Subgroups — C₂₃×#1711 #15669330

Order 2944.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#487	C₂	1	3	yes	maximal, complemented
2	C₂₃×#486	C₂	1	3	yes	maximal
3	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×C₄⋊Q₈	C₂²	1	3	yes	—
5	C₂₃×#127	C₂²	1	1	yes	characteristic
6	C₂₃×#103	—	2	6	no	—
7	C₂₃×#102	—	2	6	no	—
8	C₄×C₈×C₂₃	C₂²	1	3	yes	—
9	C₂×Q₈×C₂₃	—	2	3	no	—
10	C₂×D₄×C₂₃	—	2	3	no	—
11	C₂×C₈×C₂₃	D₄	1	6	yes	—
12	C₄⋊C₄×C₂₃	—	2	3	no	—
13	C₄⋊C₄×C₂₃	—	2	3	no	—
14	C₄²×C₂₃	C₂³	1	1	yes	characteristic
15	C₂³×C₂₃	—	4	1	no	—
16	Q₈×C₂₃	—	4	6	no	—
17	D₄×C₂₃	—	4	6	no	—
18	C₂×C₄×C₂₃	—	4	3	no	—
19	C₂×C₄×C₂₃	C₂×D₄	1	3	yes	—
20	C₈×C₂₃	—	2	6	no	—
21	#1711	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₂₃	—	8	3	no	—
23	C₂²×C₂₃	#127	1	1	yes	characteristic
24	C₄×C₂₃	—	8	3	no	—
25	C₄×C₂₃	#135	1	6	yes	—
26	#487	C₂×C₂₃	1	3	yes	complemented
27	#486	C₂×C₂₃	1	3	yes	—
28	C₈²	C₂×C₂₃	1	1	yes	characteristic, complemented
29	C₂×C₂₃	—	16	1	no	—
30	C₂×C₂₃	#495	1	3	yes	—
31	C₄⋊Q₈	C₂²×C₂₃	1	3	yes	—
32	#127	C₂²×C₂₃	1	1	yes	characteristic
33	#103	—	2	6	no	—
34	#102	—	2	6	no	—
35	C₄×C₈	C₂²×C₂₃	1	3	yes	—
36	C₂₃	#1711	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×Q₈	—	2	3	no	—
38	C₂×D₄	—	2	3	no	—
39	C₂×C₈	D₄×C₂₃	1	6	yes	—
40	C₄⋊C₄	—	2	3	no	—
41	C₄⋊C₄	—	2	3	no	—
42	C₄²	C₂³×C₂₃	1	1	yes	characteristic
43	C₂³	—	4	1	no	—
44	Q₈	—	4	6	no	—
45	D₄	—	4	6	no	—
46	C₂×C₄	—	4	3	no	—
47	C₂×C₄	C₂×D₄×C₂₃	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	8	3	no	—
50	C₂²	C₂₃×#127	1	1	yes	characteristic
51	C₄	—	8	3	no	—
52	C₄	C₂₃×#135	1	6	yes	—
53	C₂	—	16	1	no	—
54	C₂	C₂₃×#495	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
prime radical	C₂₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#487	C₂	semidirect
3. C₈²×C₂₃	C₂	semidirect
21. #1711	C₂₃	direct (N × H)
26. #487	C₂×C₂₃	semidirect
28. C₈²	C₂×C₂₃	semidirect
36. C₂₃	#1711	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×#487	2
C₂₃×#486	2
C₈²×C₂₃	2
#1711	23

Subgroups — C23×#1711 #15669330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1711 #15669330