Subgroups — C₂₃×#7545 #19155171

Order 5888.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1423	C₂	1	2	yes	maximal
3	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
4	C₂₃×#366	—	2	2	no	—
5	C₂₃×C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
7	C₂₃×#107	—	4	2	no	—
8	C₂₃×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₂₃×C₃₂	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
11	C₄⋊C₄×C₂₃	—	8	2	no	—
12	C₁₆×C₂₃	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₂₃	Q₁₆	1	1	yes	characteristic
14	#7545	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₄×C₂₃	—	16	2	no	—
16	C₂×C₄×C₂₃	D₁₆	1	1	yes	characteristic
17	C₈×C₂₃	#107	1	1	yes	characteristic
18	C₈×C₂₃	Q₃₂	1	1	yes	characteristic
19	C₂×C₆₄	C₂×C₂₃	1	1	yes	characteristic
20	#1423	C₂×C₂₃	1	2	yes	—
21	C₂²×C₂₃	D₃₂	1	1	yes	characteristic
22	C₄×C₂₃	—	32	2	no	—
23	C₄×C₂₃	#366	1	1	yes	characteristic
24	C₄×C₂₃	Q₆₄	1	1	yes	characteristic
25	C₂×C₃₂	C₂²×C₂₃	1	1	yes	characteristic
26	#366	—	2	2	no	—
27	C₆₄	C₄×C₂₃	1	2	yes	complemented
28	C₂×C₂₃	#1423	1	1	yes	characteristic
29	C₂×C₂₃	D₆₄	1	1	yes	characteristic
30	C₂×C₂₃	Q₁₂₈	1	1	yes	characteristic
31	C₂×C₁₆	D₄×C₂₃	1	1	yes	characteristic
32	#107	—	4	2	no	—
33	C₃₂	C₂×C₄×C₂₃	1	1	yes	characteristic
34	C₃₂	Q₈×C₂₃	1	1	yes	characteristic
35	C₂₃	#7545	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₈	D₈×C₂₃	1	1	yes	characteristic
37	C₄⋊C₄	—	8	2	no	—
38	C₁₆	C₄⋊C₄×C₂₃	1	1	yes	characteristic
39	C₁₆	Q₁₆×C₂₃	1	1	yes	characteristic
40	C₂×C₄	—	16	2	no	—
41	C₂×C₄	C₂₃×D₁₆	1	1	yes	characteristic
42	C₈	C₂₃×#107	1	1	yes	characteristic
43	C₈	C₂₃×Q₃₂	1	1	yes	characteristic
44	C₂²	C₂₃×D₃₂	1	1	yes	characteristic
45	C₄	—	32	2	no	—
46	C₄	C₂₃×#366	1	1	yes	characteristic
47	C₄	C₂₃×Q₆₄	1	1	yes	characteristic
48	C₂	C₂₃×#1423	1	1	yes	characteristic
49	C₂	C₂₃×D₆₄	1	1	yes	characteristic
50	C₂	C₂₃×Q₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	D₃₂
commutator	C₃₂	C₂×C₄×C₂₃
Frattini, cosocle	C₂×C₃₂	C₂²×C₂₃
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×C₈×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ C₂×C₂₃×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂₃×C₆₄	C₄	semidirect
14. #7545	C₂₃	direct (N × H)
27. C₆₄	C₄×C₂₃	semidirect
35. C₂₃	#7545	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×C₆₄	2
C₂₃×#1423	2
#7545	23

Subgroups — C23×#7545 #19155171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7545 #19155171