Subgroups — #127×D₂₃ #13092955

Order 1472.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×D₂₃	C₂	1	6	yes	maximal, complemented
2	C₂₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	#10625111	C₂	1	6	yes	maximal, complemented
4	#10625045	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄²×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₂₃	C₂²	1	4	yes	—
7	C₂×D₄×C₂₃	C₂²	1	6	yes	complemented
8	C₂×C₂²⋊D₂₃	C₂²	1	12	yes	complemented
9	D₄×D₂₃	—	2	24	no	—
10	C₂×D₉₂	C₂²	1	6	yes	complemented
11	C₂×C₄×D₂₃	C₂²	1	3	yes	—
12	C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
13	C₄×Dic₂₃	C₂²	1	3	yes	complemented
14	C₂³×C₂₃	C₂³	1	4	yes	—
15	C₂²×D₂₃	—	2	24	no	—
16	C₂²×D₂₃	C₂³	1	4	yes	—
17	C₂²×D₂₃	C₂³	1	1	yes	characteristic
18	D₄×C₂₃	—	2	12	no	—
19	C₂×C₄×C₂₃	C₂³	1	3	yes	—
20	C₂²⋊D₂₃	—	2	24	no	—
21	C₂×Dic₂₃	C₂³	1	3	yes	—
22	D₉₂	—	2	12	no	—
23	C₄×D₂₃	D₄	1	12	yes	complemented
24	C₂²×C₂₃	—	2	12	no	—
25	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
26	C₂×D₂₃	—	2	12	no	—
27	C₂×D₂₃	—	4	16	no	—
28	C₂×D₂₃	C₂×D₄	1	6	yes	—
29	C₄×C₂₃	C₂×D₄	1	6	yes	complemented
30	Dic₂₃	C₂×D₄	1	6	yes	complemented
31	C₂×#127	—	23	1	no	maximal, Sylow
32	C₂×C₂₃	—	4	4	no	—
33	C₂×C₂₃	C₂²×D₄	1	3	yes	—
34	D₂₃	—	4	4	no	—
35	D₂₃	#127	1	4	yes	direct product factor
36	C₂²×D₄	—	23	6	no	—
37	#127	—	23	6	no	—
38	#127	—	23	1	no	—
39	#127	D₂₃	1	1	yes	characteristic, direct product factor
40	C₂×C₄²	—	23	1	no	—
41	C₂₃	C₂×#127	1	1	yes	characteristic, complemented, Sylow
42	C₂⁴	—	23	4	no	—
43	C₂×D₄	—	23	12	no	—
44	C₂×D₄	—	23	6	no	—
45	C₂×D₄	—	46	24	no	—
46	C₂×D₄	C₂×D₂₃	1	6	yes	complemented
47	C₂²×C₄	—	23	3	no	—
48	C₄²	—	23	3	no	—
49	C₄²	C₂×D₂₃	1	1	yes	characteristic, complemented
50	C₂³	—	23	1	no	—
51	C₂³	—	23	4	no	—
52	C₂³	—	46	24	no	—
53	C₂³	C₂²×D₂₃	1	4	yes	—
54	D₄	—	2	12	no	—
55	D₄	—	46	24	no	—
56	D₄	—	46	12	no	—
57	C₂×C₄	—	23	3	no	—
58	C₂×C₄	—	23	12	no	—
59	C₂×C₄	C₂²×D₂₃	1	3	yes	—
60	C₂²	—	2	12	no	—
61	C₂²	—	23	6	no	—
62	C₂²	—	46	12	no	—
63	C₂²	—	92	16	no	—
64	C₂²	C₂³×D₂₃	1	1	yes	characteristic
65	C₄	—	23	6	no	—
66	C₄	D₄×D₂₃	1	6	yes	complemented
67	C₂	—	4	4	no	—
68	C₂	—	23	4	no	—
69	C₂	—	92	4	no	—
70	C₂	C₂×D₄×D₂₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₃
commutator, socle, cosocle	C₂²×C₂₃	C₂⁴
Fitting	C₂₃×#127	C₂
hypercenter	#127	D₂₃
hypocenter	C₂₃	C₂×#127
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×D₂₃	C₂	semidirect
2. C₂₃×#127	C₂	semidirect
3. #10625111	C₂	semidirect
4. #10625045	C₂	semidirect
5. C₄²×D₂₃	C₂	semidirect
7. C₂×D₄×C₂₃	C₂²	semidirect
8. C₂×C₂²⋊D₂₃	C₂²	semidirect
10. C₂×D₉₂	C₂²	semidirect
12. C₄²×C₂₃	C₂²	semidirect
13. C₄×Dic₂₃	C₂²	semidirect
23. C₄×D₂₃	D₄	semidirect
29. C₄×C₂₃	C₂×D₄	semidirect
30. Dic₂₃	C₂×D₄	semidirect
35. D₂₃	#127	direct (N × H)
39. #127	D₂₃	direct (N × H)
41. C₂₃	C₂×#127	semidirect
46. C₂×D₄	C₂×D₂₃	semidirect
49. C₄²	C₂×D₂₃	semidirect
66. C₄	D₄×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×D₂₃	2
C₂₃×#127	2
#10625111	2
#10625045	2
C₄²×D₂₃	2
C₂×#127	23

Subgroups — #127×D23 #13092955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #127×D₂₃ #13092955