Subgroups — C₂₃×#2845 #15670464

Order 2944.

340 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#398	C₂	1	12	yes	maximal
2	C₂₃×#382	C₂	1	3	yes	maximal
3	C₂×C₄⋊C₄×C₂₃	C₂²	1	6	yes	—
4	C₂×C₄⋊C₄×C₂₃	C₂²	1	12	yes	—
5	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂₃×#95	C₂²	1	12	yes	—
7	C₂₃×#95	C₂²	1	4	yes	—
8	C₂²×C₄×C₂₃	C₂³	1	12	yes	—
9	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
10	C₄⋊C₄×C₂₃	—	4	6	no	—
11	C₄⋊C₄×C₂₃	—	4	12	no	—
12	C₄²×C₂₃	Q₈	1	4	yes	—
13	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
14	C₂×C₄×C₂₃	—	2	3	no	—
15	C₂×C₄×C₂₃	—	2	3	no	—
16	C₂×C₄×C₂₃	—	2	12	no	—
17	C₂×C₄×C₂₃	—	2	12	no	—
18	C₂×C₄×C₂₃	—	2	12	no	—
19	C₂×C₄×C₂₃	C₂×Q₈	1	6	yes	—
20	#2845	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₂₃	C₂²×Q₈	1	1	yes	characteristic
22	C₂²×C₂₃	H(5,𝔽₂)	1	3	yes	—
23	C₂²×C₂₃	2₋¹⁺⁴	1	3	yes	—
24	C₄×C₂₃	—	2	6	no	—
25	C₄×C₂₃	—	4	12	no	—
26	#398	C₂×C₂₃	1	12	yes	—
27	#382	C₂×C₂₃	1	3	yes	—
28	C₂×C₂₃	#544	1	3	yes	—
29	C₂×C₂₃	#562	1	3	yes	—
30	C₂×C₂₃	#564	1	1	yes	characteristic
31	C₂×C₄⋊C₄	C₂²×C₂₃	1	6	yes	—
32	C₂×C₄⋊C₄	C₂²×C₂₃	1	12	yes	—
33	C₂×C₄²	C₂²×C₂₃	1	1	yes	characteristic
34	#95	C₂²×C₂₃	1	12	yes	—
35	#95	C₂²×C₂₃	1	4	yes	—
36	C₂₃	#2845	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₄	C₂³×C₂₃	1	12	yes	—
38	C₂²×C₄	C₂³×C₂₃	1	3	yes	—
39	C₄⋊C₄	—	4	6	no	—
40	C₄⋊C₄	—	4	12	no	—
41	C₄²	Q₈×C₂₃	1	4	yes	—
42	C₂³	C₂⁴×C₂₃	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	3	no	—
45	C₂×C₄	—	2	12	no	—
46	C₂×C₄	—	2	12	no	—
47	C₂×C₄	—	2	12	no	—
48	C₂×C₄	C₂×Q₈×C₂₃	1	6	yes	—
49	C₂²	C₂²×Q₈×C₂₃	1	1	yes	characteristic
50	C₂²	C₂₃×H(5,𝔽₂)	1	3	yes	—
51	C₂²	C₂₃×2₋¹⁺⁴	1	3	yes	—
52	C₄	—	2	6	no	—
53	C₄	—	4	12	no	—
54	C₂	C₂₃×#544	1	3	yes	—
55	C₂	C₂₃×#562	1	3	yes	—
56	C₂	C₂₃×#564	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
20. #2845	C₂₃	direct (N × H)
36. C₂₃	#2845	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×#398	2
C₂₃×#382	2
#2845	23

Subgroups — C23×#2845 #15670464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2845 #15670464