Subgroups — C₂₃×#7453 #19155079

Order 5888.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2254	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×#500	—	2	1	no	—
5	C₂₃×M₆₄	—	2	1	no	—
6	C₂₃×#367	—	2	1	no	—
7	C₂₃×#367	C₄	1	2	yes	—
8	C₂₃×#364	—	2	1	no	—
9	C₄×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂₃×C₄⋊Q₈	—	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×#107	—	4	1	no	—
16	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
17	C₂₃×C₃₂	—	4	1	no	—
18	C₂×Q₈×C₂₃	—	8	1	no	—
19	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
21	C₄⋊C₄×C₂₃	—	4	2	no	—
22	C₄⋊C₄×C₂₃	—	8	1	no	—
23	C₄²×C₂₃	SD₁₆	1	1	yes	characteristic
24	C₁₆×C₂₃	—	2	1	no	—
25	C₁₆×C₂₃	—	8	1	no	—
26	C₁₆×C₂₃	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₂₃	Q₁₆	1	1	yes	characteristic
28	#7453	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	Q₈×C₂₃	—	16	2	no	—
30	C₂×C₄×C₂₃	—	2	1	no	—
31	C₂×C₄×C₂₃	—	8	2	no	—
32	C₂×C₄×C₂₃	#102	1	1	yes	characteristic
33	C₈×C₂₃	#101	1	1	yes	characteristic
34	C₈×C₂₃	#103	1	1	yes	characteristic
35	C₈×C₂₃	SD₃₂	1	1	yes	characteristic
36	C₈×C₂₃	Q₃₂	1	1	yes	characteristic
37	#2254	C₂×C₂₃	1	1	yes	characteristic
38	#1422	C₂×C₂₃	1	1	yes	characteristic
39	#1373	C₂×C₂₃	1	1	yes	characteristic
40	C₂²×C₂₃	#361	1	1	yes	characteristic
41	C₄×C₂₃	—	2	2	no	—
42	C₄×C₂₃	—	16	2	no	—
43	C₄×C₂₃	#332	1	1	yes	characteristic
44	C₄×C₂₃	#358	1	1	yes	characteristic
45	#500	—	2	1	no	—
46	M₆₄	—	2	1	no	—
47	#367	—	2	1	no	—
48	#367	C₄×C₂₃	1	2	yes	—
49	#364	—	2	1	no	—
50	C₄×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
51	C₂×C₂₃	—	2	1	no	—
52	C₂×C₂₃	#1365	1	1	yes	characteristic
53	C₄⋊Q₈	—	4	1	no	—
54	M₃₂	—	4	1	no	—
55	C₂×C₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
56	C₂×C₁₆	D₄×C₂₃	1	1	yes	characteristic
57	#107	—	2	2	no	—
58	#107	—	4	1	no	—
59	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
60	C₃₂	—	4	1	no	—
61	C₂₃	#7453	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×Q₈	—	8	1	no	—
63	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
64	C₂×C₈	D₈×C₂₃	1	1	yes	characteristic
65	C₄⋊C₄	—	4	2	no	—
66	C₄⋊C₄	—	8	1	no	—
67	C₄²	SD₁₆×C₂₃	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	8	1	no	—
70	C₁₆	SD₁₆×C₂₃	1	1	yes	characteristic
71	C₁₆	Q₁₆×C₂₃	1	1	yes	characteristic
72	Q₈	—	16	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	8	2	no	—
75	C₂×C₄	C₂₃×#102	1	1	yes	characteristic
76	C₈	C₂₃×#101	1	1	yes	characteristic
77	C₈	C₂₃×#103	1	1	yes	characteristic
78	C₈	C₂₃×SD₃₂	1	1	yes	characteristic
79	C₈	C₂₃×Q₃₂	1	1	yes	characteristic
80	C₂²	C₂₃×#361	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	16	2	no	—
83	C₄	C₂₃×#332	1	1	yes	characteristic
84	C₄	C₂₃×#358	1	1	yes	characteristic
85	C₂	—	2	1	no	—
86	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
28. #7453	C₂₃	direct (N × H)
61. C₂₃	#7453	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×#2254	2
C₂₃×#1422	2
C₂₃×#1373	2
#7453	23

Subgroups — C23×#7453 #19155079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7453 #19155079