Subgroups — C₂×#6229 #88737

Order 432.

209 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×#1084	C₂	1	2	yes	maximal
3	#6229	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×Dic₆	—	3	4	no	maximal
5	C₂²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₄×H(3,𝔽₃)	C₂²	1	2	yes	—
7	#1084	C₂²	1	4	yes	—
8	C₂×C₃²×C₄	D₃	1	4	yes	—
9	C₂×C₃×Dic₃	—	3	8	no	—
10	C₃×Dic₆	—	3	16	no	—
11	C₂×H(3,𝔽₃)	Q₈	1	2	yes	complemented
12	C₂×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
13	C₂×C₃×Q₈	—	9	1	no	—
14	C₂×Dic₆	—	3	4	no	—
15	C₂²×C₃²	C₂×D₃	1	4	yes	—
16	C₃²×C₄	C₂×D₃	1	8	yes	—
17	C₃×Dic₃	—	3	16	no	—
18	H(3,𝔽₃)	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
19	C₃×Q₈	—	9	4	no	—
20	C₂×C₃×C₄	—	3	4	no	—
21	C₂×C₃×C₄	—	9	2	no	—
22	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
23	C₂×Dic₃	—	3	8	no	—
24	Dic₆	—	3	16	no	—
25	C₂×C₃²	Dic₆	1	8	yes	complemented
26	C₂×C₃²	C₂²×D₃	1	4	yes	—
27	C₂×Q₈	—	9	1	no	Sylow
28	C₂²×C₃	—	3	4	no	—
29	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
30	C₃×C₄	—	3	8	no	—
31	C₃×C₄	—	9	4	no	—
32	C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
33	Dic₃	—	3	16	no	—
34	C₃²	C₂×Dic₆	1	4	yes	complemented
35	Q₈	—	9	4	no	—
36	C₂×C₄	—	9	2	no	—
37	C₂×C₄	#272	1	1	yes	characteristic
38	C₂×C₃	—	3	8	no	—
39	C₂×C₃	—	3	4	no	—
40	C₂×C₃	#634	1	2	yes	—
41	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
42	C₂²	C₂×#272	1	1	yes	characteristic
43	C₄	—	9	4	no	—
44	C₄	C₂×#272	1	2	yes	—
45	C₃	—	3	4	no	—
46	C₃	C₂×#634	1	1	yes	characteristic
47	C₂	#6229	1	2	yes	direct product factor
48	C₂	C₂²×#272	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×C₃⋊D₃
commutator, cosocle	C₂×H(3,𝔽₃)	C₂³
Frattini	C₂×C₃	C₂²×C₃⋊D₃
Fitting	C₂×C₄×H(3,𝔽₃)	C₂
prime radical	C₂²×H(3,𝔽₃)	C₂²
hypercenter	C₂×C₃×C₄	C₃⋊D₃
hypocenter	H(3,𝔽₃)	C₂×Q₈
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #6229	C₂	direct (N × H)
11. C₂×H(3,𝔽₃)	Q₈	semidirect
18. H(3,𝔽₃)	C₂×Q₈	semidirect
25. C₂×C₃²	Dic₆	semidirect
34. C₃²	C₂×Dic₆	semidirect
47. C₂	#6229	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×H(3,𝔽₃)	2
C₂×#1084	2
#6229	2
C₂×C₃×Dic₆	3

Subgroups — C2×#6229 #88737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6229 #88737