Subgroups — C₂₃×#1372 #15668991

Order 2944.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#335	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
5	C₂₃×C₄⋊C₈	—	2	2	no	—
6	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₂₃	—	4	2	no	—
8	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
10	C₄²×C₂₃	D₄	1	1	yes	characteristic
11	C₁₆×C₂₃	—	2	1	no	—
12	C₁₆×C₂₃	C₈	1	2	yes	complemented
13	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
15	C₂×C₄×C₂₃	Q₁₆	1	1	yes	characteristic
16	C₈×C₂₃	—	2	1	no	—
17	C₈×C₂₃	—	8	2	no	—
18	C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₃	M₁₆	1	1	yes	characteristic
20	#1372	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₂₃	#107	1	1	yes	characteristic
22	C₄×C₂₃	—	2	1	no	—
23	C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₂₃	#108	1	1	yes	characteristic
25	C₄×C₂₃	SD₃₂	1	2	yes	—
26	C₄×C₁₆	C₂×C₂₃	1	1	yes	characteristic
27	#335	C₂×C₂₃	1	2	yes	—
28	C₂×C₂₃	#335	1	1	yes	characteristic
29	C₂×C₂₃	#367	1	1	yes	characteristic
30	C₂×C₂₃	#368	1	1	yes	characteristic
31	C₂×C₁₆	C₄×C₂₃	1	1	yes	characteristic
32	C₂×C₁₆	C₄×C₂₃	1	1	yes	characteristic
33	C₄⋊C₈	—	2	2	no	—
34	C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
35	C₂₃	#1372	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₈	—	4	2	no	—
37	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
38	C₂×C₈	Q₈×C₂₃	1	1	yes	characteristic
39	C₄²	D₄×C₂₃	1	1	yes	characteristic
40	C₁₆	—	2	1	no	—
41	C₁₆	C₈×C₂₃	1	2	yes	complemented
42	C₂×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
43	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
44	C₂×C₄	Q₁₆×C₂₃	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	8	2	no	—
47	C₈	C₂×C₈×C₂₃	1	1	yes	characteristic
48	C₈	M₁₆×C₂₃	1	1	yes	characteristic
49	C₂²	C₂₃×#107	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	C₂₃×C₄⋊C₈	1	1	yes	characteristic
52	C₄	C₂₃×#108	1	1	yes	characteristic
53	C₄	C₂₃×SD₃₂	1	2	yes	—
54	C₂	C₂₃×#335	1	1	yes	characteristic
55	C₂	C₂₃×#367	1	1	yes	characteristic
56	C₂	C₂₃×#368	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	D₈
commutator	C₈	C₂×C₈×C₂₃
Frattini, cosocle	C₄×C₈	C₂²×C₂₃
socle, prime radical	C₂²×C₂₃	#107
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₂₃	C₈	semidirect
20. #1372	C₂₃	direct (N × H)
35. C₂₃	#1372	direct (N × H)
41. C₁₆	C₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₆×C₂₃	2
C₂₃×#335	2
#1372	23

Subgroups — C23×#1372 #15668991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1372 #15668991