Subgroups — #19212017

Order 5888.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15671608	C₂	1	2	yes	maximal, complemented
2	C₂×C₂₃×M₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂₃⋊C₆₄	—	2	2	no	—
4	C₂²×C₁₆×C₂₃	C₄	1	1	yes	characteristic
5	C₂₃×M₆₄	—	2	2	no	—
6	C₂×C₂₃×C₃₂	C₄	1	1	yes	characteristic
7	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₂₃	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₂₃	—	2	1	no	—
10	C₂×C₁₆×C₂₃	—	2	1	no	—
11	C₂×C₁₆×C₂₃	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂₃×C₃₂	—	2	1	no	—
14	C₂₃×C₃₂	D₄	1	2	yes	—
15	C₂²×C₄×C₂₃	C₁₆	1	1	yes	characteristic
16	C₂×C₈×C₂₃	—	2	1	no	—
17	C₂×C₈×C₂₃	—	2	1	no	—
18	C₂×C₈×C₂₃	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
20	C₁₆×C₂₃	—	2	1	no	—
21	C₁₆×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₁₆×C₂₃	M₁₆	1	1	yes	characteristic
23	#7513	—	23	1	no	maximal, Sylow
24	C₂³×C₂₃	C₃₂	1	1	yes	characteristic
25	C₂×C₄×C₂₃	—	2	1	no	—
26	C₂×C₄×C₂₃	—	2	1	no	—
27	C₂×C₄×C₂₃	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₂₃	C₂×C₁₆	1	1	yes	characteristic
29	C₈×C₂₃	—	2	1	no	—
30	C₈×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₈×C₂₃	M₃₂	1	1	yes	characteristic
32	C₂×M₆₄	D₂₃	1	1	yes	characteristic
33	M₁₂₈	—	23	2	no	—
34	C₂²×C₂₃	—	2	1	no	—
35	C₂²×C₂₃	—	4	1	no	—
36	C₂²×C₂₃	C₂×C₃₂	1	1	yes	characteristic
37	C₄×C₂₃	—	2	1	no	—
38	C₄×C₂₃	C₂²⋊C₁₆	1	1	yes	characteristic
39	C₄×C₂₃	M₆₄	1	1	yes	characteristic
40	C₂²×C₁₆	Dic₂₃	1	1	yes	characteristic
41	M₆₄	—	2	2	no	—
42	C₂×C₃₂	Dic₂₃	1	1	yes	characteristic
43	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
44	C₆₄	—	46	2	no	—
45	C₂×C₂₃	—	2	1	no	—
46	C₂×C₂₃	—	4	1	no	—
47	C₂×C₂₃	C₂²⋊C₃₂	1	1	yes	characteristic
48	C₂²×C₈	C₂₃⋊C₈	1	1	yes	characteristic
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	2	1	no	—
51	C₂×C₁₆	C₂₃⋊C₈	1	1	yes	characteristic
52	C₂×C₁₆	C₂×Dic₂₃	1	1	yes	characteristic
53	C₃₂	—	2	1	no	—
54	C₃₂	C₂²⋊D₂₃	1	2	yes	—
55	C₂₃	#7513	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	C₂₃⋊C₁₆	1	1	yes	characteristic
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	—	2	1	no	—
59	C₂×C₈	C₂₃⋊C₁₆	1	1	yes	characteristic
60	C₂×C₈	C₂×C₂₃⋊C₈	1	1	yes	characteristic
61	C₁₆	—	2	1	no	—
62	C₁₆	#67267	1	1	yes	characteristic
63	C₁₆	C₂²⋊Dic₂₃	1	1	yes	characteristic
64	C₂³	C₂₃⋊C₃₂	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	C₂₃⋊C₃₂	1	1	yes	characteristic
68	C₂×C₄	C₂×C₂₃⋊C₁₆	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	#10624994	1	1	yes	characteristic
71	C₈	C₂²⋊(C₂₃⋊C₈)	1	1	yes	characteristic
72	C₂²	—	2	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	C₂×C₂₃⋊C₃₂	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	C₂²⋊(C₂₃⋊C₁₆)	1	1	yes	characteristic
77	C₄	#13092251	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	4	1	no	—
80	C₂	C₂²⋊(C₂₃⋊C₃₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊Dic₂₃
commutator	C₂²×C₂₃	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₂₃
Fitting	C₂×C₂₃×M₆₄	C₂
socle	C₂×C₂₃	C₂²⋊C₃₂
hypercenter	C₂×M₆₄	D₂₃
hypocenter	C₂₃	#7513
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₃₂ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
1. #15671608	C₂	semidirect
55. C₂₃	#7513	semidirect