Subgroups — C₂×C₄²×D₂₃ #13092861

Order 1472.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₂₃	C₂	1	3	yes	maximal
2	C₂×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×Dic₂₃	C₂	1	3	yes	maximal, complemented
4	C₄²×D₂₃	C₂	1	8	yes	maximal, direct product factor
5	C₂³×D₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₂₃	C₂²	1	3	yes	—
7	C₂²×Dic₂₃	C₂²	1	3	yes	—
8	C₂×C₄×D₂₃	C₄	1	24	yes	direct product factor
9	C₂×C₄×D₂₃	C₂²	1	12	yes	—
10	C₄²×C₂₃	C₂²	1	4	yes	complemented
11	C₄×Dic₂₃	C₂²	1	12	yes	complemented
12	C₂³×C₂₃	C₂³	1	1	yes	characteristic
13	C₂²×D₂₃	C₂×C₄	1	12	yes	—
14	C₂²×D₂₃	C₂³	1	2	yes	—
15	C₂×C₄×C₂₃	C₂×C₄	1	12	yes	complemented
16	C₂×C₄×C₂₃	C₂³	1	6	yes	—
17	C₂×Dic₂₃	C₂×C₄	1	12	yes	complemented
18	C₂×Dic₂₃	C₂³	1	6	yes	—
19	C₄×D₂₃	C₂×C₄	1	48	yes	direct product factor
20	C₂²×C₂₃	C₂²×C₄	1	6	yes	—
21	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
22	C₂×D₂₃	C₄²	1	16	yes	direct product factor
23	C₂×D₂₃	C₂²×C₄	1	12	yes	—
24	C₄×C₂₃	C₂²×C₄	1	12	yes	complemented
25	Dic₂₃	C₂²×C₄	1	12	yes	complemented
26	C₂²×C₄²	—	23	1	no	maximal, Sylow
27	C₂×C₂₃	C₂×C₄²	1	4	yes	complemented
28	C₂×C₂₃	C₂³×C₄	1	3	yes	—
29	D₂₃	C₂×C₄²	1	8	yes	direct product factor
30	C₂³×C₄	—	23	3	no	—
31	C₂×C₄²	—	23	3	no	—
32	C₂×C₄²	—	23	8	no	—
33	C₂×C₄²	D₂₃	1	1	yes	characteristic, direct product factor
34	C₂₃	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	—	23	1	no	—
36	C₂²×C₄	—	23	3	no	—
37	C₂²×C₄	—	23	24	no	—
38	C₂²×C₄	—	23	12	no	—
39	C₂²×C₄	C₂×D₂₃	1	3	yes	—
40	C₄²	—	23	12	no	—
41	C₄²	C₂×D₂₃	1	4	yes	direct product factor
42	C₂³	—	23	12	no	—
43	C₂³	—	23	2	no	—
44	C₂³	C₂²×D₂₃	1	1	yes	characteristic
45	C₂×C₄	—	23	12	no	—
46	C₂×C₄	—	23	6	no	—
47	C₂×C₄	—	23	48	no	—
48	C₂×C₄	C₄×D₂₃	1	12	yes	direct product factor
49	C₂×C₄	C₂²×D₂₃	1	6	yes	—
50	C₂²	—	23	16	no	—
51	C₂²	—	23	12	no	—
52	C₂²	C₂×C₄×D₂₃	1	6	yes	—
53	C₂²	C₂³×D₂₃	1	1	yes	characteristic
54	C₄	—	23	12	no	—
55	C₄	C₂×C₄×D₂₃	1	12	yes	direct product factor
56	C₂	—	23	8	no	—
57	C₂	C₄²×D₂₃	1	4	yes	direct product factor
58	C₂	C₂²×C₄×D₂₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₂₃
commutator, hypocenter	C₂₃	C₂²×C₄²
Frattini	C₂²	C₂³×D₂₃
Fitting	C₂×C₄²×C₂₃	C₂
socle	C₂³×C₂₃	C₂³
prime radical	C₂³×D₂₃	C₂²
cosocle	C₂²×C₂₃	C₂⁴
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄²×C₂₃	C₂	semidirect
3. C₂×C₄×Dic₂₃	C₂	semidirect
4. C₄²×D₂₃	C₂	direct (N × H)
8. C₂×C₄×D₂₃	C₄	direct (N × H)
10. C₄²×C₂₃	C₂²	semidirect
11. C₄×Dic₂₃	C₂²	semidirect
15. C₂×C₄×C₂₃	C₂×C₄	semidirect
17. C₂×Dic₂₃	C₂×C₄	semidirect
19. C₄×D₂₃	C₂×C₄	direct (N × H)
22. C₂×D₂₃	C₄²	direct (N × H)
24. C₄×C₂₃	C₂²×C₄	semidirect
25. Dic₂₃	C₂²×C₄	semidirect
27. C₂×C₂₃	C₂×C₄²	semidirect
29. D₂₃	C₂×C₄²	direct (N × H)
33. C₂×C₄²	D₂₃	direct (N × H)
34. C₂₃	C₂²×C₄²	semidirect
41. C₄²	C₂×D₂₃	direct (N × H)
48. C₂×C₄	C₄×D₂₃	direct (N × H)
55. C₄	C₂×C₄×D₂₃	direct (N × H)
57. C₂	C₄²×D₂₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₂₃	2
C₂×C₄²×C₂₃	2
C₂×C₄×Dic₂₃	2
C₄²×D₂₃	2
C₂²×C₄²	23

Subgroups — C2×C42×D23 #13092861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄²×D₂₃ #13092861