Subgroups — C₂₃×#2110 #15669729

Order 2944.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×M₃₂	C₂	1	2	yes	maximal
2	C₂₃×#405	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#347	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₂₃	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂₃×#117	C₄	1	1	yes	characteristic
7	C₂₃×M₃₂	C₄	1	4	yes	complemented
8	C₂₃×M₃₂	C₂²	1	4	yes	—
9	C₂×C₁₆×C₂₃	C₄	1	4	yes	complemented
10	C₂₃×#97	C₂²	1	2	yes	—
11	C₄×C₈×C₂₃	C₄	1	2	yes	—
12	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
13	M₁₆×C₂₃	—	2	2	no	—
14	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₂₃	—	2	1	no	—
20	C₂²⋊C₄×C₂₃	—	2	1	no	—
21	C₄²×C₂₃	C₂×C₄	1	2	yes	—
22	C₁₆×C₂₃	C₂×C₄	1	8	yes	—
23	C₂³×C₂₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₂₃	—	2	2	no	—
25	C₂×C₄×C₂₃	C₄²	1	2	yes	—
26	C₂×C₄×C₂₃	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₂₃	M₁₆	1	2	yes	—
28	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₂₃	—	2	2	no	—
30	C₈×C₂₃	C₄²	1	1	yes	characteristic
31	C₈×C₂₃	C₄²	1	1	yes	characteristic
32	C₈×C₂₃	C₂²×C₄	1	2	yes	—
33	#2110	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂²×C₂₃	—	4	1	no	—
35	C₂²×C₂₃	#97	1	2	yes	—
36	C₂²×C₂₃	C₂×M₁₆	1	1	yes	characteristic
37	C₄×C₂₃	—	4	2	no	—
38	C₄×C₂₃	#97	1	2	yes	—
39	C₄×C₂₃	C₂×C₄²	1	1	yes	characteristic
40	C₄×C₂₃	C₂×M₁₆	1	1	yes	characteristic
41	C₂×M₃₂	C₂×C₂₃	1	2	yes	—
42	#405	C₂×C₂₃	1	1	yes	characteristic
43	#347	C₂×C₂₃	1	4	yes	complemented
44	C₂×C₂₃	—	2	1	no	—
45	C₂×C₂₃	—	2	2	no	—
46	C₂×C₂₃	C₂×#97	1	1	yes	characteristic
47	C₂×M₁₆	C₄×C₂₃	1	1	yes	characteristic
48	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
49	#117	C₄×C₂₃	1	1	yes	characteristic
50	M₃₂	C₄×C₂₃	1	4	yes	complemented
51	M₃₂	C₂²×C₂₃	1	4	yes	—
52	C₂×C₁₆	C₄×C₂₃	1	4	yes	complemented
53	#97	C₂²×C₂₃	1	2	yes	—
54	C₄×C₈	C₄×C₂₃	1	2	yes	—
55	C₂₃	#2110	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
57	M₁₆	—	2	2	no	—
58	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
59	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
60	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
61	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
62	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×C₄×C₂₃	1	2	yes	—
66	C₁₆	C₂×C₄×C₂₃	1	8	yes	—
67	C₂³	M₁₆×C₂₃	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	C₄²×C₂₃	1	2	yes	—
70	C₂×C₄	M₁₆×C₂₃	1	2	yes	—
71	C₂×C₄	M₁₆×C₂₃	1	1	yes	characteristic
72	C₂×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₈	C₄²×C₂₃	1	1	yes	characteristic
75	C₈	C₄²×C₂₃	1	1	yes	characteristic
76	C₈	C₂²×C₄×C₂₃	1	2	yes	—
77	C₂²	—	4	1	no	—
78	C₂²	C₂₃×#97	1	2	yes	—
79	C₂²	C₂×M₁₆×C₂₃	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	C₂₃×#97	1	2	yes	—
82	C₄	C₂×C₄²×C₂₃	1	1	yes	characteristic
83	C₄	C₂×M₁₆×C₂₃	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×C₂₃×#97	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₂₃	C₄²
commutator	C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
socle	C₂×C₂₃	C₂×#97
prime radical	C₂³×C₂₃	M₁₆
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
3. C₂₃×#347	C₂	semidirect
7. C₂₃×M₃₂	C₄	semidirect
9. C₂×C₁₆×C₂₃	C₄	semidirect
33. #2110	C₂₃	direct (N × H)
43. #347	C₂×C₂₃	semidirect
50. M₃₂	C₄×C₂₃	semidirect
52. C₂×C₁₆	C₄×C₂₃	semidirect
55. C₂₃	#2110	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×M₃₂	2
C₂₃×#405	2
C₂₃×#347	2
#2110	23

Subgroups — C23×#2110 #15669729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2110 #15669729