Finite Group Databasebeta

← #14583575

Subgroups — #14583575

Order 2752.

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
1#13063318C211yesmaximal, characteristic, complemented
2#13063318C211yesmaximal, characteristic, complemented
3#13063311C211yesmaximal, characteristic, complemented
4#13063309C211yesmaximal, characteristic, complemented
5#13063308C211yesmaximal, characteristic, complemented
6#13063307C211yesmaximal, characteristic, complemented
7#13063304C211yesmaximal, characteristic, complemented
8#13063302C211yesmaximal, characteristic, complemented
9#13063294C211yesmaximal, characteristic
10C4×C22⋊D43C211yesmaximal, characteristic, complemented
11(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
12#13063284C211yesmaximal, characteristic, complemented
13#13063281C211yesmaximal, characteristic, complemented
14C2×C22⋊Dic43C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C24×C43C2211yescharacteristic
17C22×C4×C43C2211yescharacteristic
18C22×C4×C43C2211yescharacteristic
19C2×C22⋊D43C2211yescharacteristic
20C2×C22⋊D43C2211yescharacteristic
21C2×C22⋊D43C2211yescharacteristic
22C22×Dic43C2211yescharacteristic
23C22×Dic43C2211yescharacteristic
24C2×C4×D43C2211yescharacteristic, complemented
25C2×Dic86C2211yescharacteristic, complemented
26C22⋊C4×C43C2211yescharacteristic
27C22⋊C4×C43C2211yescharacteristic
28C22⋊C4×C43C2211yescharacteristic
29C22⋊C4×C43C2211yescharacteristic
30C22⋊Dic43C2211yescharacteristic
31C22⋊Dic43C2211yescharacteristic
32C22⋊Dic43C2211yescharacteristic
33C22⋊Dic43C2211yescharacteristic
34C22⋊Dic43C2211yescharacteristic
35C22⋊Dic43C2211yescharacteristic
36C22⋊Dic43C2211yescharacteristic
37(C2×D43)⋊C4C2211yescharacteristic, complemented
38(C2×D43)⋊C4C2211yescharacteristic, complemented
39(C2×D43)⋊C4C2211yescharacteristic, complemented
40C4⋊Dic43C2211yescharacteristic, complemented
41C4⋊Dic43C2211yescharacteristic, complemented
42C4⋊Dic43C2211yescharacteristic, complemented
43Dic43⋊C4C2211yescharacteristic, complemented
44Dic43⋊C4C2211yescharacteristic, complemented
45Dic43⋊C4C2211yescharacteristic, complemented
46Dic43⋊C4C2211yescharacteristic, complemented
47Dic43⋊C4C2211yescharacteristic, complemented
48C4×Dic43C2211yescharacteristic, complemented
49C4×Dic43C2211yescharacteristic, complemented
50C4×Dic43C2211yescharacteristic, complemented
51C23×C43—22no—
52C23×C43—22no—
53C23×C43—41no—
54C23×C43C2311yescharacteristic
55C23×C43C2311yescharacteristic
56C23×C43C2311yescharacteristic
57C22×D43C2311yescharacteristic
58C2×C4×C43—22no—
59C2×C4×C43—41no—
60C2×C4×C43C2311yescharacteristic
61C2×C4×C43C2311yescharacteristic
62C2×C4×C43C2311yescharacteristic
63C2×C4×C43C2311yescharacteristic
64C22⋊D43—22no—
65C22⋊D43—22no—
66C22⋊D43—41no—
67C2×Dic43—22no—
68C2×Dic43—41no—
69C2×Dic43C2311yescharacteristic
70C2×Dic43C2311yescharacteristic
71C2×Dic43C2311yescharacteristic
72C2×Dic43C2311yescharacteristic
73C2×Dic43C2311yescharacteristic
74C2×Dic43C2311yescharacteristic
75C2×Dic43C2311yescharacteristic
76C4×D43—41no—
77Dic86—41no—
78C22×C43—21no—
79C22×C43—21no—
80C22×C43—21no—
81C22×C43—21no—
82C22×C43—21no—
83C22×C43—21no—
84C22×C43—21no—
85C22×C43—44no—
86C22×C43#4112yes—
87C22×C43#4112yes—
88C22×C43C2411yescharacteristic
89C2×D43—21no—
90C2×D43—21no—
91C2×D43—21no—
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—21no—
95C4×C43—21no—
96Dic43—21no—
97Dic43—21no—
98Dic43—21no—
99Dic43—21no—
100Dic43—21no—
101Dic43—21no—
102Dic43—21no—
103C2×C43—22no—
104C2×C43—22no—
