Subgroups — D₃₂×D₁₂₇ #30641026

Order 16256.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₆×D₁₂₇	C₂	1	2	yes	maximal, complemented
2	D₄₀₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#22549711	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃₂×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₈×D₁₂₇	—	2	2	no	—
7	D₂₀₃₂	C₂²	1	2	yes	complemented
8	#16861150	—	2	2	no	—
9	C₁₆×D₁₂₇	C₂²	1	1	yes	characteristic
10	C₁₂₇⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
11	D₁₆×C₁₂₇	C₂²	1	2	yes	complemented
12	C₃₂×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
13	D₄×D₁₂₇	—	4	2	no	—
14	D₁₀₁₆	—	2	2	no	—
15	#14523233	—	4	2	no	—
16	C₈×D₁₂₇	D₄	1	1	yes	characteristic
17	C₁₂₇⋊C₁₆	D₄	1	1	yes	characteristic
18	D₈×C₁₂₇	—	2	2	no	—
19	C₁₆×C₁₂₇	C₂³	1	1	yes	characteristic
20	C₂²×D₁₂₇	—	8	2	no	—
21	D₅₀₈	—	4	2	no	—
22	C₂²⋊D₁₂₇	—	8	2	no	—
23	C₄×D₁₂₇	D₈	1	1	yes	characteristic
24	C₁₂₇⋊C₈	D₈	1	1	yes	characteristic
25	D₄×C₁₂₇	—	4	2	no	—
26	C₈×C₁₂₇	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₁₂₇	—	8	2	no	—
28	C₂×D₁₂₇	—	8	2	no	—
29	C₂×D₁₂₇	—	16	4	no	—
30	C₂×D₁₂₇	D₁₆	1	1	yes	characteristic
31	C₄×C₁₂₇	C₂×D₈	1	1	yes	characteristic
32	Dic₁₂₇	D₁₆	1	1	yes	characteristic
33	C₂×C₁₂₇	—	16	2	no	—
34	C₂×C₁₂₇	C₂×D₁₆	1	1	yes	characteristic
35	D₁₂₇	—	16	2	no	—
36	D₁₂₇	D₃₂	1	2	yes	direct product factor
37	C₂×D₃₂	—	127	1	no	maximal, Sylow
38	C₁₂₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₆	—	127	2	no	—
40	D₃₂	—	127	2	no	—
41	D₃₂	—	127	1	no	—
42	D₃₂	D₁₂₇	1	1	yes	characteristic, direct product factor
43	C₂×C₃₂	—	127	1	no	—
44	C₂×D₈	—	254	2	no	—
45	D₁₆	—	127	2	no	—
46	D₁₆	—	254	2	no	—
47	D₁₆	C₂×D₁₂₇	1	2	yes	complemented
48	C₂×C₁₆	—	127	1	no	—
49	C₃₂	—	127	1	no	—
50	C₃₂	C₂×D₁₂₇	1	1	yes	characteristic, complemented
51	C₂×D₄	—	508	2	no	—
52	D₈	—	2	2	no	—
53	D₈	—	508	2	no	—
54	D₈	—	254	2	no	—
55	C₂×C₈	—	127	1	no	—
56	C₁₆	—	127	1	no	—
57	C₁₆	C₂²×D₁₂₇	1	1	yes	characteristic
58	C₂³	—	1016	2	no	—
59	D₄	—	4	2	no	—
60	D₄	—	1016	2	no	—
61	D₄	—	508	2	no	—
62	C₂×C₄	—	127	1	no	—
63	C₈	—	127	1	no	—
64	C₈	D₄×D₁₂₇	1	1	yes	characteristic
65	C₂²	—	8	2	no	—
66	C₂²	—	127	1	no	—
67	C₂²	—	2032	4	no	—
68	C₂²	—	1016	2	no	—
69	C₄	—	127	1	no	—
70	C₄	D₈×D₁₂₇	1	1	yes	characteristic
71	C₂	—	16	2	no	—
72	C₂	—	127	2	no	—
73	C₂	—	2032	2	no	—
74	C₂	D₁₆×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₂₇
commutator, cosocle	C₁₆×C₁₂₇	C₂³
Frattini	C₁₆	C₂²×D₁₂₇
Fitting	D₃₂×C₁₂₇	C₂
socle	C₂×C₁₂₇	C₂×D₁₆
hypercenter	D₃₂	D₁₂₇
hypocenter	C₁₂₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₁₂₇ ▷ C₈×C₁₂₇ ▷ C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. D₁₆×D₁₂₇	C₂	semidirect
2. D₄₀₆₄	C₂	semidirect
3. #22549711	C₂	semidirect
4. C₃₂×D₁₂₇	C₂	semidirect
5. D₃₂×C₁₂₇	C₂	semidirect
7. D₂₀₃₂	C₂²	semidirect
10. C₁₂₇⋊C₃₂	C₂²	semidirect
11. D₁₆×C₁₂₇	C₂²	semidirect
12. C₃₂×C₁₂₇	C₂²	semidirect
36. D₁₂₇	D₃₂	direct (N × H)
38. C₁₂₇	C₂×D₃₂	semidirect
42. D₃₂	D₁₂₇	direct (N × H)
47. D₁₆	C₂×D₁₂₇	semidirect
50. C₃₂	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
D₁₆×D₁₂₇	2
D₄₀₆₄	2
#22549711	2
C₃₂×D₁₂₇	2
D₃₂×C₁₂₇	2
C₂×D₃₂	127

Subgroups — D32×D127 #30641026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₂×D₁₂₇ #30641026