Subgroups — C₂₃×#1398 #15669017

Order 2944.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×M₆₄	C₂	1	2	yes	maximal
2	C₂₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₂₃	C₄	1	1	yes	characteristic
6	C₂₃×C₃₂	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₃	C₈	1	1	yes	characteristic
10	C₁₆×C₂₃	C₈	1	2	yes	—
11	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₂₃	—	2	1	no	—
13	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
14	C₈×C₂₃	—	2	1	no	—
15	C₈×C₂₃	C₄²	1	1	yes	characteristic
16	C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
17	#1398	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₂₃	M₃₂	1	1	yes	characteristic
19	C₄×C₂₃	—	4	1	no	—
20	C₄×C₂₃	C₄×C₈	1	1	yes	characteristic
21	C₄×C₂₃	M₃₂	1	1	yes	characteristic
22	M₆₄	C₂×C₂₃	1	2	yes	—
23	#346	C₂×C₂₃	1	1	yes	characteristic
24	C₂×C₂₃	—	2	1	no	—
25	C₂×C₂₃	#346	1	1	yes	characteristic
26	C₂×C₁₆	C₄×C₂₃	1	1	yes	characteristic
27	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
28	C₄×C₈	C₄×C₂₃	1	1	yes	characteristic
29	C₃₂	C₄×C₂₃	1	4	yes	complemented
30	C₂₃	#1398	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₈	C₈×C₂₃	1	1	yes	characteristic
32	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
33	C₄²	C₈×C₂₃	1	1	yes	characteristic
34	C₁₆	C₈×C₂₃	1	2	yes	—
35	C₁₆	C₂×C₄×C₂₃	1	2	yes	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×C₈×C₂₃	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₄²×C₂₃	1	1	yes	characteristic
40	C₈	C₂×C₈×C₂₃	1	1	yes	characteristic
41	C₂²	C₂₃×M₃₂	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	C₄×C₈×C₂₃	1	1	yes	characteristic
44	C₄	C₂₃×M₃₂	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	C₂₃×#346	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₂₃	C₄²
commutator	C₄	C₄×C₈×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
socle	C₂×C₂₃	#346
prime radical	C₂²×C₂₃	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂₃×C₃₂	C₄	semidirect
17. #1398	C₂₃	direct (N × H)
29. C₃₂	C₄×C₂₃	semidirect
30. C₂₃	#1398	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×#346	2
#1398	23

Subgroups — C23×#1398 #15669017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1398 #15669017