Subgroups — C₂₃×#7454 #19155080

Order 5888.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2253	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#1422	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1373	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#499	—	2	1	no	—
5	C₂₃×M₆₄	—	2	1	no	—
6	C₂₃×#367	C₄	1	2	yes	—
7	C₂₃×#366	—	2	1	no	—
8	C₂₃×#364	—	2	1	no	—
9	C₄×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂₃×#125	—	4	1	no	—
11	C₂₃×M₃₂	—	4	1	no	—
12	C₂×C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
14	C₂₃×#107	—	2	2	no	—
15	C₂₃×#106	—	4	1	no	—
16	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂₃×C₃₂	—	4	1	no	—
18	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
20	C₄⋊C₄×C₂₃	—	4	2	no	—
21	C₄⋊C₄×C₂₃	—	8	2	no	—
22	C₄²×C₂₃	SD₁₆	1	1	yes	characteristic
23	C₁₆×C₂₃	—	2	1	no	—
24	C₁₆×C₂₃	—	8	1	no	—
25	C₁₆×C₂₃	SD₁₆	1	1	yes	characteristic
26	C₁₆×C₂₃	Q₁₆	1	1	yes	characteristic
27	#7454	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₄×C₂₃	—	2	1	no	—
29	C₂×C₄×C₂₃	—	8	2	no	—
30	C₂×C₄×C₂₃	#102	1	1	yes	characteristic
31	C₈×C₂₃	#101	1	1	yes	characteristic
32	C₈×C₂₃	#103	1	1	yes	characteristic
33	C₈×C₂₃	SD₃₂	1	1	yes	characteristic
34	C₈×C₂₃	Q₃₂	1	1	yes	characteristic
35	#2253	C₂×C₂₃	1	1	yes	characteristic
36	#1422	C₂×C₂₃	1	1	yes	characteristic
37	#1373	C₂×C₂₃	1	1	yes	characteristic
38	C₂²×C₂₃	#361	1	1	yes	characteristic
39	C₄×C₂₃	—	4	1	no	—
40	C₄×C₂₃	—	16	2	no	—
41	C₄×C₂₃	#332	1	1	yes	characteristic
42	C₄×C₂₃	#358	1	1	yes	characteristic
43	#499	—	2	1	no	—
44	M₆₄	—	2	1	no	—
45	#367	C₄×C₂₃	1	2	yes	—
46	#366	—	2	1	no	—
47	#364	—	2	1	no	—
48	C₄×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
49	C₂×C₂₃	—	2	1	no	—
50	C₂×C₂₃	#1365	1	1	yes	characteristic
51	#125	—	4	1	no	—
52	M₃₂	—	4	1	no	—
53	C₂×C₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
54	C₂×C₁₆	D₄×C₂₃	1	1	yes	characteristic
55	#107	—	2	2	no	—
56	#106	—	4	1	no	—
57	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
58	C₃₂	—	4	1	no	—
59	C₂₃	#7454	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
61	C₂×C₈	D₈×C₂₃	1	1	yes	characteristic
62	C₄⋊C₄	—	4	2	no	—
63	C₄⋊C₄	—	8	2	no	—
64	C₄²	SD₁₆×C₂₃	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	8	1	no	—
67	C₁₆	SD₁₆×C₂₃	1	1	yes	characteristic
68	C₁₆	Q₁₆×C₂₃	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	8	2	no	—
71	C₂×C₄	C₂₃×#102	1	1	yes	characteristic
72	C₈	C₂₃×#101	1	1	yes	characteristic
73	C₈	C₂₃×#103	1	1	yes	characteristic
74	C₈	C₂₃×SD₃₂	1	1	yes	characteristic
75	C₈	C₂₃×Q₃₂	1	1	yes	characteristic
76	C₂²	C₂₃×#361	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	16	2	no	—
79	C₄	C₂₃×#332	1	1	yes	characteristic
80	C₄	C₂₃×#358	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	C₂₃×#1365	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₃	#1365
commutator	C₂×C₁₆	C₂×C₄×C₂₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₂₃
prime radical	C₂²×C₂₃	#361
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₄×C₈×C₂₃ ◁ C₄×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
27. #7454	C₂₃	direct (N × H)
59. C₂₃	#7454	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×#2253	2
C₂₃×#1422	2
C₂₃×#1373	2
#7454	23

Subgroups — C23×#7454 #19155080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7454 #19155080