Subgroups — #15675638

Order 2944.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092819	C₂	1	1	yes	maximal, characteristic, complemented
2	#13092218	C₂	1	4	yes	maximal, complemented
3	#13092193	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#493	C₂	1	1	yes	maximal, characteristic
5	C₂×D₈×C₂₃	—	2	1	no	—
6	C₂×D₈×C₂₃	C₂²	1	2	yes	—
7	C₂₃×#127	—	2	1	no	—
8	#10625041	—	2	1	no	—
9	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
10	#10625000	C₂²	1	2	yes	—
11	#10624999	—	2	1	no	—
12	C₂×C₂₃⋊C₁₆	C₂²	1	2	yes	—
13	C₂×D₄×C₂₃	—	2	2	no	—
14	C₂×D₄×C₂₃	—	4	2	no	—
15	D₈×C₂₃	—	2	4	no	—
16	D₈×C₂₃	—	4	2	no	—
17	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
19	C₄²×C₂₃	D₄	1	1	yes	characteristic
20	C₄⋊Dic₂₃	—	2	2	no	—
21	Dic₂₃⋊C₄	—	4	2	no	—
22	C₂₃⋊C₁₆	—	2	2	no	—
23	C₂³×C₂₃	—	4	2	no	—
24	D₄×C₂₃	—	4	2	no	—
25	D₄×C₂₃	—	4	2	no	—
26	D₄×C₂₃	—	8	4	no	—
27	C₂×C₄×C₂₃	D₈	1	2	yes	—
28	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₂₃	—	4	2	no	—
30	C₈×C₂₃	SD₁₆	1	2	yes	—
31	C₈×C₂₃	#41	1	2	yes	—
32	#2244	—	23	1	no	maximal, Sylow
33	C₂²×C₂₃	—	8	2	no	—
34	C₂²×C₂₃	—	8	4	no	—
35	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₂₃	—	2	2	no	—
37	C₄×C₂₃	#124	1	1	yes	characteristic
38	C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
39	Dic₂₃	—	8	2	no	—
40	#499	—	23	1	no	—
41	#493	D₂₃	1	1	yes	characteristic
42	#357	—	23	4	no	—
43	#346	—	23	1	no	—
44	C₂×C₂₃	—	16	2	no	—
45	C₂×C₂₃	#486	1	1	yes	characteristic
46	C₂×C₂₃	#509	1	2	yes	—
47	C₂×D₈	—	2	1	no	—
48	C₂×D₈	C₂×D₂₃	1	2	yes	—
49	#127	—	2	1	no	—
50	#125	—	46	1	no	—
51	C₂×C₁₆	—	23	2	no	—
52	#107	—	23	2	no	—
53	#106	—	46	1	no	—
54	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
55	C₂₃	#2244	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₄	—	2	2	no	—
57	C₂×D₄	—	4	2	no	—
58	D₈	—	2	4	no	—
59	D₈	—	4	2	no	—
60	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
62	C₄⋊C₄	—	46	2	no	—
63	C₄⋊C₄	—	92	2	no	—
64	C₄²	C₂²⋊D₂₃	1	1	yes	characteristic
65	C₁₆	—	46	2	no	—
66	C₂³	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	8	4	no	—
70	C₂×C₄	—	92	2	no	—
71	C₂×C₄	#67272	1	2	yes	—
72	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
73	C₈	#67273	1	2	yes	—
74	C₈	#67290	1	2	yes	—
75	C₂²	—	8	2	no	—
76	C₂²	—	8	4	no	—
77	C₂²	C₂×#67272	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	184	2	no	—
80	C₄	C₂×#67273	1	1	yes	characteristic
81	C₄	#10625107	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	#13092763	1	1	yes	characteristic
84	C₂	#13092853	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#67272
commutator, cosocle	C₂×C₈×C₂₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₃
Fitting, prime radical	C₂₃×#493	C₂
socle	C₂²×C₂₃	C₂×D₈
hypercenter	#493	D₂₃
hypocenter	C₂₃	#2244
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. #13092819	C₂	semidirect
2. #13092218	C₂	semidirect
3. #13092193	C₂	semidirect
55. C₂₃	#2244	semidirect

Maximal subgroups

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

subgroup	index
#13092819	2
#13092218	2
#13092193	2
C₂₃×#493	2
#2244	23