Subgroups — #13092814

Order 1472.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625059	C₂	1	2	yes	maximal
2	C₂₃×#106	C₂	1	1	yes	maximal, characteristic
3	#10624999	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic
5	#10624990	C₂	1	2	yes	maximal
6	C₂×Dic₄₆	—	2	2	no	—
7	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
9	C₄⋊Dic₂₃	C₂²	1	2	yes	—
10	Dic₂₃⋊C₄	—	2	2	no	—
11	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂₃	—	2	2	no	—
14	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
15	C₂×Dic₂₃	—	2	2	no	—
16	C₂×Dic₂₃	D₄	1	2	yes	—
17	Dic₄₆	—	4	4	no	—
18	C₈×C₂₃	Q₈	1	2	yes	complemented
19	C₂₃⋊C₈	Q₈	1	2	yes	complemented
20	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
21	C₄×C₂₃	—	4	2	no	—
22	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
24	Dic₂₃	—	4	2	no	—
25	Dic₂₃	SD₁₆	1	4	yes	—
26	#498	—	23	1	no	maximal, Sylow
27	C₂×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₂₃	C₂×SD₁₆	1	2	yes	—
29	C₄⋊Q₈	—	23	2	no	—
30	#106	—	23	1	no	—
31	#106	—	23	2	no	—
32	#106	D₂₃	1	1	yes	characteristic
33	C₄×C₈	—	23	1	no	—
34	C₂₃	#498	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	—	46	2	no	—
36	C₂×C₈	—	23	1	no	—
37	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
38	C₄⋊C₄	—	23	2	no	—
39	C₄⋊C₄	—	46	2	no	—
40	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
41	C₄²	—	23	1	no	—
42	Q₈	—	92	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	23	2	no	—
45	C₂×C₄	—	46	2	no	—
46	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
47	C₈	—	23	2	no	—
48	C₈	Dic₄₆	1	2	yes	complemented
49	C₂²	D₄×D₂₃	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	23	4	no	—
52	C₄	—	92	2	no	—
53	C₄	C₂×Dic₄₆	1	1	yes	characteristic
54	C₄	Q₈×D₂₃	1	1	yes	characteristic
55	C₂	#10625059	1	1	yes	characteristic
56	C₂	SD₁₆×D₂₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#106	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
hypercenter	#106	D₂₃
hypocenter	C₂₃	#498
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
18. C₈×C₂₃	Q₈	semidirect
19. C₂₃⋊C₈	Q₈	semidirect
34. C₂₃	#498	semidirect
48. C₈	Dic₄₆	semidirect

Maximal subgroups

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

subgroup	index
#10625059	2
C₂₃×#106	2
#10624999	2
C₈×Dic₂₃	2
#10624990	2
#498	23