Subgroups — #15671316

Order 2944.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₃	C₄	1	2	yes	—
5	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₂₃⋊C₁₆	C₄	1	2	yes	—
7	C₄×C₂₃⋊C₈	C₄	1	1	yes	characteristic
8	C₄×C₂₃⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₂₃⋊C₈	C₈	1	2	yes	—
13	C₂×C₂₃⋊C₈	C₈	1	2	yes	—
14	C₁₆×C₂₃	—	2	2	no	—
15	C₂₃⋊C₁₆	—	2	2	no	—
16	C₂×C₄×C₂₃	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₃	M₁₆	1	2	yes	—
20	C₈×C₂₃	M₁₆	1	2	yes	—
21	C₂₃⋊C₈	—	2	2	no	—
22	C₂₃⋊C₈	C₁₆	1	4	yes	complemented
23	#1312	—	23	1	no	maximal, Sylow
24	C₂²×C₂₃	C₄×C₈	1	1	yes	characteristic
25	C₄×C₂₃	#97	1	1	yes	characteristic
26	C₄×C₂₃	#97	1	1	yes	characteristic
27	C₄×C₂₃	C₂×C₁₆	1	2	yes	—
28	C₄×C₂₃	M₃₂	1	2	yes	—
29	C₄×C₁₆	—	23	1	no	—
30	C₄×C₁₆	D₂₃	1	1	yes	characteristic
31	C₈²	—	23	1	no	—
32	C₂×C₂₃	#322	1	1	yes	characteristic
33	C₂×C₂₃	C₄×C₁₆	1	1	yes	characteristic
34	C₂×C₂₃	#346	1	1	yes	characteristic
35	C₂×C₁₆	—	23	2	no	—
36	C₂×C₁₆	Dic₂₃	1	2	yes	—
37	C₄×C₈	—	23	1	no	—
38	C₄×C₈	—	23	1	no	—
39	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
40	C₂₃	#1312	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₈	—	23	2	no	—
42	C₂×C₈	—	23	2	no	—
43	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
44	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
45	C₄²	C₄×D₂₃	1	1	yes	characteristic
46	C₁₆	—	2	2	no	—
47	C₁₆	—	46	2	no	—
48	C₂×C₄	C₈×D₂₃	1	1	yes	characteristic
49	C₂×C₄	C₈×D₂₃	1	1	yes	characteristic
50	C₂×C₄	C₄×Dic₂₃	1	1	yes	characteristic
51	C₈	—	23	4	no	—
52	C₈	—	46	2	no	—
53	C₈	#67262	1	2	yes	—
54	C₈	#67267	1	2	yes	—
55	C₂²	C₈×Dic₂₃	1	1	yes	characteristic
56	C₄	C₁₆×D₂₃	1	2	yes	—
57	C₄	#10624980	1	2	yes	—
58	C₄	#10624985	1	1	yes	characteristic
59	C₄	#10624997	1	1	yes	characteristic
60	C₂	#13092139	1	1	yes	characteristic
61	C₂	C₁₆×Dic₂₃	1	1	yes	characteristic
62	C₂	#13092192	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₂₃
commutator	C₂×C₂₃	C₄×C₁₆
Fitting	C₄×C₁₆×C₂₃	C₂
socle, prime radical	C₂²×C₂₃	C₄×C₈
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	C₄×C₁₆	D₂₃
hypocenter	C₂₃	#1312
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₂₃⋊C₈	C₁₆	semidirect
40. C₂₃	#1312	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂₃⋊C₁₆	2
C₈×C₂₃⋊C₈	2
C₄×C₁₆×C₂₃	2
#1312	23