Subgroups — #15671489

Order 2944.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625000	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
4	C₂×C₄⋊Dic₂₃	—	2	2	no	—
5	C₂×C₁₆×C₂₃	—	2	2	no	—
6	C₂×C₁₆×C₂₃	C₄	1	2	yes	complemented
7	#10625000	—	2	2	no	—
8	#10625000	C₄	1	4	yes	complemented
9	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
10	C₂²×Dic₂₃	—	4	2	no	—
11	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃	D₄	1	2	yes	—
14	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
15	C₄⋊Dic₂₃	—	2	4	no	—
16	C₄⋊Dic₂₃	—	4	2	no	—
17	C₁₆×C₂₃	—	2	2	no	—
18	C₂³×C₂₃	D₈	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	SD₁₆	1	2	yes	—
22	C₂×C₄×C₂₃	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₂₃	—	4	4	no	—
24	C₂×Dic₂₃	—	8	2	no	—
25	C₂×Dic₂₃	—	8	2	no	—
26	C₈×C₂₃	C₄²	1	1	yes	characteristic
27	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
29	#1380	—	23	1	no	maximal, Sylow
30	C₂²×C₂₃	#102	1	2	yes	—
31	C₂²×C₂₃	#107	1	1	yes	characteristic
32	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
33	C₂²×C₂₃	SD₃₂	1	2	yes	—
34	C₂²×C₂₃	Q₃₂	1	1	yes	characteristic
35	C₄×C₂₃	#95	1	1	yes	characteristic
36	C₄×C₂₃	#103	1	2	yes	—
37	C₄×C₂₃	#106	1	1	yes	characteristic
38	Dic₂₃	—	8	4	no	—
39	C₂²×C₁₆	D₂₃	1	1	yes	characteristic
40	C₂×#107	—	23	2	no	—
41	C₂×C₂₃	#340	1	1	yes	characteristic
42	C₂×C₂₃	#357	1	2	yes	—
43	C₂×C₂₃	#358	1	2	yes	—
44	C₂×C₂₃	#366	1	1	yes	characteristic
45	C₂×C₂₃	#367	1	1	yes	characteristic
46	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
47	C₂×C₄⋊C₄	—	46	2	no	—
48	C₂×C₁₆	—	2	2	no	—
49	C₂×C₁₆	Dic₂₃	1	2	yes	complemented
50	#107	—	23	4	no	—
51	#107	—	46	2	no	—
52	C₂₃	#1380	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	—	92	2	no	—
54	C₂²×C₄	D₉₂	1	1	yes	characteristic
55	C₂×C₈	Dic₄₆	1	1	yes	characteristic
56	C₂×C₈	C₄×D₂₃	1	2	yes	—
57	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₂₃	1	2	yes	—
59	C₄⋊C₄	—	46	4	no	—
60	C₄⋊C₄	—	92	2	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₁₈₄	1	1	yes	characteristic
63	C₂×C₄	—	92	4	no	—
64	C₂×C₄	—	184	2	no	—
65	C₂×C₄	—	184	2	no	—
66	C₂×C₄	#67263	1	2	yes	—
67	C₂×C₄	Dic₉₂	1	1	yes	characteristic
68	C₂×C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
69	C₂×C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
70	C₈	C₄×Dic₂₃	1	1	yes	characteristic
71	C₈	Dic₂₃⋊C₄	1	2	yes	—
72	C₈	C₂²⋊Dic₂₃	1	1	yes	characteristic
73	C₂²	D₃₆₈	1	1	yes	characteristic
74	C₂²	#10624982	1	2	yes	—
75	C₂²	Dic₁₈₄	1	1	yes	characteristic
76	C₂²	#10625000	1	1	yes	characteristic
77	C₂²	#10625003	1	2	yes	—
78	C₄	—	184	4	no	—
79	C₄	#10624998	1	2	yes	—
80	C₄	#10624999	1	1	yes	characteristic
81	C₄	C₂₃⋊#95	1	1	yes	characteristic
82	C₂	#13092180	1	1	yes	characteristic
83	C₂	#13092219	1	2	yes	—
84	C₂	#13092222	1	2	yes	—
85	C₂	#13092243	1	1	yes	characteristic
86	C₂	#13092245	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₈₄
commutator	C₈×C₂₃	C₄²
Frattini	C₂²×C₈	C₂×D₂₃
Fitting	C₂²×C₁₆×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	D₈
cosocle	C₂²×C₈×C₂₃	C₂²
hypercenter	C₂²×C₁₆	D₂₃
hypocenter	C₂₃	#1380
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₆×C₂₃	C₄	semidirect
8. #10625000	C₄	semidirect
49. C₂×C₁₆	Dic₂₃	semidirect
52. C₂₃	#1380	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625000	2
C₂²×C₁₆×C₂₃	2
#1380	23