Subgroups — C₂₃×#1384 #15669003

Order 2944.

132 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	C₂₃×#427	C₂	1	2	yes	maximal
3	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
4	C₂₃×#117	—	2	2	no	—
5	C₂₃×M₃₂	—	2	2	no	—
6	C₂×C₁₆×C₂₃	C₄	1	2	yes	complemented
7	C₂₃×#107	—	2	2	no	—
8	C₂₃×#106	C₄	1	4	yes	complemented
9	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
10	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₂₃	D₄	1	2	yes	—
13	C₂×C₈×C₂₃	Q₈	1	1	yes	characteristic
14	C₄⋊C₄×C₂₃	—	2	4	no	—
15	C₂²⋊C₄×C₂₃	—	4	2	no	—
16	C₄²×C₂₃	—	4	2	no	—
17	C₁₆×C₂₃	—	2	2	no	—
18	C₂³×C₂₃	D₈	1	1	yes	characteristic
19	C₂×C₄×C₂₃	—	4	4	no	—
20	C₂×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₃	SD₁₆	1	2	yes	—
23	C₂×C₄×C₂₃	Q₁₆	1	1	yes	characteristic
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	#1384	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₂₃	—	4	1	no	—
29	C₂²×C₂₃	#102	1	2	yes	—
30	C₂²×C₂₃	#107	1	1	yes	characteristic
31	C₄×C₂₃	—	8	4	no	—
32	C₄×C₂₃	#95	1	1	yes	characteristic
33	C₄×C₂₃	#103	1	2	yes	—
34	C₄×C₂₃	#106	1	1	yes	characteristic
35	C₂×M₃₂	C₂×C₂₃	1	1	yes	characteristic
36	#427	C₂×C₂₃	1	2	yes	—
37	C₂×C₂₃	—	2	2	no	—
38	C₂×C₂₃	—	2	1	no	—
39	C₂×C₂₃	#340	1	1	yes	characteristic
40	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
41	#117	—	2	2	no	—
42	M₃₂	—	2	2	no	—
43	C₂×C₁₆	C₄×C₂₃	1	2	yes	complemented
44	#107	—	2	2	no	—
45	#106	C₄×C₂₃	1	4	yes	complemented
46	C₂₃	#1384	1	1	yes	characteristic, direct product factor, Sylow
47	C₂²×C₄	D₄×C₂₃	1	1	yes	characteristic
48	C₂×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
49	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
50	C₂×C₈	D₄×C₂₃	1	2	yes	—
51	C₂×C₈	Q₈×C₂₃	1	1	yes	characteristic
52	C₄⋊C₄	—	2	4	no	—
53	C₂²⋊C₄	—	4	2	no	—
54	C₄²	—	4	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₈×C₂₃	1	1	yes	characteristic
57	C₂×C₄	—	4	4	no	—
58	C₂×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
59	C₂×C₄	C₄⋊C₄×C₂₃	1	1	yes	characteristic
60	C₂×C₄	SD₁₆×C₂₃	1	2	yes	—
61	C₂×C₄	Q₁₆×C₂₃	1	1	yes	characteristic
62	C₈	C₄²×C₂₃	1	1	yes	characteristic
63	C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
64	C₈	C₄⋊C₄×C₂₃	1	2	yes	—
65	C₂²	—	4	1	no	—
66	C₂²	C₂₃×#102	1	2	yes	—
67	C₂²	C₂₃×#107	1	1	yes	characteristic
68	C₄	—	8	4	no	—
69	C₄	C₂₃×#95	1	1	yes	characteristic
70	C₄	C₂₃×#103	1	2	yes	—
71	C₄	C₂₃×#106	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	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	D₈
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
6. C₂×C₁₆×C₂₃	C₄	semidirect
8. C₂₃×#106	C₄	semidirect
27. #1384	C₂₃	direct (N × H)
43. C₂×C₁₆	C₄×C₂₃	semidirect
45. #106	C₄×C₂₃	semidirect
46. C₂₃	#1384	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
C₂₃×#427	2
#1384	23

Subgroups — C23×#1384 #15669003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1384 #15669003