Subgroups — C₂×C₂₃×#366 #15669775

Order 2944.

168 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	C₂×C₂₃×#107	C₂	1	2	yes	maximal
3	C₂₃×#366	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
6	C₂×C₁₆×C₂₃	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₂₃	C₂²	1	2	yes	—
8	C₂₃×#107	—	2	2	no	—
9	C₂₃×#107	C₂²	1	4	yes	—
10	C₂²×C₄×C₂₃	—	4	2	no	—
11	C₂²×C₄×C₂₃	D₄	1	1	yes	characteristic
12	C₂×C₈×C₂₃	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₃	Q₈	1	2	yes	—
15	C₂×C₈×C₂₃	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₂₃	—	2	4	no	—
17	C₄⋊C₄×C₂₃	—	4	2	no	—
18	C₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
19	C₂³×C₂₃	D₈	1	1	yes	characteristic
20	C₂×C₄×C₂₃	—	4	4	no	—
21	C₂×C₄×C₂₃	—	8	4	no	—
22	C₂×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
24	C₂×C₄×C₂₃	Q₁₆	1	2	yes	—
25	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
26	C₈×C₂₃	C₄⋊C₄	1	2	yes	—
27	C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×#366	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂²×C₂₃	#107	1	2	yes	—
31	C₂²×C₂₃	D₁₆	1	2	yes	—
32	C₂²×C₂₃	Q₃₂	1	2	yes	—
33	C₂²×C₂₃	C₂×D₈	1	1	yes	characteristic
34	C₄×C₂₃	—	8	4	no	—
35	C₄×C₂₃	#107	1	2	yes	—
36	C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
38	C₂²×C₁₆	C₂×C₂₃	1	1	yes	characteristic
39	C₂×#107	C₂×C₂₃	1	2	yes	—
40	#366	C₂×C₂₃	1	4	yes	direct product factor
41	C₂×C₂₃	#366	1	4	yes	direct product factor
42	C₂×C₂₃	C₂×#107	1	1	yes	characteristic
43	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
44	C₂×C₂₃	C₂×Q₃₂	1	1	yes	characteristic
45	C₂²×C₈	C₂²×C₂₃	1	1	yes	characteristic
46	C₂×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₆	C₄×C₂₃	1	4	yes	complemented
48	C₂×C₁₆	C₂²×C₂₃	1	2	yes	—
49	#107	—	2	2	no	—
50	#107	C₂²×C₂₃	1	4	yes	—
51	C₂₃	C₂×#366	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²×C₄	—	4	2	no	—
53	C₂²×C₄	D₄×C₂₃	1	1	yes	characteristic
54	C₂×C₈	C₂×C₄×C₂₃	1	2	yes	—
55	C₂×C₈	D₄×C₂₃	1	1	yes	characteristic
56	C₂×C₈	Q₈×C₂₃	1	2	yes	—
57	C₂×C₈	C₂³×C₂₃	1	1	yes	characteristic
58	C₄⋊C₄	—	2	4	no	—
59	C₄⋊C₄	—	4	2	no	—
60	C₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
61	C₂³	D₈×C₂₃	1	1	yes	characteristic
62	C₂×C₄	—	4	4	no	—
63	C₂×C₄	—	8	4	no	—
64	C₂×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
65	C₂×C₄	D₈×C₂₃	1	1	yes	characteristic
66	C₂×C₄	Q₁₆×C₂₃	1	2	yes	—
67	C₂×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
68	C₈	C₄⋊C₄×C₂₃	1	2	yes	—
69	C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
70	C₈	C₂×Q₈×C₂₃	1	1	yes	characteristic
71	C₂²	C₂₃×#107	1	2	yes	—
72	C₂²	C₂₃×D₁₆	1	2	yes	—
73	C₂²	C₂₃×Q₃₂	1	2	yes	—
74	C₂²	C₂×D₈×C₂₃	1	1	yes	characteristic
75	C₄	—	8	4	no	—
76	C₄	C₂₃×#107	1	2	yes	—
77	C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
78	C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
79	C₂	C₂₃×#366	1	4	yes	direct product factor
80	C₂	C₂×C₂₃×#107	1	1	yes	characteristic
81	C₂	C₂×C₂₃×D₁₆	1	1	yes	characteristic
82	C₂	C₂×C₂₃×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	D₈
commutator	C₈	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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×#366	C₂	direct (N × H)
6. C₂×C₁₆×C₂₃	C₄	semidirect
18. C₁₆×C₂₃	C₂×C₄	semidirect
29. C₂×#366	C₂₃	direct (N × H)
40. #366	C₂×C₂₃	direct (N × H)
41. C₂×C₂₃	#366	direct (N × H)
47. C₂×C₁₆	C₄×C₂₃	semidirect
51. C₂₃	C₂×#366	direct (N × H)
60. C₁₆	C₂×C₄×C₂₃	semidirect
79. C₂	C₂₃×#366	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
C₂×C₂₃×#107	2
C₂₃×#366	2
C₂×#366	23

Subgroups — C2×C23×#366 #15669775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#366 #15669775