Finite Group Databasebeta

← #14521725

Subgroups — #14521725

Order 1984.

248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×C22⋊C4×C31C211yesmaximal, characteristic, complemented
2#11758530C211yesmaximal, characteristic
3C2×C22⋊Dic31C211yesmaximal, characteristic, complemented
4#11758506C211yesmaximal, characteristic, complemented
5C4×C22⋊D31C211yesmaximal, characteristic, complemented
6#11758503C211yesmaximal, characteristic, complemented
7#11758501C211yesmaximal, characteristic, complemented
8#11758463C211yesmaximal, characteristic, complemented
9#11758462C211yesmaximal, characteristic, complemented
10#11758460C211yesmaximal, characteristic, complemented
11(C22⋊D31)⋊C4C211yesmaximal, characteristic, complemented
12#11758456C211yesmaximal, characteristic, complemented
13#11758456C211yesmaximal, characteristic, complemented
14#11758455C211yesmaximal, characteristic, complemented
15#11758454C211yesmaximal, characteristic, complemented
16C24×C31C2211yescharacteristic
17C22×C4×C31C2211yescharacteristic
18C22×C4×C31C2211yescharacteristic
19C2×C22⋊D31C2211yescharacteristic
20C2×C22⋊D31C2211yescharacteristic
21C2×C22⋊D31C2211yescharacteristic
22C22×Dic31C2211yescharacteristic
23C22×Dic31C2211yescharacteristic
24C2×C4×D31C2211yescharacteristic, complemented
25C2×Dic62C2211yescharacteristic, complemented
26C22⋊C4×C31C2211yescharacteristic
27C22⋊C4×C31C2211yescharacteristic
28C22⋊C4×C31C2211yescharacteristic
29C22⋊C4×C31C2211yescharacteristic
30C22⋊Dic31C2211yescharacteristic
31C22⋊Dic31C2211yescharacteristic
32C22⋊Dic31C2211yescharacteristic
33C22⋊Dic31C2211yescharacteristic
34C22⋊Dic31C2211yescharacteristic
35C22⋊Dic31C2211yescharacteristic
36C22⋊Dic31C2211yescharacteristic
37(C2×D31)⋊C4C2211yescharacteristic, complemented
38(C2×D31)⋊C4C2211yescharacteristic, complemented
39(C2×D31)⋊C4C2211yescharacteristic, complemented
40C4⋊Dic31C2211yescharacteristic, complemented
41C4⋊Dic31C2211yescharacteristic, complemented
42C4⋊Dic31C2211yescharacteristic, complemented
43Dic31⋊C4C2211yescharacteristic, complemented
44Dic31⋊C4C2211yescharacteristic, complemented
45Dic31⋊C4C2211yescharacteristic, complemented
46Dic31⋊C4C2211yescharacteristic, complemented
47Dic31⋊C4C2211yescharacteristic, complemented
48C4×Dic31C2211yescharacteristic, complemented
49C4×Dic31C2211yescharacteristic, complemented
50C4×Dic31C2211yescharacteristic, complemented
51C23×C31—22no—
52C23×C31—22no—
53C23×C31—41no—
54C23×C31C2311yescharacteristic
55C23×C31C2311yescharacteristic
56C23×C31C2311yescharacteristic
57C22×D31C2311yescharacteristic
58C2×C4×C31—22no—
59C2×C4×C31—41no—
60C2×C4×C31C2311yescharacteristic
61C2×C4×C31C2311yescharacteristic
62C2×C4×C31C2311yescharacteristic
63C2×C4×C31C2311yescharacteristic
64C22⋊D31—22no—
65C22⋊D31—22no—
66C22⋊D31—41no—
67C2×Dic31—22no—
68C2×Dic31—41no—
69C2×Dic31C2311yescharacteristic
70C2×Dic31C2311yescharacteristic
71C2×Dic31C2311yescharacteristic
72C2×Dic31C2311yescharacteristic
73C2×Dic31C2311yescharacteristic
74C2×Dic31C2311yescharacteristic
75C2×Dic31C2311yescharacteristic
76C4×D31—41no—
77Dic62—41no—
78C22×C31—21no—
79C22×C31—21no—
80C22×C31—21no—
81C22×C31—21no—
82C22×C31—21no—
83C22×C31—21no—
84C22×C31—21no—
85C22×C31—44no—
86C22×C31#4112yes—
87C22×C31#4112yes—
88C22×C31C2411yescharacteristic
89C2×D31—21no—
90C2×D31—21no—
91C2×D31—21no—
92C4×C31—21no—
93C4×C31—21no—
94C4×C31—21no—
95C4×C31—21no—
96Dic31—21no—
97Dic31—21no—
98Dic31—21no—
99Dic31—21no—
100Dic31—21no—
101Dic31—21no—
102Dic31—21no—
