Subgroups — C₈×C₁₂₇⋊C₁₆ #30636645

Order 16256.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₂₇⋊C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₂₇⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₁₂₇	C₄	1	2	yes	—
5	C₄×C₈×C₁₂₇	C₂²	1	1	yes	characteristic
6	C₁₂₇⋊C₁₆	C₈	1	8	yes	direct product factor
7	C₂×C₈×C₁₂₇	C₈	1	4	yes	—
8	C₂×C₈×C₁₂₇	C₂×C₄	1	2	yes	—
9	C₄²×C₁₂₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₂₇	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₁₂₇	C₂×C₈	1	2	yes	—
12	C₈×C₁₂₇	C₁₆	1	8	yes	complemented
13	C₈×C₁₂₇	C₂×C₈	1	4	yes	—
14	C₂²×C₁₂₇	C₄×C₈	1	1	yes	characteristic
15	C₄×C₁₂₇	C₄×C₈	1	2	yes	—
16	C₄×C₁₂₇	C₂×C₁₆	1	4	yes	—
17	C₂×C₁₂₇	C₈²	1	1	yes	characteristic
18	C₂×C₁₂₇	C₄×C₁₆	1	2	yes	—
19	C₈×C₁₆	—	127	1	no	maximal, Sylow
20	C₁₂₇	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₄×C₁₆	—	127	2	no	—
22	C₈²	D₁₂₇	1	1	yes	characteristic
23	C₂×C₁₆	—	127	4	no	—
24	C₄×C₈	Dic₁₂₇	1	2	yes	—
25	C₄×C₈	C₂×D₁₂₇	1	1	yes	characteristic
26	C₂×C₈	C₁₂₇⋊C₈	1	4	yes	—
27	C₂×C₈	C₄×D₁₂₇	1	2	yes	—
28	C₄²	C₂×Dic₁₂₇	1	1	yes	characteristic
29	C₁₆	—	127	8	no	—
30	C₂×C₄	C₄×Dic₁₂₇	1	1	yes	characteristic
31	C₂×C₄	C₂×C₁₂₇⋊C₈	1	2	yes	—
32	C₈	C₁₂₇⋊C₁₆	1	8	yes	direct product factor
33	C₈	C₈×D₁₂₇	1	4	yes	—
34	C₂²	C₄×C₁₂₇⋊C₈	1	1	yes	characteristic
35	C₄	C₈×Dic₁₂₇	1	2	yes	—
36	C₄	C₂×C₁₂₇⋊C₁₆	1	4	yes	—
37	C₂	C₈×C₁₂₇⋊C₈	1	1	yes	characteristic
38	C₂	C₄×C₁₂₇⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₈²	D₁₂₇
commutator, hypocenter	C₁₂₇	C₈×C₁₆
Frattini	C₄×C₈	C₂×D₁₂₇
Fitting	C₈²×C₁₂₇	C₂
socle, prime radical	C₂²×C₁₂₇	C₄×C₈
cosocle	C₄×C₈×C₁₂₇	C₂²
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₈²

Complements

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

N	H ≅ G/N	type
6. C₁₂₇⋊C₁₆	C₈	direct (N × H)
12. C₈×C₁₂₇	C₁₆	semidirect
20. C₁₂₇	C₈×C₁₆	semidirect
32. C₈	C₁₂₇⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₂₇⋊C₁₆	2
C₈²×C₁₂₇	2
C₈×C₁₆	127

Subgroups — C8×C127⋊C16 #30636645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₁₂₇⋊C₁₆ #30636645