Subgroups — C₂₃×#2263 #15669882

Order 2944.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×SD₆₄	C₂	1	2	yes	maximal, complemented
4	C₂₃×D₃₂	C₂	1	2	yes	maximal, complemented
5	C₂₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#135	—	2	1	no	—
7	C₂×D₈×C₂₃	—	2	1	no	—
8	C₂₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
9	C₂₃×SD₃₂	—	2	1	no	—
10	C₂₃×D₁₆	—	2	1	no	—
11	C₂₃×D₁₆	C₂²	1	2	yes	—
12	C₂₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂₃×C₃₂	C₂²	1	2	yes	complemented
15	#41×C₂₃	—	4	1	no	—
16	C₂×D₄×C₂₃	—	4	1	no	—
17	Q₁₆×C₂₃	—	2	1	no	—
18	SD₁₆×C₂₃	—	4	1	no	—
19	D₈×C₂₃	—	2	2	no	—
20	D₈×C₂₃	—	2	1	no	—
21	D₈×C₂₃	—	4	1	no	—
22	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
23	C₁₆×C₂₃	D₄	1	1	yes	characteristic
24	C₁₆×C₂₃	C₂³	1	1	yes	characteristic
25	C₂³×C₂₃	—	8	1	no	—
26	Q₈×C₂₃	—	4	1	no	—
27	D₄×C₂₃	—	4	2	no	—
28	D₄×C₂₃	—	4	1	no	—
29	D₄×C₂₃	—	8	1	no	—
30	D₄×C₂₃	—	8	1	no	—
31	C₂×C₄×C₂₃	—	8	1	no	—
32	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
33	C₈×C₂₃	D₈	1	1	yes	characteristic
34	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
35	#2263	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₂₃	—	8	1	no	—
37	C₂²×C₂₃	—	8	2	no	—
38	C₂²×C₂₃	—	16	2	no	—
39	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
40	C₄×C₂₃	—	8	1	no	—
41	C₄×C₂₃	D₁₆	1	1	yes	characteristic
42	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
43	#508	C₂×C₂₃	1	1	yes	characteristic, complemented
44	C₂×D₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
45	SD₆₄	C₂×C₂₃	1	2	yes	complemented
46	D₃₂	C₂×C₂₃	1	2	yes	complemented
47	M₆₄	C₂×C₂₃	1	1	yes	characteristic, complemented
48	C₂×C₂₃	—	2	1	no	—
49	C₂×C₂₃	—	16	1	no	—
50	C₂×C₂₃	—	16	2	no	—
51	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
52	#135	—	2	1	no	—
53	C₂×D₈	—	2	1	no	—
54	Q₃₂	C₂²×C₂₃	1	1	yes	characteristic, complemented
55	SD₃₂	—	2	1	no	—
56	D₁₆	—	2	1	no	—
57	D₁₆	C₂²×C₂₃	1	2	yes	—
58	D₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
59	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
60	C₃₂	C₂²×C₂₃	1	2	yes	complemented
61	C₂₃	#2263	1	1	yes	characteristic, direct product factor, Sylow
62	#41	—	4	1	no	—
63	C₂×D₄	—	4	1	no	—
64	Q₁₆	—	2	1	no	—
65	SD₁₆	—	4	1	no	—
66	D₈	—	2	2	no	—
67	D₈	—	2	1	no	—
68	D₈	—	4	1	no	—
69	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
70	C₁₆	D₄×C₂₃	1	1	yes	characteristic
71	C₁₆	C₂³×C₂₃	1	1	yes	characteristic
72	C₂³	—	8	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	2	no	—
75	D₄	—	4	1	no	—
76	D₄	—	8	1	no	—
77	D₄	—	8	1	no	—
78	C₂×C₄	—	8	1	no	—
79	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
80	C₈	D₈×C₂₃	1	1	yes	characteristic
81	C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
82	C₂²	—	8	1	no	—
83	C₂²	—	8	2	no	—
84	C₂²	—	16	2	no	—
85	C₂²	C₂₃×D₁₆	1	1	yes	characteristic
86	C₄	—	8	1	no	—
87	C₄	C₂₃×D₁₆	1	1	yes	characteristic
88	C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	16	2	no	—
91	C₂	—	16	1	no	—
92	C₂	C₂×C₂₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₂₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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. C₂×C₂₃×D₁₆	C₂	semidirect
3. C₂₃×SD₆₄	C₂	semidirect
4. C₂₃×D₃₂	C₂	semidirect
5. C₂₃×M₆₄	C₂	semidirect
8. C₂₃×Q₃₂	C₂²	semidirect
12. C₂₃×D₁₆	C₂²	semidirect
14. C₂₃×C₃₂	C₂²	semidirect
35. #2263	C₂₃	direct (N × H)
43. #508	C₂×C₂₃	semidirect
44. C₂×D₁₆	C₂×C₂₃	semidirect
45. SD₆₄	C₂×C₂₃	semidirect
46. D₃₂	C₂×C₂₃	semidirect
47. M₆₄	C₂×C₂₃	semidirect
54. Q₃₂	C₂²×C₂₃	semidirect
58. D₁₆	C₂²×C₂₃	semidirect
60. C₃₂	C₂²×C₂₃	semidirect
61. C₂₃	#2263	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
C₂×C₂₃×D₁₆	2
C₂₃×SD₆₄	2
C₂₃×D₃₂	2
C₂₃×M₆₄	2
#2263	23

Subgroups — C23×#2263 #15669882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2263 #15669882