103#551—311nomaximal, Sylow
104C2×C31—22no—
105C2×C31—22no—
106C2×C31—41no—
107C2×C31C2×#4111yescharacteristic
108C2×C31C2×#4111yescharacteristic
109C2×C31H(5,𝔽2)11yescharacteristic
110D31—41no—
111#126—311no—
112#126—311no—
113#124—311no—
114#123—311no—
115#123—311no—
116#123—311no—
117C22⋊Q8—311no—
118C22⋊Q8—311no—
119#120—311no—
120C4×D4—311no—
121C4×D4—311no—
122#117—311no—
123#117—311no—
124C2×C22⋊C4—311no—
125C2×C22⋊C4D3111yescharacteristic, complemented
126C31#55111yescharacteristic, complemented, Sylow
127C24C2×D3111yescharacteristic
128C2×Q8—311no—
129C2×D4—311no—
130C2×D4—311no—
131C2×D4—311no—
132C22×C4—311no—
133C22×C4—311no—
134C22×C4—311no—
135C22×C4C2×D3111yescharacteristic
136C22×C4C2×D3111yescharacteristic
137C4⋊C4—311no—
138C4⋊C4—311no—
139C4⋊C4—311no—
140C4⋊C4—311no—
141C4⋊C4—311no—
142C4⋊C4—311no—
143C4⋊C4—311no—
144C4⋊C4—311no—
145C22⋊C4—311no—
146C22⋊C4—311no—
147C22⋊C4—311no—
148C22⋊C4—311no—
149C22⋊C4—311no—
150C22⋊C4—311no—
151C22⋊C4—311no—
152C22⋊C4—311no—
153C22⋊C4—311no—
154C22⋊C4—311no—
155C22⋊C4C2×D3111yescharacteristic
156C22⋊C4C2×D3111yescharacteristic
157C22⋊C4C2×D3111yescharacteristic
158C22⋊C4C2×D3111yescharacteristic
159C42—311no—
160C42—311no—
161C42—311no—
162C23—22no—
163C23—22no—
164C23—41no—
165C23—311no—
166C23C22×D3111yescharacteristic
167C23C22×D3111yescharacteristic
168C23C22×D3111yescharacteristic
169Q8—1241no—
170D4—622no—
171D4—622no—
172D4—1241no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—311no—
176C2×C4—311no—
177C2×C4—311no—
178C2×C4—311no—
179C2×C4—311no—
180C2×C4—311no—
181C2×C4—311no—
182C2×C4—622no—
183C2×C4—1241no—
184C2×C4—1241no—
185C2×C4C22×D3111yescharacteristic
186C2×C4C22×D3111yescharacteristic
187C2×C4C22×D3111yescharacteristic
188C2×C4C22×D3111yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—44no—
197C22—621no—
198C22—621no—
199C22—621no—
200C22#9249512yes—
201C22#9249712yes—
202C22C23×D3111yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—621no—
208C4—621no—
209C4—621no—
210C4—621no—
211C4—621no—
212C4—621no—
213C4—621no—
214C2—22no—
215C2—22no—
216C2—41no—
217C2—1241no—
218C2C2×#9249511yescharacteristic
219C2C2×#9249711yescharacteristic
220C2#1175856111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D31
commutator, socle, cosocleC22×C31C24
FittingC2×C22⋊C4×C31C2
prime radical#11758530C2
hypercenterC2×C22⋊C4D31
hypocenterC31#551
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊C4×C31C2semidirect
3. C2×C22⋊Dic31C2semidirect
4. #11758506C2semidirect
5. C4×C22⋊D31C2semidirect
6. #11758503C2semidirect
7. #11758501C2semidirect
8. #11758463C2semidirect
9. #11758462C2semidirect
10. #11758460C2semidirect
11. (C22⋊D31)⋊C4C2semidirect
12. #11758456C2semidirect
13. #11758456C2semidirect
14. #11758455C2semidirect
15. #11758454C2semidirect
24. C2×C4×D31C22semidirect
25. C2×Dic62C22semidirect
37. (C2×D31)⋊C4C22semidirect
38. (C2×D31)⋊C4C22semidirect
39. (C2×D31)⋊C4C22semidirect
40. C4⋊Dic31C22semidirect
41. C4⋊Dic31C22semidirect
42. C4⋊Dic31C22semidirect
43. Dic31⋊C4C22semidirect
44. Dic31⋊C4C22semidirect
45. Dic31⋊C4C22semidirect
46. Dic31⋊C4C22semidirect
47. Dic31⋊C4C22semidirect
48. C4×Dic31C22semidirect
49. C4×Dic31C22semidirect
50. C4×Dic31C22semidirect
125. C2×C22⋊C4D31semidirect
126. C31#551semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C312
#117585302
C2×C22⋊Dic312
#117585062
C4×C22⋊D312
#117585032
#117585012
#117584632
#117584622
#117584602
(C22⋊D31)⋊C42
#117584562
#117584552
#117584542
#55131