Subgroups — C₄×#127 #2306

Order 128.

462 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄	C₂	1	6	yes	maximal, complemented
3	#390	C₂	1	6	yes	maximal, complemented
4	#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄³	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄	C₂²	1	6	yes	—
7	C₂³×C₄	C₂²	1	4	yes	—
8	#127	C₄	1	8	yes	direct product factor
9	C₄×D₄	—	2	24	no	—
10	C₂×C₄⋊C₄	C₂²	1	6	yes	—
11	C₂×C₂²⋊C₄	C₂²	1	12	yes	—
12	C₂×C₄²	C₂²	1	3	yes	—
13	C₂×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₄²	C₂²	1	3	yes	—
15	C₂⁴	C₂³	1	4	yes	—
16	C₂×D₄	—	2	12	no	—
17	C₂×D₄	—	2	12	no	—
18	C₂×D₄	C₂×C₄	1	24	yes	complemented
19	C₂²×C₄	—	2	24	no	—
20	C₂²×C₄	C₂³	1	4	yes	—
21	C₂²×C₄	C₂³	1	3	yes	—
22	C₂²×C₄	C₂³	1	3	yes	—
23	C₂²×C₄	C₂³	1	1	yes	characteristic
24	C₄⋊C₄	—	2	12	no	—
25	C₂²⋊C₄	—	2	24	no	—
26	C₄²	—	2	6	no	—
27	C₄²	C₂×C₄	1	4	yes	complemented
28	C₄²	D₄	1	12	yes	complemented
29	C₂³	—	2	12	no	—
30	C₂³	—	2	12	no	—
31	C₂³	C₂²×C₄	1	8	yes	—
32	C₂³	C₂⁴	1	1	yes	characteristic
33	D₄	—	2	48	no	—
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	—	2	12	no	—
36	C₂×C₄	—	4	16	no	—
37	C₂×C₄	C₂²×C₄	1	6	yes	—
38	C₂×C₄	C₂×D₄	1	6	yes	—
39	C₂×C₄	C₂×D₄	1	6	yes	—
40	C₂×C₄	C₂×D₄	1	6	yes	—
41	C₂×C₄	#41	1	6	yes	—
42	C₂²	—	2	24	no	—
43	C₂²	—	4	4	no	—
44	C₂²	—	4	12	no	—
45	C₂²	C₂³×C₄	1	1	yes	characteristic
46	C₂²	C₂²×D₄	1	3	yes	—
47	C₂²	C₂×#41	1	3	yes	—
48	C₄	—	2	6	no	—
49	C₄	—	4	4	no	—
50	C₄	C₄×D₄	1	12	yes	complemented
51	C₄	#127	1	4	yes	direct product factor
52	C₂	—	4	8	no	—
53	C₂	C₂×C₄×D₄	1	3	yes	—
54	C₂	C₂×#127	1	1	yes	characteristic
55	C₂	#532	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³
commutator	C₂²	C₂³×C₄
Frattini, socle, cosocle	C₂³	C₂⁴
prime radical	C₂×#127	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄	C₂	semidirect
3. #390	C₂	semidirect
4. #384	C₂	semidirect
5. C₄³	C₂	semidirect
8. #127	C₄	direct (N × H)
18. C₂×D₄	C₂×C₄	semidirect
27. C₄²	C₂×C₄	semidirect
28. C₄²	D₄	semidirect
50. C₄	C₄×D₄	semidirect
51. C₄	#127	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×#127	2
C₂×C₄×D₄	2
#390	2
#384	2
C₄³	2

Subgroups — C4×#127 #2306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#127 #2306