Subgroups — C₄×2₋¹⁺⁴ #3430

Order 128.

746 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	#520	C₂	1	10	yes	maximal, complemented
3	#519	C₂	1	5	yes	maximal, complemented
4	C₄×#41	C₂	1	10	yes	maximal, complemented
5	C₂×C₄×Q₈	C₂	1	5	yes	maximal, complemented
6	2₋¹⁺⁴	C₄	1	16	yes	direct product factor
7	C₂×#41	C₂²	1	10	yes	—
8	C₂²×Q₈	C₂²	1	5	yes	—
9	C₄×Q₈	C₂²	1	10	yes	—
10	C₄×Q₈	C₂²	1	20	yes	—
11	C₄×Q₈	C₂²	1	10	yes	—
12	C₄×D₄	C₂²	1	10	yes	—
13	C₄×D₄	C₂²	1	30	yes	—
14	#117	C₂²	1	30	yes	—
15	C₂×C₄⋊C₄	C₂²	1	15	yes	—
16	C₂×C₄²	C₂²	1	15	yes	—
17	#41	C₂×C₄	1	80	yes	complemented
18	C₂×Q₈	C₂×C₄	1	40	yes	complemented
19	C₂×Q₈	C₂³	1	10	yes	—
20	C₂×D₄	C₂³	1	10	yes	—
21	C₂²×C₄	C₂³	1	5	yes	—
22	C₂²×C₄	C₂³	1	15	yes	—
23	C₂²×C₄	C₂³	1	15	yes	—
24	C₄⋊C₄	C₂³	1	30	yes	—
25	C₄⋊C₄	C₂³	1	10	yes	—
26	C₂²⋊C₄	C₂³	1	20	yes	—
27	C₄²	C₂³	1	30	yes	—
28	C₄²	C₂³	1	10	yes	—
29	C₂³	C₂⁴	1	5	yes	—
30	Q₈	C₂²×C₄	1	40	yes	—
31	D₄	C₂²×C₄	1	40	yes	—
32	C₂×C₄	—	2	10	no	—
33	C₂×C₄	—	4	15	no	—
34	C₂×C₄	C₂²×C₄	1	60	yes	—
35	C₂×C₄	C₂⁴	1	5	yes	—
36	C₂×C₄	C₂⁴	1	10	yes	—
37	C₂×C₄	C₂⁴	1	10	yes	—
38	C₂×C₄	C₂⁴	1	1	yes	characteristic
39	C₂²	—	2	5	no	—
40	C₂²	—	2	5	no	—
41	C₂²	C₂³×C₄	1	10	yes	—
42	C₂²	C₂⁵	1	1	yes	characteristic
43	C₄	—	2	5	no	—
44	C₄	—	2	10	no	—
45	C₄	C₂³×C₄	1	20	yes	—
46	C₄	2₋¹⁺⁴	1	2	yes	direct product factor
47	C₂	—	2	10	no	—
48	C₂	C₂⁴×C₄	1	1	yes	characteristic
49	C₂	C₂×2₋¹⁺⁴	1	1	yes	characteristic
50	C₂	#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴
commutator	C₂	C₂⁴×C₄
Frattini, socle, cosocle	C₂²	C₂⁵
prime radical	C₂×2₋¹⁺⁴	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #520	C₂	semidirect
3. #519	C₂	semidirect
4. C₄×#41	C₂	semidirect
5. C₂×C₄×Q₈	C₂	semidirect
6. 2₋¹⁺⁴	C₄	direct (N × H)
17. #41	C₂×C₄	semidirect
18. C₂×Q₈	C₂×C₄	semidirect
46. C₄	2₋¹⁺⁴	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×2₋¹⁺⁴	2
#520	2
#519	2
C₄×#41	2
C₂×C₄×Q₈	2

Subgroups — C4×2−1+4 #3430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×2₋¹⁺⁴ #3430