Subgroups — C₂²×C₂²⋊Dic₂₃ #13092865

Order 1472.

674 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₂₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊Dic₂₃	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴×C₂₃	—	2	8	no	—
5	C₂⁴×C₂₃	C₄	1	8	yes	complemented
6	C₂⁴×C₂₃	C₂²	1	6	yes	—
7	C₂⁴×C₂₃	C₂²	1	1	yes	characteristic
8	C₂²×Dic₂₃	—	2	8	no	—
9	C₂²×Dic₂₃	C₂²	1	12	yes	complemented
10	C₂²⋊Dic₂₃	C₂²	1	16	yes	direct product factor
11	C₂³×C₂₃	—	2	32	no	—
12	C₂³×C₂₃	—	2	24	no	—
13	C₂³×C₂₃	C₂×C₄	1	4	yes	—
14	C₂³×C₂₃	C₂×C₄	1	24	yes	complemented
15	C₂³×C₂₃	D₄	1	8	yes	—
16	C₂³×C₂₃	C₂³	1	4	yes	—
17	C₂³×C₂₃	C₂³	1	3	yes	—
18	C₂×Dic₂₃	—	2	24	no	—
19	C₂×Dic₂₃	C₂³	1	8	yes	complemented
20	C₂²×C₂₃	—	2	48	no	—
21	C₂²×C₂₃	—	2	8	no	—
22	C₂²×C₂₃	C₂²⋊C₄	1	16	yes	complemented
23	C₂²×C₂₃	C₂²×C₄	1	6	yes	—
24	C₂²×C₂₃	C₂²×C₄	1	8	yes	complemented
25	C₂²×C₂₃	C₂×D₄	1	12	yes	—
26	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
27	Dic₂₃	—	2	8	no	—
28	C₂²×C₂²⋊C₄	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	—	2	8	no	—
30	C₂×C₂₃	C₂×C₂²⋊C₄	1	12	yes	complemented
31	C₂×C₂₃	C₂³×C₄	1	1	yes	characteristic
32	C₂×C₂₃	C₂²×D₄	1	2	yes	—
33	C₂⁵	D₂₃	1	1	yes	characteristic
34	C₂³×C₄	—	23	2	no	—
35	C₂×C₂²⋊C₄	—	23	12	no	—
36	C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
37	C₂⁴	—	2	8	no	—
38	C₂⁴	Dic₂₃	1	8	yes	complemented
39	C₂⁴	C₂×D₂₃	1	6	yes	—
40	C₂⁴	C₂×D₂₃	1	1	yes	characteristic
41	C₂²×C₄	—	23	12	no	—
42	C₂²×C₄	—	46	8	no	—
43	C₂²⋊C₄	—	23	16	no	—
44	C₂³	—	2	32	no	—
45	C₂³	—	2	24	no	—
46	C₂³	C₂×Dic₂₃	1	4	yes	—
47	C₂³	C₂×Dic₂₃	1	24	yes	complemented
48	C₂³	C₂²⋊D₂₃	1	8	yes	—
49	C₂³	C₂²×D₂₃	1	4	yes	—
50	C₂³	C₂²×D₂₃	1	3	yes	—
51	C₂×C₄	—	23	8	no	—
52	C₂×C₄	—	46	24	no	—
53	C₂²	—	2	48	no	—
54	C₂²	—	2	8	no	—
55	C₂²	C₂²⋊Dic₂₃	1	16	yes	direct product factor
56	C₂²	C₂²×Dic₂₃	1	6	yes	—
57	C₂²	C₂²×Dic₂₃	1	8	yes	complemented
58	C₂²	C₂×C₂²⋊D₂₃	1	12	yes	—
59	C₂²	C₂³×D₂₃	1	1	yes	characteristic
60	C₄	—	46	8	no	—
61	C₂	—	2	8	no	—
62	C₂	C₂×C₂²⋊Dic₂₃	1	12	yes	direct product factor
63	C₂	C₂³×Dic₂₃	1	1	yes	characteristic
64	C₂	C₂²×C₂²⋊D₂₃	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₂₃
commutator	C₂×C₂₃	C₂³×C₄
Frattini	C₂²	C₂³×D₂₃
Fitting, prime radical	C₂⁵×C₂₃	C₂
socle	C₂⁴×C₂₃	C₂²
cosocle	C₂²×C₂₃	C₂⁴
hypercenter	C₂⁵	D₂₃
hypocenter	C₂₃	C₂²×C₂²⋊C₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
2. C₂³×Dic₂₃	C₂	semidirect
3. C₂×C₂²⋊Dic₂₃	C₂	direct (N × H)
5. C₂⁴×C₂₃	C₄	semidirect
9. C₂²×Dic₂₃	C₂²	semidirect
10. C₂²⋊Dic₂₃	C₂²	direct (N × H)
14. C₂³×C₂₃	C₂×C₄	semidirect
19. C₂×Dic₂₃	C₂³	semidirect
22. C₂²×C₂₃	C₂²⋊C₄	semidirect
24. C₂²×C₂₃	C₂²×C₄	semidirect
30. C₂×C₂₃	C₂×C₂²⋊C₄	semidirect
36. C₂₃	C₂²×C₂²⋊C₄	semidirect
38. C₂⁴	Dic₂₃	semidirect
47. C₂³	C₂×Dic₂₃	semidirect
55. C₂²	C₂²⋊Dic₂₃	direct (N × H)
57. C₂²	C₂²×Dic₂₃	semidirect
62. C₂	C₂×C₂²⋊Dic₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₂₃	2
C₂³×Dic₂₃	2
C₂×C₂²⋊Dic₂₃	2
C₂²×C₂²⋊C₄	23

Subgroups — C22×C22⋊Dic23 #13092865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂²⋊Dic₂₃ #13092865