Subgroups — #15671537

Order 2944.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092251	C₂	1	2	yes	maximal, complemented
2	C₂×C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₂₃×M₃₂	—	2	2	no	—
5	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
7	C₂₃⋊C₃₂	—	2	2	no	—
8	C₂²×C₄×C₂₃	C₈	1	1	yes	characteristic
9	C₂×C₈×C₂₃	—	2	1	no	—
10	C₂×C₈×C₂₃	—	2	1	no	—
11	C₂×C₈×C₂₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₂₃	—	2	1	no	—
14	C₁₆×C₂₃	D₄	1	2	yes	—
15	C₂³×C₂₃	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₂₃	—	2	1	no	—
17	C₂×C₄×C₂₃	—	2	1	no	—
18	C₂×C₄×C₂₃	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
20	C₈×C₂₃	—	2	1	no	—
21	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₂₃	M₁₆	1	1	yes	characteristic
23	#1400	—	23	1	no	maximal, Sylow
24	C₂²×C₂₃	—	2	1	no	—
25	C₂²×C₂₃	—	4	1	no	—
26	C₂²×C₂₃	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₂₃	—	2	1	no	—
28	C₄×C₂₃	C₂²⋊C₈	1	1	yes	characteristic
29	C₄×C₂₃	M₃₂	1	1	yes	characteristic
30	C₂×M₃₂	D₂₃	1	1	yes	characteristic
31	M₆₄	—	23	2	no	—
32	C₂×C₂₃	—	2	1	no	—
33	C₂×C₂₃	—	4	1	no	—
34	C₂×C₂₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	C₂²×C₈	Dic₂₃	1	1	yes	characteristic
36	M₃₂	—	2	2	no	—
37	C₂×C₁₆	Dic₂₃	1	1	yes	characteristic
38	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
39	C₃₂	—	46	2	no	—
40	C₂₃	#1400	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	C₂₃⋊C₈	1	1	yes	characteristic
42	C₂×C₈	—	2	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	C₂₃⋊C₈	1	1	yes	characteristic
45	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	C₂²⋊D₂₃	1	2	yes	—
48	C₂³	C₂₃⋊C₁₆	1	1	yes	characteristic
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₂₃⋊C₁₆	1	1	yes	characteristic
52	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	#67267	1	1	yes	characteristic
55	C₈	C₂²⋊Dic₂₃	1	1	yes	characteristic
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×C₂₃⋊C₁₆	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#10624994	1	1	yes	characteristic
61	C₄	C₂²⋊(C₂₃⋊C₈)	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊(C₂₃⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊Dic₂₃
commutator	C₂²×C₂₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₂₃
Fitting	C₂×C₂₃×M₃₂	C₂
socle	C₂×C₂₃	C₂²⋊C₁₆
prime radical	C₂³×C₂₃	C₁₆
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	C₂×M₃₂	D₂₃
hypocenter	C₂₃	#1400
LCS	G ▷ C₂²×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
1. #13092251	C₂	semidirect
40. C₂₃	#1400	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13092251	2
C₂×C₂₃×M₃₂	2
#1400	23