Subgroups — C₂₃×#1710 #15669329

Order 2944.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#500	C₂	1	2	yes	maximal
2	C₂₃×#487	C₂	1	4	yes	maximal
3	C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×C₄⋊Q₈	C₂²	1	4	yes	—
5	C₂₃×#107	—	2	4	no	—
6	C₂₃×#103	—	2	8	no	—
7	C₄×C₈×C₂₃	C₂²	1	2	yes	—
8	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₂₃	—	2	4	no	—
10	C₂×C₈×C₂₃	D₄	1	4	yes	—
11	C₂×C₈×C₂₃	D₄	1	2	yes	—
12	C₄⋊C₄×C₂₃	—	2	4	no	—
13	C₄⋊C₄×C₂₃	—	2	4	no	—
14	C₄²×C₂₃	C₂³	1	1	yes	characteristic
15	Q₈×C₂₃	—	4	8	no	—
16	C₂×C₄×C₂₃	—	4	4	no	—
17	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
19	C₈×C₂₃	—	2	4	no	—
20	C₈×C₂₃	Q₁₆	1	4	yes	—
21	#1710	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₂₃	#127	1	1	yes	characteristic
23	C₄×C₂₃	—	8	4	no	—
24	C₄×C₂₃	C₂×Q₁₆	1	2	yes	—
25	C₄×C₂₃	#135	1	4	yes	—
26	#500	C₂×C₂₃	1	2	yes	—
27	#487	C₂×C₂₃	1	4	yes	—
28	C₈²	C₂×C₂₃	1	1	yes	characteristic
29	C₂×C₂₃	#494	1	1	yes	characteristic
30	C₂×C₂₃	#495	1	2	yes	—
31	C₄⋊Q₈	C₂²×C₂₃	1	4	yes	—
32	#107	—	2	4	no	—
33	#103	—	2	8	no	—
34	C₄×C₈	C₂²×C₂₃	1	2	yes	—
35	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
36	C₂₃	#1710	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×Q₈	—	2	4	no	—
38	C₂×C₈	D₄×C₂₃	1	4	yes	—
39	C₂×C₈	D₄×C₂₃	1	2	yes	—
40	C₄⋊C₄	—	2	4	no	—
41	C₄⋊C₄	—	2	4	no	—
42	C₄²	C₂³×C₂₃	1	1	yes	characteristic
43	Q₈	—	4	8	no	—
44	C₂×C₄	—	4	4	no	—
45	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
46	C₂×C₄	C₂×D₄×C₂₃	1	2	yes	—
47	C₈	—	2	4	no	—
48	C₈	Q₁₆×C₂₃	1	4	yes	—
49	C₂²	C₂₃×#127	1	1	yes	characteristic
50	C₄	—	8	4	no	—
51	C₄	C₂×Q₁₆×C₂₃	1	2	yes	—
52	C₄	C₂₃×#135	1	4	yes	—
53	C₂	C₂₃×#494	1	1	yes	characteristic
54	C₂	C₂₃×#495	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₂₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
21. #1710	C₂₃	direct (N × H)
36. C₂₃	#1710	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×#500	2
C₂₃×#487	2
C₈²×C₂₃	2
#1710	23

Subgroups — C23×#1710 #15669329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1710 #15669329