Subgroups — C₂²⋊#1088 #88632

Order 432.

115 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#272	C₂	1	1	yes	maximal, characteristic
2	C₂×#1088	C₂	1	2	yes	maximal, complemented
3	C₂²×H(3,𝔽₃)	C₄	1	1	yes	characteristic, complemented
4	C₂×#272	—	2	2	no	—
5	C₂×#272	C₄	1	1	yes	characteristic, complemented
6	C₂×#272	C₂²	1	1	yes	characteristic
7	#1088	—	2	2	no	—
8	C₂²×C₃×D₃	—	6	2	no	—
9	C₂×H(3,𝔽₃)	—	2	1	no	—
10	C₂×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
11	#272	—	2	1	no	—
12	#272	D₄	1	2	yes	—
13	C₃×C₂²⋊C₄	—	9	1	no	maximal
14	C₂²×C₃²	—	2	2	no	—
15	C₂×C₃×D₃	—	6	2	no	—
16	C₂×C₃×D₃	—	6	2	no	—
17	C₂×C₃×D₃	—	6	8	no	—
18	H(3,𝔽₃)	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₃	—	9	1	no	—
20	C₂²×D₃	—	6	2	no	—
21	C₂×C₃×C₄	—	9	2	no	—
22	C₂×C₃²	—	2	4	no	—
23	C₂×C₃²	—	2	2	no	—
24	C₃×D₃	—	6	4	no	—
25	C₃×D₃	—	6	4	no	—
26	C₂²⋊C₄	—	9	1	no	Sylow
27	C₂²×C₃	—	6	2	no	—
28	C₂²×C₃	—	9	1	no	—
29	C₂²×C₃	—	9	1	no	—
30	C₂²×C₃	—	18	2	no	—
31	C₂²×C₃	#157	1	1	yes	characteristic
32	C₂×D₃	—	6	2	no	—
33	C₂×D₃	—	6	2	no	—
34	C₂×D₃	—	6	8	no	—
35	C₃×C₄	—	18	2	no	—
36	C₃²	—	2	2	no	—
37	C₂³	—	9	1	no	—
38	C₂×C₄	—	9	2	no	—
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	—	6	4	no	—
41	C₂×C₃	—	6	2	no	—
42	C₂×C₃	—	9	2	no	—
43	C₂×C₃	—	18	1	no	—
44	C₂×C₃	C₂×#157	1	1	yes	characteristic
45	D₃	—	6	4	no	—
46	D₃	—	6	4	no	—
47	C₂²	—	9	1	no	—
48	C₂²	—	9	1	no	—
49	C₂²	—	18	2	no	—
50	C₂²	#1088	1	1	yes	characteristic, complemented
51	C₄	—	18	2	no	—
52	C₃	—	6	2	no	—
53	C₃	C₂²⋊#157	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	9	2	no	—
56	C₂	—	18	1	no	—
57	C₂	C₂×#1088	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, socle	C₂×C₃	C₂×#157
commutator	C₂×H(3,𝔽₃)	C₂×C₄
Fitting	C₂²×H(3,𝔽₃)	C₄
prime radical	C₂²×#272	C₂
cosocle	C₂×#272	C₂²
hypercenter	C₂²×C₃	#157
hypocenter	H(3,𝔽₃)	C₂²⋊C₄
LCS	G ▷ C₂×H(3,𝔽₃) ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
2. C₂×#1088	C₂	semidirect
3. C₂²×H(3,𝔽₃)	C₄	semidirect
5. C₂×#272	C₄	semidirect
18. H(3,𝔽₃)	C₂²⋊C₄	semidirect
50. C₂²	#1088	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#272	2
C₂×#1088	2
C₃×C₂²⋊C₄	9

Subgroups — C22⋊#1088 #88632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#1088 #88632