Subgroups — #13092824

Order 1472.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625061	C₂	1	1	yes	maximal, characteristic
2	#10625059	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#106	C₂	1	1	yes	maximal, characteristic
4	#10625000	C₂	1	1	yes	maximal, characteristic
5	#10624997	C₂	1	1	yes	maximal, characteristic
6	#10624990	C₂	1	1	yes	maximal, characteristic
7	#10624989	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₄₆	—	2	1	no	—
9	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₂₃	—	2	1	no	—
13	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
15	Dic₂₃⋊C₄	—	2	1	no	—
16	Dic₂₃⋊C₄	—	2	1	no	—
17	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₂₃	—	2	1	no	—
20	C₂×C₄×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₂₃	—	2	1	no	—
23	C₂×Dic₂₃	—	2	1	no	—
24	C₂×Dic₂₃	D₄	1	1	yes	characteristic
25	C₂×Dic₂₃	D₄	1	1	yes	characteristic
26	Dic₄₆	—	4	2	no	—
27	C₈×C₂₃	Q₈	1	2	yes	complemented
28	C₂₃⋊C₈	Q₈	1	2	yes	complemented
29	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
30	C₄×C₂₃	—	4	1	no	—
31	C₄×C₂₃	—	4	1	no	—
32	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₂₃	C₂×Q₈	1	1	yes	characteristic
34	Dic₂₃	—	2	1	no	—
35	Dic₂₃	—	2	1	no	—
36	Dic₂₃	—	4	1	no	—
37	Dic₂₃	—	4	1	no	—
38	#501	—	23	1	no	maximal, Sylow
39	C₂×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×C₂₃	AGL(1,ℤ/8)	1	1	yes	characteristic
41	C₂×C₂₃	#137	1	1	yes	characteristic
42	C₄⋊Q₈	—	23	1	no	—
43	#125	—	23	1	no	—
44	#107	—	23	1	no	—
45	#107	—	23	1	no	—
46	#106	—	23	1	no	—
47	#106	D₂₃	1	1	yes	characteristic
48	#97	—	23	1	no	—
49	C₂₃	#501	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	46	1	no	—
51	C₂×C₈	—	23	1	no	—
52	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
53	C₄⋊C₄	—	23	1	no	—
54	C₄⋊C₄	—	23	1	no	—
55	C₄⋊C₄	—	46	1	no	—
56	C₄⋊C₄	—	46	1	no	—
57	C₄⋊C₄	—	46	1	no	—
58	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
60	C₄²	—	23	1	no	—
61	Q₈	—	92	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	23	1	no	—
65	C₂×C₄	—	23	1	no	—
66	C₂×C₄	—	46	1	no	—
67	C₂×C₄	—	46	1	no	—
68	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
69	C₈	—	23	2	no	—
70	C₈	Dic₄₆	1	2	yes	complemented
71	C₂²	D₄×D₂₃	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	46	1	no	—
75	C₄	—	46	1	no	—
76	C₄	—	92	1	no	—
77	C₄	—	92	1	no	—
78	C₄	C₂×Dic₄₆	1	1	yes	characteristic
79	C₄	Q₈×D₂₃	1	1	yes	characteristic
80	C₂	#10625059	1	1	yes	characteristic
81	C₂	#10625085	1	1	yes	characteristic
82	C₂	#10625086	1	1	yes	characteristic

	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	#501
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
27. C₈×C₂₃	Q₈	semidirect
28. C₂₃⋊C₈	Q₈	semidirect
49. C₂₃	#501	semidirect
70. C₈	Dic₄₆	semidirect

Maximal subgroups

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

subgroup	index
#10625061	2
#10625059	2
C₂₃×#106	2
#10625000	2
#10624997	2
#10624990	2
#10624989	2
#501	23