Subgroups — D₄₇×C₁₂₈ #26104186

Order 12032.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₄×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇⋊C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₄₇	C₄	1	1	yes	characteristic
5	C₄₇⋊C₆₄	C₄	1	1	yes	characteristic
6	C₄₇×C₆₄	C₂²	1	1	yes	characteristic
7	C₁₆×D₄₇	C₈	1	1	yes	characteristic
8	C₄₇⋊C₃₂	C₈	1	1	yes	characteristic
9	C₃₂×C₄₇	C₂×C₄	1	1	yes	characteristic
10	C₈×D₄₇	C₁₆	1	1	yes	characteristic
11	C₁₆×C₄₇	C₂×C₈	1	1	yes	characteristic
12	C₄₇⋊C₁₆	C₁₆	1	1	yes	characteristic
13	C₄×D₄₇	C₃₂	1	1	yes	characteristic
14	C₈×C₄₇	C₂×C₁₆	1	1	yes	characteristic
15	C₄₇⋊C₈	C₃₂	1	1	yes	characteristic
16	C₂×C₁₂₈	—	47	1	no	maximal, Sylow
17	C₂×D₄₇	C₆₄	1	1	yes	characteristic
18	C₄×C₄₇	C₂×C₃₂	1	1	yes	characteristic
19	Dic₄₇	C₆₄	1	1	yes	characteristic
20	C₂×C₆₄	—	47	1	no	—
21	C₁₂₈	—	47	1	no	—
22	C₁₂₈	D₄₇	1	1	yes	characteristic, direct product factor
23	C₂×C₄₇	C₂×C₆₄	1	1	yes	characteristic
24	D₄₇	C₁₂₈	1	2	yes	direct product factor
25	C₂×C₃₂	—	47	1	no	—
26	C₆₄	—	47	1	no	—
27	C₆₄	C₂×D₄₇	1	1	yes	characteristic
28	C₄₇	C₂×C₁₂₈	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	—	47	1	no	—
30	C₃₂	—	47	1	no	—
31	C₃₂	C₄×D₄₇	1	1	yes	characteristic
32	C₂×C₈	—	47	1	no	—
33	C₁₆	—	47	1	no	—
34	C₁₆	C₈×D₄₇	1	1	yes	characteristic
35	C₂×C₄	—	47	1	no	—
36	C₈	—	47	1	no	—
37	C₈	C₁₆×D₄₇	1	1	yes	characteristic
38	C₂²	—	47	1	no	—
39	C₄	—	47	1	no	—
40	C₄	C₃₂×D₄₇	1	1	yes	characteristic
41	C₂	—	47	2	no	—
42	C₂	C₆₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₂₈	D₄₇
commutator, hypocenter	C₄₇	C₂×C₁₂₈
Frattini	C₆₄	C₂×D₄₇
Fitting	C₄₇×C₁₂₈	C₂
socle	C₂×C₄₇	C₂×C₆₄
prime radical	C₂×D₄₇	C₆₄
cosocle	C₄₇×C₆₄	C₂²
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₁₂₈

Complements

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

N	H ≅ G/N	type
2. C₄₇⋊C₁₂₈	C₂	semidirect
3. C₄₇×C₁₂₈	C₂	semidirect
22. C₁₂₈	D₄₇	direct (N × H)
24. D₄₇	C₁₂₈	direct (N × H)
28. C₄₇	C₂×C₁₂₈	semidirect

Maximal subgroups

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

subgroup	index
C₆₄×D₄₇	2
C₄₇⋊C₁₂₈	2
C₄₇×C₁₂₈	2
C₂×C₁₂₈	47

Subgroups — D47×C128 #26104186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×C₁₂₈ #26104186