Subgroups — Dic₁₂₇⋊C₃₂ #30636925

Order 16256.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₁₂₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₂₇⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₁₂₇	C₄	1	1	yes	characteristic
6	C₁₂₇⋊C₃₂	—	2	1	no	—
7	C₂×C₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₂₇	—	2	1	no	—
9	C₂×C₁₂₇⋊C₈	C₈	1	1	yes	characteristic
10	C₄×Dic₁₂₇	C₈	1	1	yes	characteristic
11	C₁₂₇⋊C₁₆	—	2	1	no	—
12	C₂×C₈×C₁₂₇	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₁₂₇	D₄	1	1	yes	characteristic
14	C₁₆×C₁₂₇	Q₈	1	1	yes	characteristic
15	C₂×Dic₁₂₇	C₁₆	1	1	yes	characteristic
16	C₂×Dic₁₂₇	C₁₆	1	1	yes	characteristic
17	C₁₂₇⋊C₈	—	2	1	no	—
18	C₂×C₄×C₁₂₇	C₂×C₈	1	1	yes	characteristic
19	C₈×C₁₂₇	C₄⋊C₄	1	1	yes	characteristic
20	C₈×C₁₂₇	M₁₆	1	1	yes	characteristic
21	C₂²×C₁₂₇	C₂×C₁₆	1	1	yes	characteristic
22	C₄×C₁₂₇	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₁₂₇	M₃₂	1	1	yes	characteristic
24	Dic₁₂₇	—	2	1	no	—
25	Dic₁₂₇	C₃₂	1	2	yes	complemented
26	C₂×C₁₂₇	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₁₂₇	C₂×C₃₂	1	1	yes	characteristic
28	C₂×C₁₂₇	M₆₄	1	1	yes	characteristic
29	C₄⋊C₃₂	—	127	1	no	maximal, Sylow
30	C₁₂₇	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃₂	—	127	1	no	—
32	C₂×C₃₂	D₁₂₇	1	1	yes	characteristic
33	C₄×C₁₆	—	127	1	no	—
34	C₂×C₁₆	—	127	1	no	—
35	C₂×C₁₆	C₂×D₁₂₇	1	1	yes	characteristic
36	C₄×C₈	—	127	1	no	—
37	C₃₂	—	2	1	no	—
38	C₃₂	—	254	1	no	—
39	C₂×C₈	—	127	1	no	—
40	C₂×C₈	C₄×D₁₂₇	1	1	yes	characteristic
41	C₄²	—	127	1	no	—
42	C₁₆	—	254	1	no	—
43	C₁₆	C₂²⋊D₁₂₇	1	1	yes	characteristic
44	C₁₆	Dic₂₅₄	1	1	yes	characteristic
45	C₂×C₄	—	127	1	no	—
46	C₂×C₄	—	127	1	no	—
47	C₂×C₄	C₈×D₁₂₇	1	1	yes	characteristic
48	C₈	—	254	1	no	—
49	C₈	Dic₁₂₇⋊C₄	1	1	yes	characteristic
50	C₈	#14523231	1	1	yes	characteristic
51	C₂²	C₁₆×D₁₂₇	1	1	yes	characteristic
52	C₄	—	127	2	no	—
53	C₄	—	254	1	no	—
54	C₄	Dic₁₂₇⋊C₈	1	1	yes	characteristic
55	C₄	#16861148	1	1	yes	characteristic
56	C₂	Dic₁₂₇⋊C₁₆	1	1	yes	characteristic
57	C₂	C₃₂×D₁₂₇	1	1	yes	characteristic
58	C₂	#22549709	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₁₂₇
commutator	C₂×C₁₂₇	C₂×C₃₂
Fitting	C₂×C₃₂×C₁₂₇	C₂
socle, prime radical	C₂²×C₁₂₇	C₂×C₁₆
cosocle	C₂×C₁₆×C₁₂₇	C₂²
hypercenter	C₂×C₃₂	D₁₂₇
hypocenter	C₁₂₇	C₄⋊C₃₂
LCS	G ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
25. Dic₁₂₇	C₃₂	semidirect
30. C₁₂₇	C₄⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₂₇⋊C₃₂	2
C₁₆×Dic₁₂₇	2
C₂×C₃₂×C₁₂₇	2
C₄⋊C₃₂	127

Subgroups — Dic127⋊C32 #30636925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₂₇⋊C₃₂ #30636925