Subgroups — #13092766

Order 1472.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10625115	C₂	1	1	yes	maximal, characteristic
2	#10625059	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#103	C₂	1	1	yes	maximal, characteristic
4	#10625017	C₂	1	1	yes	maximal, characteristic
5	#10624998	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic
7	#10624992	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₆	—	2	1	no	—
10	C₂×Dic₄₆	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
14	Dic₂₃⋊C₄	—	2	1	no	—
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	Q₈×C₂₃	—	2	1	no	—
20	Q₈×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	—	2	1	no	—
23	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
24	C₂×Dic₂₃	—	2	1	no	—
25	C₂×Dic₂₃	—	2	1	no	—
26	C₂×Dic₂₃	D₄	1	1	yes	characteristic
27	C₂×Dic₂₃	D₄	1	1	yes	characteristic
28	Dic₄₆	—	2	1	no	—
29	Dic₄₆	—	2	1	no	—
30	Dic₄₆	—	4	2	no	—
31	C₈×C₂₃	—	2	1	no	—
32	C₂₃⋊C₈	—	2	1	no	—
33	C₂²×C₂₃	C₂×D₄	1	1	yes	characteristic
34	C₄×C₂₃	—	4	1	no	—
35	C₄×C₂₃	—	4	1	no	—
36	C₄×C₂₃	#41	1	1	yes	characteristic
37	C₄×C₂₃	#41	1	1	yes	characteristic
38	Dic₂₃	—	4	1	no	—
39	Dic₂₃	—	4	1	no	—
40	Dic₂₃	SD₁₆	1	2	yes	—
41	Dic₂₃	Q₁₆	1	2	yes	—
42	#487	—	23	1	no	maximal, Sylow
43	C₂×C₂₃	#124	1	1	yes	characteristic
44	C₂×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
46	C₄⋊Q₈	—	23	1	no	—
47	C₄⋊Q₈	—	23	1	no	—
48	#103	—	23	1	no	—
49	#103	—	23	1	no	—
50	#103	—	23	1	no	—
51	#103	D₂₃	1	1	yes	characteristic
52	C₄×C₈	—	23	1	no	—
53	C₂₃	#487	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	23	1	no	—
55	C₂×Q₈	—	46	1	no	—
56	C₂×Q₈	C₂×D₂₃	1	1	yes	characteristic
57	C₂×C₈	—	23	1	no	—
58	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
59	C₄⋊C₄	—	23	1	no	—
60	C₄⋊C₄	—	46	1	no	—
61	C₄⋊C₄	—	46	1	no	—
62	C₄⋊C₄	—	46	1	no	—
63	C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
64	C₄²	—	23	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	46	1	no	—
68	Q₈	—	46	1	no	—
69	Q₈	—	92	2	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	23	1	no	—
73	C₂×C₄	—	23	1	no	—
74	C₂×C₄	—	46	1	no	—
75	C₂×C₄	—	46	1	no	—
76	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	46	1	no	—
79	C₂²	D₄×D₂₃	1	1	yes	characteristic
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	23	2	no	—
83	C₄	—	23	2	no	—
84	C₄	—	92	1	no	—
85	C₄	—	92	1	no	—
86	C₄	#67288	1	1	yes	characteristic
87	C₄	#67290	1	1	yes	characteristic
88	C₂	#10625056	1	1	yes	characteristic
89	C₂	SD₁₆×D₂₃	1	1	yes	characteristic
90	C₂	Q₁₆×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₃
commutator, cosocle	C₂×C₄×C₂₃	C₂³
Frattini	C₂×C₄	C₂²×D₂₃
Fitting	C₂₃×#103	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₄
hypercenter	#103	D₂₃
hypocenter	C₂₃	#487
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
53. C₂₃	#487	semidirect

Maximal subgroups

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

subgroup	index
#10625115	2
#10625059	2
C₂₃×#103	2
#10625017	2
#10624998	2
C₈×Dic₂₃	2
#10624992	2
#487	23