Subgroups — #15671272

Order 2944.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092441	C₂	1	2	yes	maximal
2	C₂×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₃	C₄	1	2	yes	—
4	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×#67267	—	2	2	no	—
6	C₂₃×C₄⋊C₈	—	2	2	no	—
7	C₄⋊(C₂₃⋊C₈)	—	2	2	no	—
8	C₄⋊(C₂₃⋊C₈)	C₄	1	4	yes	—
9	C₂²×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₃	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₂₃	—	2	2	no	—
13	C₂×C₈×C₂₃	—	4	2	no	—
14	C₄²×C₂₃	C₂×C₄	1	2	yes	—
15	C₄²×C₂₃	D₄	1	2	yes	—
16	#67267	—	4	2	no	—
17	#67267	—	4	2	no	—
18	C₂×C₂₃⋊C₈	—	2	4	no	—
19	C₂³×C₂₃	C₄⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₃	—	2	1	no	—
21	C₂×C₄×C₂₃	—	2	1	no	—
22	C₂×C₄×C₂₃	—	4	1	no	—
23	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
25	C₂×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₂₃	SD₁₆	1	2	yes	—
29	C₂×C₄×C₂₃	Q₁₆	1	1	yes	characteristic
30	C₈×C₂₃	—	4	2	no	—
31	C₂₃⋊C₈	—	4	4	no	—
32	#1292	—	23	1	no	maximal, Sylow
33	C₂²×C₂₃	—	2	1	no	—
34	C₂²×C₂₃	—	2	1	no	—
35	C₂²×C₂₃	#95	1	1	yes	characteristic
36	C₂²×C₂₃	#106	1	1	yes	characteristic
37	C₂²×C₂₃	#107	1	1	yes	characteristic
38	C₄×C₂₃	—	2	2	no	—
39	C₄×C₂₃	—	2	1	no	—
40	C₄×C₂₃	#100	1	1	yes	characteristic
41	C₄×C₂₃	#101	1	1	yes	characteristic
42	C₄×C₂₃	#102	1	2	yes	—
43	C₄×C₂₃	#103	1	2	yes	—
44	#423	—	23	2	no	—
45	C₂×C₄⋊C₈	D₂₃	1	1	yes	characteristic
46	C₂×C₂₃	—	2	1	no	—
47	C₂×C₂₃	—	2	1	no	—
48	C₂×C₂₃	#338	1	1	yes	characteristic
49	C₂×C₂₃	#340	1	1	yes	characteristic
50	C₂×C₂₃	#343	1	1	yes	characteristic
51	C₂×M₁₆	—	46	2	no	—
52	C₂²×C₈	Dic₂₃	1	2	yes	—
53	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
54	C₄⋊C₈	—	2	2	no	—
55	C₄⋊C₈	—	23	4	no	—
56	C₄⋊C₈	—	46	2	no	—
57	C₂₃	#1292	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	Dic₄₆	1	1	yes	characteristic
59	C₂²×C₄	D₉₂	1	1	yes	characteristic
60	C₂²×C₄	C₂×Dic₂₃	1	1	yes	characteristic
61	M₁₆	—	92	2	no	—
62	M₁₆	—	92	2	no	—
63	C₂×C₈	—	2	2	no	—
64	C₂×C₈	—	4	2	no	—
65	C₂×C₈	—	46	4	no	—
66	C₄²	C₄×D₂₃	1	2	yes	—
67	C₄²	C₂²⋊D₂₃	1	2	yes	—
68	C₂³	C₄⋊Dic₂₃	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	#67263	1	2	yes	—
73	C₂×C₄	D₁₈₄	1	1	yes	characteristic
74	C₂×C₄	Dic₉₂	1	1	yes	characteristic
75	C₂×C₄	C₄×Dic₂₃	1	1	yes	characteristic
76	C₂×C₄	Dic₂₃⋊C₄	1	2	yes	—
77	C₂×C₄	(C₂×D₂₃)⋊C₄	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₂₃	1	1	yes	characteristic
79	C₈	—	4	2	no	—
80	C₈	—	92	4	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	#10624999	1	1	yes	characteristic
84	C₂²	#10625000	1	1	yes	characteristic
85	C₂²	C₂₃⋊#95	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#10624998	1	2	yes	—
89	C₄	#10625003	1	2	yes	—
90	C₄	#10625015	1	1	yes	characteristic
91	C₄	#10625018	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	C₂₃⋊#338	1	1	yes	characteristic
95	C₂	#13092180	1	1	yes	characteristic
96	C₂	#13092186	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂₃⋊#95
commutator	C₂×C₄×C₂₃	C₄²
Frattini	C₂×C₄²	C₂×D₂₃
Fitting	C₂×C₂₃×C₄⋊C₈	C₂
socle	C₂²×C₂₃	#95
prime radical	C₂³×C₂₃	C₄⋊C₄
cosocle	C₂×C₄²×C₂₃	C₂²
hypercenter	C₂×C₄⋊C₈	D₂₃
hypocenter	C₂₃	#1292
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
57. C₂₃	#1292	semidirect

Maximal subgroups

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

subgroup	index
#13092441	2
C₂×C₂₃×C₄⋊C₈	2
#1292	23