105C2×C43—41no—
106C2×C43C2×#4111yescharacteristic
107C2×C43C2×#4111yescharacteristic
108C2×C43H(5,𝔽2)11yescharacteristic
109D43—41no—
110#551—431nomaximal, Sylow
111C43#55111yescharacteristic, complemented, Sylow
112#126—431no—
113#126—431no—
114#124—431no—
115#123—431no—
116#123—431no—
117#123—431no—
118C22⋊Q8—431no—
119C22⋊Q8—431no—
120#120—431no—
121C4×D4—431no—
122C4×D4—431no—
123#117—431no—
124#117—431no—
125C2×C22⋊C4—431no—
126C2×C22⋊C4D4311yescharacteristic, complemented
127C24C2×D4311yescharacteristic
128C2×Q8—431no—
129C2×D4—431no—
130C2×D4—431no—
131C2×D4—431no—
132C22×C4—431no—
133C22×C4—431no—
134C22×C4—431no—
135C22×C4C2×D4311yescharacteristic
136C22×C4C2×D4311yescharacteristic
137C4⋊C4—431no—
138C4⋊C4—431no—
139C4⋊C4—431no—
140C4⋊C4—431no—
141C4⋊C4—431no—
142C4⋊C4—431no—
143C4⋊C4—431no—
144C4⋊C4—431no—
145C22⋊C4—431no—
146C22⋊C4—431no—
147C22⋊C4—431no—
148C22⋊C4—431no—
149C22⋊C4—431no—
150C22⋊C4—431no—
151C22⋊C4—431no—
152C22⋊C4—431no—
153C22⋊C4—431no—
154C22⋊C4—431no—
155C22⋊C4C2×D4311yescharacteristic
156C22⋊C4C2×D4311yescharacteristic
157C22⋊C4C2×D4311yescharacteristic
158C22⋊C4C2×D4311yescharacteristic
159C42—431no—
160C42—431no—
161C42—431no—
162C23—22no—
163C23—22no—
164C23—41no—
165C23—431no—
166C23C22×D4311yescharacteristic
167C23C22×D4311yescharacteristic
168C23C22×D4311yescharacteristic
169Q8—1721no—
170D4—862no—
171D4—862no—
172D4—1721no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—431no—
176C2×C4—431no—
177C2×C4—431no—
178C2×C4—431no—
179C2×C4—431no—
180C2×C4—431no—
181C2×C4—431no—
182C2×C4—862no—
183C2×C4—1721no—
184C2×C4—1721no—
185C2×C4C22×D4311yescharacteristic
186C2×C4C22×D4311yescharacteristic
187C2×C4C22×D4311yescharacteristic
188C2×C4C22×D4311yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—44no—
197C22—861no—
198C22—861no—
199C22—861no—
200C22#1062189812yes—
201C22#1062190012yes—
202C22C23×D4311yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—861no—
208C4—861no—
209C4—861no—
210C4—861no—
211C4—861no—
212C4—861no—
213C4—861no—
214C2—22no—
215C2—22no—
216C2—41no—
217C2—1721no—
218C2C2×#1062190011yescharacteristic
219C2C2×#1062189811yescharacteristic
220C2#1306337011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
FittingC2×C22⋊C4×C43C2
prime radical#13063294C2
hypercenterC2×C22⋊C4D43
hypocenterC43#551
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #13063318C2semidirect
2. #13063318C2semidirect
3. #13063311C2semidirect
4. #13063309C2semidirect
5. #13063308C2semidirect
6. #13063307C2semidirect
7. #13063304C2semidirect
8. #13063302C2semidirect
10. C4×C22⋊D43C2semidirect
11. (C22⋊D43)⋊C4C2semidirect
12. #13063284C2semidirect
13. #13063281C2semidirect
14. C2×C22⋊Dic43C2semidirect
15. C2×C22⋊C4×C43C2semidirect
24. C2×C4×D43C22semidirect
25. C2×Dic86C22semidirect
37. (C2×D43)⋊C4C22semidirect
38. (C2×D43)⋊C4C22semidirect
39. (C2×D43)⋊C4C22semidirect
40. C4⋊Dic43C22semidirect
41. C4⋊Dic43C22semidirect
42. C4⋊Dic43C22semidirect
43. Dic43⋊C4C22semidirect
44. Dic43⋊C4C22semidirect
45. Dic43⋊C4C22semidirect
46. Dic43⋊C4C22semidirect
47. Dic43⋊C4C22semidirect
48. C4×Dic43C22semidirect
49. C4×Dic43C22semidirect
50. C4×Dic43C22semidirect
111. C43#551semidirect
126. C2×C22⋊C4D43semidirect

Maximal subgroups

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

subgroupindex
#130633182
#130633112
#130633092
#130633082
#130633072
#130633042
#130633022
#130632942
C4×C22⋊D432
(C22⋊D43)⋊C42
#130632842
#130632812
C2×C22⋊Dic432
C2×C22⋊C4×C432
#55143