Subgroups — C₂₃×#1747 #15669366

Order 2944.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#405	C₂	1	3	yes	maximal
2	C₂₃×#338	C₂	1	1	yes	maximal, characteristic
3	C₂₃×H(3,ℤ/4)	C₂	1	3	yes	maximal
4	C₂×M₁₆×C₂₃	C₂²	1	3	yes	—
5	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂₃×#117	C₂²	1	3	yes	—
7	C₂₃×#97	C₄	1	6	yes	complemented
8	C₄×C₈×C₂₃	C₄	1	6	yes	complemented
9	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
10	M₁₆×C₂₃	—	2	6	no	—
11	C₂×C₈×C₂₃	C₂×C₄	1	6	yes	—
12	C₂×C₈×C₂₃	C₂×C₄	1	3	yes	—
13	C₂×C₈×C₂₃	C₂×C₄	1	3	yes	—
14	C₄⋊C₄×C₂₃	—	2	3	no	—
15	C₂²⋊C₄×C₂₃	—	2	3	no	—
16	C₄²×C₂₃	C₂×C₄	1	6	yes	—
17	C₂³×C₂₃	#41	1	1	yes	characteristic
18	C₂×C₄×C₂₃	—	2	6	no	—
19	C₂×C₄×C₂₃	C₂²×C₄	1	3	yes	—
20	C₂×C₄×C₂₃	#41	1	3	yes	—
21	C₈×C₂₃	—	2	6	no	—
22	C₈×C₂₃	C₄²	1	3	yes	—
23	C₈×C₂₃	C₄²	1	1	yes	characteristic
24	#1747	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₂₃	—	4	1	no	—
26	C₂²×C₂₃	#117	1	3	yes	—
27	C₄×C₂₃	—	4	6	no	—
28	C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
29	C₄×C₂₃	#117	1	3	yes	—
30	#405	C₂×C₂₃	1	3	yes	—
31	#338	C₂×C₂₃	1	1	yes	characteristic
32	H(3,ℤ/4)	C₂×C₂₃	1	3	yes	—
33	C₂×C₂₃	—	2	3	no	—
34	C₂×C₂₃	#376	1	1	yes	characteristic
35	C₂×M₁₆	C₂²×C₂₃	1	3	yes	—
36	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
37	#117	C₂²×C₂₃	1	3	yes	—
38	#97	C₄×C₂₃	1	6	yes	complemented
39	C₄×C₈	C₄×C₂₃	1	6	yes	complemented
40	C₂₃	#1747	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²×C₄	C₂³×C₂₃	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	C₂×C₄×C₂₃	1	6	yes	—
44	C₂×C₈	C₂×C₄×C₂₃	1	3	yes	—
45	C₂×C₈	C₂×C₄×C₂₃	1	3	yes	—
46	C₄⋊C₄	—	2	3	no	—
47	C₂²⋊C₄	—	2	3	no	—
48	C₄²	C₂×C₄×C₂₃	1	6	yes	—
49	C₂³	#41×C₂₃	1	1	yes	characteristic
50	C₂×C₄	—	2	6	no	—
51	C₂×C₄	C₂²×C₄×C₂₃	1	3	yes	—
52	C₂×C₄	#41×C₂₃	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	C₄²×C₂₃	1	3	yes	—
55	C₈	C₄²×C₂₃	1	1	yes	characteristic
56	C₂²	—	4	1	no	—
57	C₂²	C₂₃×#117	1	3	yes	—
58	C₄	—	4	6	no	—
59	C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
60	C₄	C₂₃×#117	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	C₂₃×#376	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₂₃	C₄²
commutator	C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#376
prime radical	C₂³×C₂₃	#41
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₂₃×#97	C₄	semidirect
8. C₄×C₈×C₂₃	C₄	semidirect
24. #1747	C₂₃	direct (N × H)
38. #97	C₄×C₂₃	semidirect
39. C₄×C₈	C₄×C₂₃	semidirect
40. C₂₃	#1747	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#405	2
C₂₃×#338	2
C₂₃×H(3,ℤ/4)	2
#1747	23

Subgroups — C23×#1747 #15669366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1747 #15669366