Subgroups — C₂₃×#1415 #15669034

Order 2944.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₂₃	—	2	1	no	—
5	C₂₃×D₁₆	—	2	1	no	—
6	C₂₃×D₁₆	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
8	C₂₃×#107	—	2	1	no	—
9	C₂₃×C₃₂	—	2	1	no	—
10	C₂×D₄×C₂₃	—	4	1	no	—
11	D₈×C₂₃	—	2	2	no	—
12	D₈×C₂₃	—	4	1	no	—
13	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
14	C₄⋊C₄×C₂₃	—	4	1	no	—
15	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₃	D₄	1	1	yes	characteristic
17	C₂³×C₂₃	—	8	1	no	—
18	D₄×C₂₃	—	4	2	no	—
19	D₄×C₂₃	—	8	1	no	—
20	C₂×C₄×C₂₃	—	8	1	no	—
21	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
22	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
24	#1415	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₂₃	—	8	2	no	—
26	C₂²×C₂₃	—	16	1	no	—
27	C₂²×C₂₃	—	16	1	no	—
28	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
29	C₄×C₂₃	—	16	1	no	—
30	C₄×C₂₃	#102	1	1	yes	characteristic
31	C₄×C₂₃	SD₃₂	1	1	yes	characteristic
32	C₂×D₁₆	C₂×C₂₃	1	1	yes	characteristic
33	C₂×C₃₂	C₂×C₂₃	1	1	yes	characteristic, complemented
34	#366	C₂×C₂₃	1	1	yes	characteristic, complemented
35	C₂×C₂₃	—	16	2	no	—
36	C₂×C₂₃	#357	1	1	yes	characteristic
37	C₂×C₂₃	D₃₂	1	1	yes	characteristic
38	C₂×C₂₃	SD₆₄	1	1	yes	characteristic
39	C₂×D₈	—	2	1	no	—
40	D₁₆	—	2	1	no	—
41	D₁₆	C₄×C₂₃	1	2	yes	complemented
42	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
43	#107	—	2	1	no	—
44	C₃₂	—	2	1	no	—
45	C₂₃	#1415	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×D₄	—	4	1	no	—
47	D₈	—	2	2	no	—
48	D₈	—	4	1	no	—
49	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
50	C₄⋊C₄	—	4	1	no	—
51	C₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
52	C₁₆	D₄×C₂₃	1	1	yes	characteristic
53	C₂³	—	8	1	no	—
54	D₄	—	4	2	no	—
55	D₄	—	8	1	no	—
56	C₂×C₄	—	8	1	no	—
57	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
58	C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
59	C₈	SD₁₆×C₂₃	1	1	yes	characteristic
60	C₂²	—	8	2	no	—
61	C₂²	—	16	1	no	—
62	C₂²	—	16	1	no	—
63	C₂²	C₂₃×D₁₆	1	1	yes	characteristic
64	C₄	—	16	1	no	—
65	C₄	C₂₃×#102	1	1	yes	characteristic
66	C₄	C₂₃×SD₃₂	1	1	yes	characteristic
67	C₂	—	16	2	no	—
68	C₂	C₂₃×#357	1	1	yes	characteristic
69	C₂	C₂₃×D₃₂	1	1	yes	characteristic
70	C₂	C₂₃×SD₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	D₁₆
commutator	C₁₆	C₂×C₄×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
prime radical	C₂×C₂₃×D₁₆	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×C₈×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×C₃₂	C₂	semidirect
3. C₂₃×#366	C₂	semidirect
6. C₂₃×D₁₆	C₄	semidirect
24. #1415	C₂₃	direct (N × H)
33. C₂×C₃₂	C₂×C₂₃	semidirect
34. #366	C₂×C₂₃	semidirect
41. D₁₆	C₄×C₂₃	semidirect
45. C₂₃	#1415	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×D₁₆	2
C₂×C₂₃×C₃₂	2
C₂₃×#366	2
#1415	23

Subgroups — C23×#1415 #15669034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#1415 #15669034