Subgroups — C₂²×C₈×D₂₃ #13093173

Order 1472.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₂₃	C₂	1	12	yes	maximal, direct product factor
5	C₂³×D₂₃	C₄	1	1	yes	characteristic
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₃	C₄	1	1	yes	characteristic
8	C₂×C₄×D₂₃	C₄	1	6	yes	—
9	C₂×C₄×D₂₃	C₂²	1	6	yes	—
10	C₂×C₈×C₂₃	C₂²	1	6	yes	complemented
11	C₂×C₂₃⋊C₈	C₂²	1	6	yes	complemented
12	C₈×D₂₃	C₂²	1	16	yes	direct product factor
13	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×D₂₃	C₈	1	8	yes	direct product factor
15	C₂²×D₂₃	C₂×C₄	1	6	yes	—
16	C₂×C₄×C₂₃	C₂×C₄	1	3	yes	—
17	C₂×C₄×C₂₃	C₂³	1	3	yes	—
18	C₂×Dic₂₃	C₂×C₄	1	6	yes	—
19	C₄×D₂₃	C₂×C₄	1	12	yes	—
20	C₄×D₂₃	C₂³	1	4	yes	—
21	C₈×C₂₃	C₂³	1	4	yes	complemented
22	C₂₃⋊C₈	C₂³	1	4	yes	complemented
23	C₂²×C₂₃	C₂×C₈	1	4	yes	complemented
24	C₂²×C₂₃	C₂²×C₄	1	3	yes	—
25	C₂×D₂₃	C₂×C₈	1	24	yes	direct product factor
26	C₂×D₂₃	C₂²×C₄	1	4	yes	—
27	C₄×C₂₃	C₂²×C₄	1	3	yes	—
28	C₄×C₂₃	C₂⁴	1	1	yes	characteristic
29	Dic₂₃	C₂²×C₄	1	4	yes	—
30	C₂³×C₈	—	23	1	no	maximal, Sylow
31	C₂×C₂₃	C₂²×C₈	1	6	yes	complemented
32	C₂×C₂₃	C₂³×C₄	1	1	yes	characteristic
33	D₂₃	C₂²×C₈	1	8	yes	direct product factor
34	C₂³×C₄	—	23	1	no	—
35	C₂²×C₈	—	23	1	no	—
36	C₂²×C₈	—	23	12	no	—
37	C₂²×C₈	D₂₃	1	1	yes	characteristic, direct product factor
38	C₂₃	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
39	C₂⁴	—	23	1	no	—
40	C₂²×C₄	—	23	1	no	—
41	C₂²×C₄	—	23	6	no	—
42	C₂²×C₄	—	23	6	no	—
43	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
44	C₂×C₈	—	23	6	no	—
45	C₂×C₈	—	23	16	no	—
46	C₂×C₈	C₂×D₂₃	1	6	yes	direct product factor
47	C₂³	—	23	8	no	—
48	C₂³	—	23	6	no	—
49	C₂³	C₄×D₂₃	1	1	yes	characteristic
50	C₂×C₄	—	23	6	no	—
51	C₂×C₄	—	23	12	no	—
52	C₂×C₄	—	23	4	no	—
53	C₂×C₄	C₄×D₂₃	1	3	yes	—
54	C₂×C₄	C₂²×D₂₃	1	3	yes	—
55	C₈	—	23	4	no	—
56	C₈	C₂²×D₂₃	1	4	yes	direct product factor
57	C₂²	—	23	24	no	—
58	C₂²	—	23	4	no	—
59	C₂²	C₈×D₂₃	1	4	yes	direct product factor
60	C₂²	C₂×C₄×D₂₃	1	3	yes	—
61	C₄	—	23	4	no	—
62	C₄	C₂×C₄×D₂₃	1	3	yes	—
63	C₄	C₂³×D₂₃	1	1	yes	characteristic
64	C₂	—	23	8	no	—
65	C₂	C₂×C₈×D₂₃	1	6	yes	direct product factor
66	C₂	C₂²×C₄×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₂₃
commutator, hypocenter	C₂₃	C₂³×C₈
Frattini	C₄	C₂³×D₂₃
Fitting	C₂²×C₈×C₂₃	C₂
socle	C₂³×C₂₃	C₂×C₄
prime radical	C₂³×D₂₃	C₄
cosocle	C₄×C₂₃	C₂⁴
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₈×C₂₃	C₂	semidirect
3. C₂²×C₂₃⋊C₈	C₂	semidirect
4. C₂×C₈×D₂₃	C₂	direct (N × H)
10. C₂×C₈×C₂₃	C₂²	semidirect
11. C₂×C₂₃⋊C₈	C₂²	semidirect
12. C₈×D₂₃	C₂²	direct (N × H)
14. C₂²×D₂₃	C₈	direct (N × H)
21. C₈×C₂₃	C₂³	semidirect
22. C₂₃⋊C₈	C₂³	semidirect
23. C₂²×C₂₃	C₂×C₈	semidirect
25. C₂×D₂₃	C₂×C₈	direct (N × H)
31. C₂×C₂₃	C₂²×C₈	semidirect
33. D₂₃	C₂²×C₈	direct (N × H)
37. C₂²×C₈	D₂₃	direct (N × H)
38. C₂₃	C₂³×C₈	semidirect
46. C₂×C₈	C₂×D₂₃	direct (N × H)
56. C₈	C₂²×D₂₃	direct (N × H)
59. C₂²	C₈×D₂₃	direct (N × H)
65. C₂	C₂×C₈×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
C₂²×C₈×C₂₃	2
C₂²×C₂₃⋊C₈	2
C₂×C₈×D₂₃	2
C₂³×C₈	23

Subgroups — C22×C8×D23 #13093173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₈×D₂₃ #13093173