Subgroups — C₄×M₃₂ #2107

Order 128.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#346	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₆	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈	C₄	1	1	yes	characteristic
6	C₂²×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄²	C₄	1	1	yes	characteristic
8	M₃₂	C₄	1	8	yes	direct product factor
9	C₂×C₁₆	C₂²	1	4	yes	—
10	C₄×C₈	C₄	1	1	yes	characteristic
11	C₄×C₈	C₄	1	1	yes	characteristic
12	C₄×C₈	C₂²	1	1	yes	characteristic
13	C₄×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₄	C₈	1	2	yes	—
15	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈	C₈	1	4	yes	—
17	C₂×C₈	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈	C₂×C₄	1	4	yes	—
19	C₂×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈	C₂³	1	1	yes	characteristic
22	C₄²	C₈	1	2	yes	—
23	C₄²	C₂×C₄	1	1	yes	characteristic
24	C₄²	C₂×C₄	1	1	yes	characteristic
25	C₁₆	C₂×C₄	1	8	yes	complemented
26	C₂³	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄	—	2	4	no	—
28	C₂×C₄	C₄²	1	2	yes	—
29	C₂×C₄	C₂×C₈	1	2	yes	—
30	C₂×C₄	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄	C₂×C₈	1	2	yes	—
32	C₂×C₄	C₂×C₈	1	2	yes	—
33	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
34	C₈	C₄²	1	2	yes	—
35	C₈	C₂×C₈	1	2	yes	—
36	C₈	C₂×C₈	1	2	yes	—
37	C₈	C₂²×C₄	1	2	yes	—
38	C₂²	—	2	2	no	—
39	C₂²	C₄×C₈	1	2	yes	—
40	C₂²	C₂²×C₈	1	1	yes	characteristic
41	C₄	—	2	2	no	—
42	C₄	C₄×C₈	1	2	yes	—
43	C₄	M₃₂	1	4	yes	direct product factor
44	C₄	C₂×C₄²	1	1	yes	characteristic
45	C₄	C₂²×C₈	1	1	yes	characteristic
46	C₂	—	2	2	no	—
47	C₂	C₂×C₄×C₈	1	1	yes	characteristic
48	C₂	C₂×M₃₂	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂²
commutator	C₂	C₂×C₄×C₈
Frattini, cosocle	C₂×C₈	C₂³
socle	C₂²	C₂²×C₈
prime radical	C₂³	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #346	C₂	semidirect
4. C₄×C₁₆	C₂	semidirect
8. M₃₂	C₄	direct (N × H)
25. C₁₆	C₂×C₄	semidirect
43. C₄	M₃₂	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×M₃₂	2
C₂×C₄×C₈	2
#346	2
C₄×C₁₆	2

Subgroups — C4×M32 #2107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×M₃₂ #2107