Subgroups — C₂₃×#2262 #15669881

Order 2944.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#508	C₂	1	2	yes	maximal, complemented
2	C₂₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×SD₆₄	C₂	1	2	yes	maximal, complemented
4	C₂₃×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#135	—	2	2	no	—
7	C₂₃×Q₃₂	C₂²	1	2	yes	—
8	C₂₃×SD₃₂	—	2	2	no	—
9	C₂₃×D₁₆	C₂²	1	2	yes	—
10	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
11	C₂₃×C₃₂	C₂²	1	1	yes	characteristic
12	C₂₃×C₃₂	C₂²	1	1	yes	characteristic
13	#41×C₂₃	—	4	2	no	—
14	Q₁₆×C₂₃	—	2	2	no	—
15	SD₁₆×C₂₃	—	4	2	no	—
16	D₈×C₂₃	—	2	2	no	—
17	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
18	C₁₆×C₂₃	D₄	1	1	yes	characteristic
19	C₁₆×C₂₃	C₂³	1	1	yes	characteristic
20	Q₈×C₂₃	—	4	2	no	—
21	D₄×C₂₃	—	4	2	no	—
22	D₄×C₂₃	—	8	2	no	—
23	C₂×C₄×C₂₃	—	8	2	no	—
24	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
25	C₈×C₂₃	D₈	1	1	yes	characteristic
26	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
27	#2262	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₂₃	—	8	2	no	—
29	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
30	C₄×C₂₃	—	8	2	no	—
31	C₄×C₂₃	D₁₆	1	1	yes	characteristic
32	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
33	#508	C₂×C₂₃	1	2	yes	complemented
34	Q₆₄	C₂×C₂₃	1	1	yes	characteristic, complemented
35	SD₆₄	C₂×C₂₃	1	2	yes	complemented
36	D₃₂	C₂×C₂₃	1	1	yes	characteristic, complemented
37	C₂×C₃₂	C₂×C₂₃	1	1	yes	characteristic, complemented
38	C₂×C₂₃	—	2	1	no	—
39	C₂×C₂₃	—	16	2	no	—
40	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
41	#135	—	2	2	no	—
42	Q₃₂	C₂²×C₂₃	1	2	yes	—
43	SD₃₂	—	2	2	no	—
44	D₁₆	C₂²×C₂₃	1	2	yes	—
45	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
46	C₃₂	C₂²×C₂₃	1	1	yes	characteristic
47	C₃₂	C₂²×C₂₃	1	1	yes	characteristic
48	C₂₃	#2262	1	1	yes	characteristic, direct product factor, Sylow
49	#41	—	4	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	4	2	no	—
52	D₈	—	2	2	no	—
53	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
54	C₁₆	D₄×C₂₃	1	1	yes	characteristic
55	C₁₆	C₂³×C₂₃	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	4	2	no	—
58	D₄	—	8	2	no	—
59	C₂×C₄	—	8	2	no	—
60	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
61	C₈	D₈×C₂₃	1	1	yes	characteristic
62	C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
63	C₂²	—	8	2	no	—
64	C₂²	C₂₃×D₁₆	1	1	yes	characteristic
65	C₄	—	8	2	no	—
66	C₄	C₂₃×D₁₆	1	1	yes	characteristic
67	C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	16	2	no	—
70	C₂	C₂×C₂₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₂₃
socle	C₂×C₂₃	C₂×D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×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
1. C₂₃×#508	C₂	semidirect
2. C₂₃×Q₆₄	C₂	semidirect
3. C₂₃×SD₆₄	C₂	semidirect
4. C₂₃×D₃₂	C₂	semidirect
5. C₂×C₂₃×C₃₂	C₂	semidirect
27. #2262	C₂₃	direct (N × H)
33. #508	C₂×C₂₃	semidirect
34. Q₆₄	C₂×C₂₃	semidirect
35. SD₆₄	C₂×C₂₃	semidirect
36. D₃₂	C₂×C₂₃	semidirect
37. C₂×C₃₂	C₂×C₂₃	semidirect
48. C₂₃	#2262	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×#508	2
C₂₃×Q₆₄	2
C₂₃×SD₆₄	2
C₂₃×D₃₂	2
C₂×C₂₃×C₃₂	2
#2262	23

Subgroups — C23×#2262 #15669881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2262 #15669881