Subgroups — C₂₃×#1385 #15669004

Order 2944.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#108	C₂	1	2	yes	maximal
3	C₂×M₁₆×C₂₃	—	2	2	no	—
4	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₂₃×M₃₂	—	2	2	no	—
6	C₂×C₁₆×C₂₃	C₄	1	2	yes	—
7	C₂₃×#108	—	2	2	no	—
8	C₂₃×#108	C₄	1	4	yes	—
9	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
10	M₁₆×C₂₃	—	2	4	no	—
11	M₁₆×C₂₃	—	4	2	no	—
12	C₂×C₈×C₂₃	—	4	2	no	—
13	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₂₃	D₄	1	2	yes	—
16	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
17	C₁₆×C₂₃	—	2	2	no	—
18	C₂³×C₂₃	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₃	SD₁₆	1	2	yes	—
23	C₈×C₂₃	—	4	4	no	—
24	C₈×C₂₃	C₄²	1	1	yes	characteristic
25	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
27	#1385	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₂₃	—	4	1	no	—
29	C₂²×C₂₃	#103	1	2	yes	—
30	C₂²×C₂₃	#107	1	1	yes	characteristic
31	C₄×C₂₃	#95	1	1	yes	characteristic
32	C₄×C₂₃	#102	1	2	yes	—
33	C₄×C₂₃	#106	1	1	yes	characteristic
34	C₂×M₃₂	C₂×C₂₃	1	1	yes	characteristic
35	C₂×#108	C₂×C₂₃	1	2	yes	—
36	C₂×C₂₃	—	2	2	no	—
37	C₂×C₂₃	—	2	1	no	—
38	C₂×C₂₃	#340	1	1	yes	characteristic
39	C₂×M₁₆	—	2	2	no	—
40	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
41	M₃₂	—	2	2	no	—
42	C₂×C₁₆	C₄×C₂₃	1	2	yes	—
43	#108	—	2	2	no	—
44	#108	C₄×C₂₃	1	4	yes	—
45	C₂₃	#1385	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₄	D₄×C₂₃	1	1	yes	characteristic
47	M₁₆	—	2	4	no	—
48	M₁₆	—	4	2	no	—
49	C₂×C₈	—	4	2	no	—
50	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
51	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
52	C₂×C₈	D₄×C₂₃	1	2	yes	—
53	C₂×C₈	Q₈×C₂₃	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₂³	Q₁₆×C₂₃	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
57	C₂×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
58	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
59	C₂×C₄	SD₁₆×C₂₃	1	2	yes	—
60	C₈	—	4	4	no	—
61	C₈	C₄²×C₂₃	1	1	yes	characteristic
62	C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
63	C₈	C₄⋊C₄×C₂₃	1	2	yes	—
64	C₂²	—	4	1	no	—
65	C₂²	C₂₃×#103	1	2	yes	—
66	C₂²	C₂₃×#107	1	1	yes	characteristic
67	C₄	C₂₃×#95	1	1	yes	characteristic
68	C₄	C₂₃×#102	1	2	yes	—
69	C₄	C₂₃×#106	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	—	2	1	no	—
72	C₂	C₂₃×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃	#106
commutator	C₈	C₄²×C₂₃
Frattini, cosocle	C₂²×C₈	C₂²×C₂₃
socle	C₂×C₂₃	#340
prime radical	C₂³×C₂₃	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
27. #1385	C₂₃	direct (N × H)
45. C₂₃	#1385	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×M₃₂	2
C₂×C₂₃×#108	2
#1385	23

Subgroups — C23×#1385 #15669004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1385 #15669004