Subgroups — C₂₃×#1369 #15668988

Order 2944.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#364	C₂	1	2	yes	maximal
2	C₂₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₂₃×M₃₂	—	2	2	no	—
4	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
9	C₄²×C₂₃	Q₈	1	1	yes	characteristic
10	C₁₆×C₂₃	—	2	1	no	—
11	C₁₆×C₂₃	—	4	2	no	—
12	C₁₆×C₂₃	C₈	1	2	yes	—
13	C₂×C₄×C₂₃	—	2	1	no	—
14	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₂₃	M₁₆	1	1	yes	characteristic
17	C₈×C₂₃	SD₁₆	1	2	yes	—
18	#1369	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₂₃	#108	1	1	yes	characteristic
20	C₄×C₂₃	—	4	1	no	—
21	C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₂₃	#106	1	1	yes	characteristic
23	#364	C₂×C₂₃	1	2	yes	—
24	#346	C₂×C₂₃	1	1	yes	characteristic
25	C₂×C₂₃	—	2	1	no	—
26	C₂×C₂₃	#334	1	1	yes	characteristic
27	M₃₂	—	2	2	no	—
28	C₂×C₁₆	C₄×C₂₃	1	1	yes	characteristic
29	C₂×C₁₆	C₄×C₂₃	1	1	yes	characteristic
30	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
31	C₂₃	#1369	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
33	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
34	C₄²	Q₈×C₂₃	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	—	4	2	no	—
37	C₁₆	C₈×C₂₃	1	2	yes	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
40	C₈	C₂×C₈×C₂₃	1	1	yes	characteristic
41	C₈	M₁₆×C₂₃	1	1	yes	characteristic
42	C₈	SD₁₆×C₂₃	1	2	yes	—
43	C₂²	C₂₃×#108	1	1	yes	characteristic
44	C₄	—	4	1	no	—
45	C₄	C₂₃×C₄⋊C₈	1	1	yes	characteristic
46	C₄	C₂₃×#106	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₂₃×#334	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	#106
commutator	C₈	C₂×C₈×C₂₃
Frattini, cosocle	C₄×C₈	C₂²×C₂₃
socle	C₂×C₂₃	#334
prime radical	C₂²×C₂₃	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂×C₈×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
18. #1369	C₂₃	direct (N × H)
31. C₂₃	#1369	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×#364	2
C₂₃×#346	2
#1369	23

Subgroups — C23×#1369 #15668988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1369 #15668988