Subgroups — C₂₃×#2158 #15669777

Order 2944.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#427	C₂	1	2	yes	maximal
3	C₂₃×#367	C₂	1	2	yes	maximal, complemented
4	C₂₃×#366	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₂₃×#117	—	2	2	no	—
7	C₂×C₁₆×C₂₃	C₄	1	4	yes	complemented
8	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
10	C₂₃×#107	C₂²	1	4	yes	—
11	C₂₃×#106	—	2	2	no	—
12	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₂₃	Q₈	1	2	yes	—
16	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₂₃	—	2	4	no	—
18	C₂²⋊C₄×C₂₃	—	4	2	no	—
19	C₄²×C₂₃	—	4	2	no	—
20	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
21	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
22	C₂³×C₂₃	D₈	1	1	yes	characteristic
23	C₂×C₄×C₂₃	—	4	4	no	—
24	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₃	Q₁₆	1	2	yes	—
27	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
28	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
29	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
31	#2158	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₂₃	—	2	2	no	—
33	C₂²×C₂₃	#107	1	2	yes	—
34	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
35	C₄×C₂₃	—	8	4	no	—
36	C₄×C₂₃	#107	1	2	yes	—
37	C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
39	C₂²×C₁₆	C₂×C₂₃	1	1	yes	characteristic
40	#427	C₂×C₂₃	1	2	yes	—
41	#367	C₂×C₂₃	1	2	yes	complemented
42	#366	C₂×C₂₃	1	2	yes	complemented
43	C₂×C₂₃	—	2	2	no	—
44	C₂×C₂₃	C₂×#107	1	1	yes	characteristic
45	C₂×C₂₃	#508	1	2	yes	—
46	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
47	#117	—	2	2	no	—
48	C₂×C₁₆	C₄×C₂₃	1	4	yes	complemented
49	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
50	C₂×C₁₆	C₂²×C₂₃	1	1	yes	characteristic
51	#107	C₂²×C₂₃	1	4	yes	—
52	#106	—	2	2	no	—
53	C₂₃	#2158	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₄	D₄×C₂₃	1	1	yes	characteristic
55	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
56	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
57	C₂×C₈	Q₈×C₂₃	1	2	yes	—
58	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
59	C₄⋊C₄	—	2	4	no	—
60	C₂²⋊C₄	—	4	2	no	—
61	C₄²	—	4	2	no	—
62	C₁₆	C₂×C₄×C₂₃	1	2	yes	—
63	C₁₆	C₂×C₄×C₂₃	1	2	yes	—
64	C₂³	D₈×C₂₃	1	1	yes	characteristic
65	C₂×C₄	—	4	4	no	—
66	C₂×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
67	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
68	C₂×C₄	Q₁₆×C₂₃	1	2	yes	—
69	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
70	C₈	C₄⋊C₄×C₂₃	1	2	yes	—
71	C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
72	C₈	C₂×Q₈×C₂₃	1	1	yes	characteristic
73	C₂²	—	2	2	no	—
74	C₂²	C₂₃×#107	1	2	yes	—
75	C₂²	C₂×D₈×C₂₃	1	1	yes	characteristic
76	C₄	—	8	4	no	—
77	C₄	C₂₃×#107	1	2	yes	—
78	C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
79	C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
80	C₂	—	2	2	no	—
81	C₂	C₂×C₂₃×#107	1	1	yes	characteristic
82	C₂	C₂₃×#508	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	D₈
commutator	C₈	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×D₈
prime radical	C₂³×C₂₃	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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
3. C₂₃×#367	C₂	semidirect
4. C₂₃×#366	C₂	semidirect
7. C₂×C₁₆×C₂₃	C₄	semidirect
31. #2158	C₂₃	direct (N × H)
41. #367	C₂×C₂₃	semidirect
42. #366	C₂×C₂₃	semidirect
48. C₂×C₁₆	C₄×C₂₃	semidirect
53. C₂₃	#2158	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×C₂₃	2
C₂₃×#427	2
C₂₃×#367	2
C₂₃×#366	2
#2158	23

Subgroups — C23×#2158 #15669777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#2158 #15669777