Subgroups — C₂²×#131 #3571

Order 128.

752 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×#131	C₂	1	24	yes	maximal, direct product factor
3	C₂²×M₁₆	C₂	1	3	yes	maximal, complemented
4	C₂³×C₈	C₂	1	3	yes	maximal, complemented
5	C₂×#41	C₄	1	12	yes	—
6	C₂×#41	C₂²	1	12	yes	—
7	C₂²×Q₈	C₄	1	1	yes	characteristic
8	C₂²×D₄	C₄	1	3	yes	—
9	C₂³×C₄	C₂²	1	3	yes	—
10	#131	C₂²	1	64	yes	direct product factor
11	C₂×M₁₆	C₂²	1	36	yes	complemented
12	C₂²×C₈	C₂²	1	3	yes	—
13	C₂²×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₈	C₂²	1	36	yes	complemented
15	C₂⁴	C₂×C₄	1	3	yes	—
16	#41	C₂×C₄	1	48	yes	—
17	#41	C₂³	1	16	yes	—
18	C₂×Q₈	C₂×C₄	1	12	yes	—
19	C₂×D₄	C₂×C₄	1	36	yes	—
20	C₂²×C₄	C₂×C₄	1	3	yes	—
21	C₂²×C₄	C₂×C₄	1	18	yes	—
22	C₂²×C₄	C₂³	1	1	yes	characteristic
23	C₂²×C₄	C₂³	1	18	yes	—
24	M₁₆	C₂³	1	48	yes	complemented
25	C₂×C₈	C₂³	1	18	yes	—
26	C₂×C₈	C₂³	1	6	yes	—
27	C₂×C₈	C₂³	1	48	yes	complemented
28	C₂³	—	2	12	no	—
29	C₂³	C₂²×C₄	1	18	yes	—
30	C₂³	C₂²×C₄	1	1	yes	characteristic
31	Q₈	C₂²×C₄	1	16	yes	—
32	D₄	C₂²×C₄	1	48	yes	—
33	C₂×C₄	C₂²×C₄	1	3	yes	—
34	C₂×C₄	C₂²×C₄	1	18	yes	—
35	C₂×C₄	C₂²×C₄	1	36	yes	—
36	C₂×C₄	C₂⁴	1	3	yes	—
37	C₂×C₄	C₂⁴	1	12	yes	—
38	C₈	C₂⁴	1	4	yes	—
39	C₈	C₂⁴	1	12	yes	—
40	C₂²	—	2	36	no	—
41	C₂²	#131	1	4	yes	direct product factor
42	C₂²	C₂³×C₄	1	12	yes	—
43	C₂²	C₂³×C₄	1	3	yes	—
44	C₄	C₂³×C₄	1	3	yes	—
45	C₄	C₂³×C₄	1	12	yes	—
46	C₄	C₂⁵	1	1	yes	characteristic
47	C₂	—	2	12	no	—
48	C₂	C₂×#131	1	6	yes	direct product factor
49	C₂	C₂⁴×C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²
commutator	C₂	C₂⁴×C₄
Frattini, cosocle	C₄	C₂⁵
socle	C₂³	C₂²×C₄
prime radical	C₂²×#41	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#131	C₂	direct (N × H)
3. C₂²×M₁₆	C₂	semidirect
4. C₂³×C₈	C₂	semidirect
10. #131	C₂²	direct (N × H)
11. C₂×M₁₆	C₂²	semidirect
14. C₂²×C₈	C₂²	semidirect
24. M₁₆	C₂³	semidirect
27. C₂×C₈	C₂³	semidirect
41. C₂²	#131	direct (N × H)
48. C₂	C₂×#131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#41	2
C₂×#131	2
C₂²×M₁₆	2
C₂³×C₈	2

Subgroups — C22×#131 #3571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#131 #3571