Subgroups — Dic₃×#14581887 #44544751

Order 32004.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14581887	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×#14581887	—	3	1	no	maximal
4	C₃×#14581887	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×#14581887	—	2	1	no	—
6	C₂×#14581887	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic
8	Dic₃×C₁₂₇⋊C₃	—	7	1	no	maximal, Hall
9	C₄×C₇×C₁₂₇	—	3	1	no	Hall
10	C₃×C₇×C₁₂₇	C₃×C₄	1	1	yes	characteristic, complemented
11	#14581887	—	2	1	no	—
12	#14581887	Dic₃	1	1	yes	characteristic, direct product factor
13	C₂×C₃×C₁₂₇⋊C₃	—	7	1	no	—
14	C₂×C₇×C₁₂₇	C₃×D₃	1	1	yes	characteristic
15	Dic₃×C₁₂₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	C₄×C₁₂₇⋊C₃	—	21	1	no	—
17	C₃×C₁₂₇⋊C₃	—	7	1	no	Hall
18	C₇×C₁₂₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₁₂₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
20	C₂×C₁₂₇⋊C₃	—	7	1	no	—
21	C₂×C₁₂₇⋊C₃	—	14	1	no	—
22	C₄×C₁₂₇	—	3	1	no	Hall
23	C₃×C₁₂₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
24	C₁₂₇⋊C₃	—	7	1	no	—
25	C₁₂₇⋊C₃	—	14	1	no	—
26	C₂×C₁₂₇	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
27	Dic₃×ΓL(1,𝔽₈)	—	127	1	no	maximal, Hall
28	C₁₂₇	Dic₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃×ΓL(1,𝔽₈)	—	127	1	no	—
30	C₇×Dic₃	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
31	C₄×ΓL(1,𝔽₈)	—	381	1	no	—
32	C₃×ΓL(1,𝔽₈)	—	127	1	no	Hall
33	C₂×C₃×C₇	C₂×C₁₂₇⋊C₃	1	1	yes	characteristic
34	C₂×ΓL(1,𝔽₈)	—	127	1	no	—
35	C₂×ΓL(1,𝔽₈)	—	254	1	no	—
36	C₃×Dic₃	—	889	1	no	Hall
37	C₄×C₇	—	3	1	no	Hall
38	C₃×C₇	C₄×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
39	ΓL(1,𝔽₈)	—	127	1	no	—
40	ΓL(1,𝔽₈)	—	254	1	no	—
41	C₂×C₃²	—	889	1	no	—
42	C₂×C₇	D₃×C₁₂₇⋊C₃	1	1	yes	characteristic
43	C₃×C₄	—	2667	1	no	—
44	Dic₃	#14581887	1	1	yes	characteristic, direct product factor
45	C₃²	—	889	1	no	Sylow
46	C₇	Dic₃×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	889	1	no	—
48	C₂×C₃	—	1778	1	no	—
49	C₂×C₃	C₂×#14581887	1	1	yes	characteristic
50	C₄	—	3	1	no	Sylow
51	C₃	—	889	1	no	—
52	C₃	—	1778	1	no	—
53	C₃	C₄×#14581887	1	1	yes	characteristic, complemented
54	C₂	D₃×#14581887	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#14581887
commutator, hypocenter	C₃×C₇×C₁₂₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₇×C₁₂₇	C₂×C₃
prime radical	C₂×C₃×#14581887	C₂
LCS	G ▷ C₃×C₇×C₁₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₃×C₁₂₇	C₃	semidirect
4. C₃×#14581887	C₄	semidirect
10. C₃×C₇×C₁₂₇	C₃×C₄	semidirect
12. #14581887	Dic₃	direct (N × H)
15. Dic₃×C₁₂₇	ΓL(1,𝔽₈)	semidirect
18. C₇×C₁₂₇	C₃×Dic₃	semidirect
23. C₃×C₁₂₇	C₄×ΓL(1,𝔽₈)	semidirect
28. C₁₂₇	Dic₃×ΓL(1,𝔽₈)	semidirect
30. C₇×Dic₃	C₁₂₇⋊C₃	semidirect
38. C₃×C₇	C₄×C₁₂₇⋊C₃	semidirect
44. Dic₃	#14581887	direct (N × H)
46. C₇	Dic₃×C₁₂₇⋊C₃	semidirect
53. C₃	C₄×#14581887	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#14581887	2
C₇×Dic₃×C₁₂₇	3
C₄×#14581887	3
Dic₃×C₁₂₇⋊C₃	7
Dic₃×ΓL(1,𝔽₈)	127

Subgroups — Dic3×#14581887 #44544751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×#14581887 #44544751