Subgroups — C₂₃×#1426 #15669045

Order 2944.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#368	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#367	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	C₂₃×#108	—	2	1	no	—
6	C₂₃×#107	—	2	1	no	—
7	C₂₃×C₃₂	C₄	1	2	yes	complemented
8	M₁₆×C₂₃	—	4	1	no	—
9	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₂₃	—	4	1	no	—
11	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₃	—	8	1	no	—
14	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
15	C₈×C₂₃	—	8	1	no	—
16	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₃	Q₁₆	1	1	yes	characteristic
18	#1426	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₂₃	SD₃₂	1	1	yes	characteristic
20	C₄×C₂₃	—	16	1	no	—
21	C₄×C₂₃	#107	1	1	yes	characteristic
22	C₄×C₂₃	SD₃₂	1	1	yes	characteristic
23	M₆₄	C₂×C₂₃	1	1	yes	characteristic
24	#368	C₂×C₂₃	1	1	yes	characteristic
25	#367	C₂×C₂₃	1	1	yes	characteristic
26	C₂×C₂₃	—	2	1	no	—
27	C₂×C₂₃	#367	1	1	yes	characteristic
28	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#107	—	2	1	no	—
31	C₃₂	C₄×C₂₃	1	2	yes	complemented
32	C₂₃	#1426	1	1	yes	characteristic, direct product factor, Sylow
33	M₁₆	—	4	1	no	—
34	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
35	C₄⋊C₄	—	4	1	no	—
36	C₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
37	C₁₆	Q₈×C₂₃	1	1	yes	characteristic
38	C₂×C₄	—	8	1	no	—
39	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
40	C₈	—	8	1	no	—
41	C₈	C₄⋊C₄×C₂₃	1	1	yes	characteristic
42	C₈	Q₁₆×C₂₃	1	1	yes	characteristic
43	C₂²	C₂₃×SD₃₂	1	1	yes	characteristic
44	C₄	—	16	1	no	—
45	C₄	C₂₃×#107	1	1	yes	characteristic
46	C₄	C₂₃×SD₃₂	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₂₃×#367	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	#367
commutator	C₁₆	C₂×C₄×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
prime radical	C₂²×C₂₃	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×C₈×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₂₃×C₃₂	C₄	semidirect
18. #1426	C₂₃	direct (N × H)
31. C₃₂	C₄×C₂₃	semidirect
32. C₂₃	#1426	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×M₆₄	2
C₂₃×#368	2
C₂₃×#367	2
#1426	23

Subgroups — C23×#1426 #15669045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1426 #15669045