Subgroups — #15675673

Order 2944.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092819	C₂	1	1	yes	maximal, characteristic
2	#13092244	C₂	1	2	yes	maximal
3	#13092242	C₂	1	2	yes	maximal
4	C₄×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#499	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#125	—	2	1	no	—
7	#10625041	—	2	1	no	—
8	C₂₃×#107	C₂²	1	2	yes	—
9	C₂₃×#106	—	2	1	no	—
10	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	#10625000	C₂²	1	2	yes	—
12	#10624999	—	2	1	no	—
13	C₂×C₂₃⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₂₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₂₃	—	2	2	no	—
18	C₄⋊C₄×C₂₃	—	4	2	no	—
19	C₄²×C₂₃	D₄	1	1	yes	characteristic
20	C₄⋊Dic₂₃	—	2	2	no	—
21	Dic₂₃⋊C₄	—	4	2	no	—
22	C₂₃⋊C₁₆	Q₈	1	2	yes	—
23	C₂₃⋊C₁₆	Q₈	1	2	yes	—
24	C₂×C₄×C₂₃	—	4	2	no	—
25	C₂×C₄×C₂₃	D₈	1	2	yes	—
26	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₂₃	—	4	2	no	—
28	C₈×C₂₃	Q₁₆	1	2	yes	—
29	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
30	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
31	#2253	—	23	1	no	maximal, Sylow
32	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
33	C₄×C₂₃	—	2	2	no	—
34	C₄×C₂₃	—	8	2	no	—
35	C₄×C₂₃	C₄⋊Q₈	1	1	yes	characteristic
36	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
37	Dic₂₃	—	8	2	no	—
38	#499	—	23	1	no	—
39	#499	D₂₃	1	1	yes	characteristic
40	#367	—	23	2	no	—
41	#366	—	23	2	no	—
42	C₄×C₁₆	—	23	1	no	—
43	C₂×C₂₃	#500	1	1	yes	characteristic
44	C₂×C₂₃	#508	1	2	yes	—
45	#125	—	2	1	no	—
46	#125	—	46	1	no	—
47	C₂×C₁₆	—	23	1	no	—
48	C₂×C₁₆	—	23	1	no	—
49	#107	—	23	2	no	—
50	#107	C₂×D₂₃	1	2	yes	—
51	#106	—	2	1	no	—
52	#106	—	46	1	no	—
53	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
54	C₂₃	#2253	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
56	C₂×C₈	C₂²×D₂₃	1	1	yes	characteristic
57	C₄⋊C₄	—	2	2	no	—
58	C₄⋊C₄	—	4	2	no	—
59	C₄⋊C₄	—	46	2	no	—
60	C₄⋊C₄	—	92	2	no	—
61	C₄²	C₂²⋊D₂₃	1	1	yes	characteristic
62	C₁₆	—	23	2	no	—
63	C₁₆	—	23	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	92	2	no	—
66	C₂×C₄	#67272	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₂₃	1	1	yes	characteristic
68	C₈	#67275	1	2	yes	—
69	C₈	Q₈×D₂₃	1	1	yes	characteristic
70	C₈	Q₈×D₂₃	1	1	yes	characteristic
71	C₂²	C₂×#67272	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	184	2	no	—
75	C₄	C₂×#67275	1	1	yes	characteristic
76	C₄	#10625115	1	1	yes	characteristic
77	C₂	#13092820	1	1	yes	characteristic
78	C₂	#13092847	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#67272
commutator, cosocle	C₂×C₈×C₂₃	C₂³
Frattini	C₂×C₈	C₂²×D₂₃
Fitting	C₂₃×#499	C₂
socle, prime radical	C₂²×C₂₃	C₂×D₈
hypercenter	#499	D₂₃
hypocenter	C₂₃	#2253
LCS	G ▷ C₂×C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
54. C₂₃	#2253	semidirect

Maximal subgroups

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

subgroup	index
#13092819	2
#13092244	2
#13092242	2
C₄×C₂₃⋊C₁₆	2
C₂₃×#499	2
#2253	23