Subgroups — C₂₃×#1424 #15669043

Order 2944.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#366	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
4	C₂₃×#107	—	2	2	no	—
5	C₂₃×C₃₂	C₄	1	2	yes	complemented
6	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
7	C₄⋊C₄×C₂₃	—	4	2	no	—
8	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₂₃	—	8	2	no	—
11	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
12	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₃	Q₁₆	1	1	yes	characteristic
14	#1424	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
16	C₄×C₂₃	—	16	2	no	—
17	C₄×C₂₃	#107	1	1	yes	characteristic
18	C₄×C₂₃	Q₃₂	1	1	yes	characteristic
19	C₂×C₃₂	C₂×C₂₃	1	1	yes	characteristic
20	#366	C₂×C₂₃	1	2	yes	—
21	C₂×C₂₃	#366	1	1	yes	characteristic
22	C₂×C₂₃	SD₆₄	1	2	yes	—
23	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
24	#107	—	2	2	no	—
25	C₃₂	C₄×C₂₃	1	2	yes	complemented
26	C₂₃	#1424	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
28	C₄⋊C₄	—	4	2	no	—
29	C₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
30	C₁₆	Q₈×C₂₃	1	1	yes	characteristic
31	C₂×C₄	—	8	2	no	—
32	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
33	C₈	C₄⋊C₄×C₂₃	1	1	yes	characteristic
34	C₈	Q₁₆×C₂₃	1	1	yes	characteristic
35	C₂²	C₂₃×D₁₆	1	1	yes	characteristic
36	C₄	—	16	2	no	—
37	C₄	C₂₃×#107	1	1	yes	characteristic
38	C₄	C₂₃×Q₃₂	1	1	yes	characteristic
39	C₂	C₂₃×#366	1	1	yes	characteristic
40	C₂	C₂₃×SD₆₄	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	D₁₆
commutator	C₁₆	C₂×C₄×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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
5. C₂₃×C₃₂	C₄	semidirect
14. #1424	C₂₃	direct (N × H)
25. C₃₂	C₄×C₂₃	semidirect
26. C₂₃	#1424	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×C₃₂	2
C₂₃×#366	2
#1424	23

Subgroups — C23×#1424 #15669043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1424 #15669043