
46Dic31⋊C4C2211yescharacteristic, complemented
47Dic31⋊C4C2211yescharacteristic, complemented
48Dic31⋊C4C2211yescharacteristic, complemented
49C4×Dic31C2211yescharacteristic, complemented
50C4×Dic31C2211yescharacteristic, complemented
51C23×C31—22no—
52C23×C31—41no—
53C23×C31—41no—
54C23×C31C2311yescharacteristic
55C23×C31C2311yescharacteristic
56C23×C31C2311yescharacteristic
57C23×C31C2311yescharacteristic
58C22×D31C2311yescharacteristic
59D4×C31—22no—
60D4×C31—41no—
61D4×C31—41no—
62C2×C4×C31C2311yescharacteristic
63C2×C4×C31C2311yescharacteristic
64C2×C4×C31C2311yescharacteristic
65C22⋊D31—22no—
66C22⋊D31—41no—
67C22⋊D31—41no—
68C22⋊D31—41no—
69C2×Dic31—41no—
70C2×Dic31—41no—
71C2×Dic31—41no—
72C2×Dic31C2311yescharacteristic
73C2×Dic31C2311yescharacteristic
74C2×Dic31C2311yescharacteristic
75C2×Dic31C2311yescharacteristic
76C2×Dic31C2311yescharacteristic
77C2×Dic31C2311yescharacteristic
78C2×Dic31C2311yescharacteristic
79C4×D31—41no—
80Dic62—41no—
81C22×C31—21no—
82C22×C31—21no—
83C22×C31—21no—
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—44no—
93C22×C31#4112yes—
94C22×C31C2411yescharacteristic
95C2×D31—21no—
96C2×D31—21no—
97C2×D31—21no—
98C4×C31—21no—
99C4×C31—21no—
100C4×C31—21no—
101Dic31—21no—
102Dic31—21no—
103Dic31—21no—
104Dic31—21no—
105Dic31—21no—
106Dic31—21no—
107Dic31—21no—
108#538—311nomaximal, Sylow
109C2×C31—22no—
110C2×C31—41no—
111C2×C31—41no—
112C2×C31—41no—
113C2×C31C2×#4111yescharacteristic
114C2×C31H(5,𝔽2)11yescharacteristic
115C2×C31H(5,𝔽2)11yescharacteristic
116D31—41no—
117#126—311no—
118#126—311no—
119#124—311no—
120#124—311no—
121#123—311no—
122#123—311no—
123C22⋊Q8—311no—
124#121—311no—
125#121—311no—
126#121—311no—
127#120—311no—
128#120D3111yescharacteristic, complemented
129C4×D4—311no—
130C4×D4—311no—
131C2×C22⋊C4—311no—
132C31#53811yescharacteristic, complemented, Sylow
133C24C2×D3111yescharacteristic
134C2×Q8—311no—
135C2×D4—311no—
136C2×D4—311no—
137C2×D4—311no—
138C2×D4—311no—
139C2×D4C2×D3111yescharacteristic
140C2×D4C2×D3111yescharacteristic
141C2×D4C2×D3111yescharacteristic
142C22×C4—311no—
143C22×C4—311no—
144C22×C4—311no—
145C22×C4—311no—
146C4⋊C4—311no—
147C4⋊C4—311no—
148C4⋊C4—311no—
149C4⋊C4—311no—
150C4⋊C4—311no—
151C4⋊C4—311no—
152C22⋊C4—311no—
153C22⋊C4—311no—
154C22⋊C4—311no—
155C22⋊C4—311no—
156C22⋊C4—311no—
157C22⋊C4—311no—
158C22⋊C4—311no—
159C22⋊C4—311no—
160C22⋊C4—311no—
161C22⋊C4—311no—
162C22⋊C4—311no—
163C22⋊C4C2×D3111yescharacteristic
164C22⋊C4C2×D3111yescharacteristic
165C22⋊C4C2×D3111yescharacteristic
166C42—311no—
167C42—311no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—311no—
172C23C22×D3111yescharacteristic
173C23C22×D3111yescharacteristic
174C23C22×D3111yescharacteristic
175C23C22×D3111yescharacteristic
176Q8—1241no—
177D4—22no—
178D4—41no—
179D4—41no—
180D4—622no—
181D4—1241no—
182D4—1241no—
183D4—1241no—
184C2×C4—311no—
185C2×C4—311no—
186C2×C4—311no—
187C2×C4—311no—
188C2×C4—311no—
189C2×C4—311no—
190C2×C4—311no—
191C2×C4—1241no—
192C2×C4—1241no—
193C2×C4—1241no—
194C2×C4—1241no—
195C2×C4C22×D3111yescharacteristic
196C2×C4C22×D3111yescharacteristic
197C2×C4C22×D3111yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22—621no—
211C22—621no—
212C22—621no—
213C22#9249712yes—
214C22C23×D3111yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—621no—
219C4—621no—
220C4—621no—
221C4—621no—
222C4—621no—
223C4—621no—
224C4—621no—
225C2—22no—
226C2—41no—
227C2—41no—
228C2—41no—
229C2—1241no—
230C2C2×#9249711yescharacteristic
231C2#1175856111yescharacteristic
232C2#1175856111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC31×#120C2
hypercenter#120D31
hypocenterC31#538
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C31×#120C2semidirect
2. #11758530C2semidirect
3. C2×C22⋊Dic31C2semidirect
4. #11758516C2semidirect
5. #11758516C2semidirect
6. #11758515C2semidirect
7. #11758513C2semidirect
8. #11758512C2semidirect
9. D4×Dic31C2semidirect
10. #11758462C2semidirect
11. #11758460C2semidirect
12. (C22⋊D31)⋊C4C2semidirect
13. #11758456C2semidirect
14. #11758456C2semidirect
15. #11758455C2semidirect
23. C2×C22⋊D31C22semidirect
26. C22×Dic31C22semidirect
27. C2×C4×D31C22semidirect
28. C2×Dic62C22semidirect
39. C22⋊Dic31C22semidirect
40. C22⋊Dic31C22semidirect
41. (C2×D31)⋊C4C22semidirect
42. (C2×D31)⋊C4C22semidirect
43. C4⋊Dic31C22semidirect
44. C4⋊Dic31C22semidirect
45. Dic31⋊C4C22semidirect
46. Dic31⋊C4C22semidirect
47. Dic31⋊C4C22semidirect
48. Dic31⋊C4C22semidirect
49. C4×Dic31C22semidirect
50. C4×Dic31C22semidirect
128. #120D31semidirect
132. C31#538semidirect

Maximal subgroups

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

subgroupindex
C31×#1202
#117585302
C2×C22⋊Dic312
#117585162
#117585152
#117585132
#117585122
D4×Dic312
#117584622
#117584602
(C22⋊D31)⋊C42
#117584562
#117584552
#53831