Subgroups — C₂×#490 #3133

Order 128.

244 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×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	#490	C₂	1	8	yes	maximal, direct product factor
4	C₂×#102	C₂	1	4	yes	maximal, complemented
5	C₂×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄	—	2	2	no	—
7	C₂²×D₄	C₂²	1	2	yes	—
8	C₂²×C₈	C₂²	1	2	yes	—
9	#127	—	2	2	no	—
10	#127	C₂²	1	4	yes	—
11	#125	—	2	2	no	—
12	#125	C₂²	1	4	yes	complemented
13	C₂×C₄⋊C₄	—	2	2	no	—
14	C₂×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₄²	C₂²	1	1	yes	characteristic
16	#102	C₂²	1	16	yes	complemented
17	#97	C₂²	1	4	yes	complemented
18	C₂⁴	—	2	2	no	—
19	C₂×D₄	—	2	2	no	—
20	C₂×D₄	—	2	8	no	—
21	C₂×D₄	—	2	8	no	—
22	C₂×D₄	—	4	8	no	—
23	C₂×D₄	C₂³	1	4	yes	—
24	C₂²×C₄	—	2	2	no	—
25	C₂²×C₄	D₄	1	2	yes	—
26	C₂²×C₄	C₂³	1	1	yes	characteristic
27	C₂×C₈	—	2	4	no	—
28	C₂×C₈	C₂³	1	4	yes	—
29	C₄⋊C₄	—	2	8	no	—
30	C₄⋊C₄	—	2	2	no	—
31	C₄⋊C₄	C₂³	1	4	yes	—
32	C₄²	D₄	1	2	yes	—
33	C₄²	C₂³	1	2	yes	—
34	C₂³	—	2	4	no	—
35	C₂³	—	4	4	no	—
36	C₂³	—	4	8	no	—
37	C₂³	C₂×D₄	1	1	yes	characteristic
38	D₄	—	2	8	no	—
39	D₄	—	4	16	no	—
40	D₄	—	4	4	no	—
41	C₂×C₄	—	2	4	no	—
42	C₂×C₄	—	2	4	no	—
43	C₂×C₄	—	4	4	no	—
44	C₂×C₄	C₂×D₄	1	4	yes	—
45	C₂×C₄	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄	#41	1	4	yes	—
47	C₂×C₄	C₂⁴	1	1	yes	characteristic
48	C₈	—	2	4	no	—
49	C₂²	—	4	4	no	—
50	C₂²	—	4	8	no	—
51	C₂²	—	8	8	no	—
52	C₂²	#124	1	2	yes	—
53	C₂²	AGL(1,ℤ/8)	1	4	yes	—
54	C₂²	C₂²×D₄	1	1	yes	characteristic
55	C₄	—	2	4	no	—
56	C₄	—	4	4	no	—
57	C₄	#124	1	2	yes	—
58	C₄	C₂×#41	1	2	yes	—
59	C₂	—	8	4	no	—
60	C₂	#490	1	4	yes	direct product factor
61	C₂	C₂×#124	1	1	yes	characteristic
62	C₂	C₂×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
prime radical	C₂×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#125	C₂	semidirect
3. #490	C₂	direct (N × H)
4. C₂×#102	C₂	semidirect
5. C₂×#97	C₂	semidirect
12. #125	C₂²	semidirect
16. #102	C₂²	semidirect
17. #97	C₂²	semidirect
60. C₂	#490	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×#125	2
#490	2
C₂×#102	2
C₂×#97	2

Subgroups — C2×#490 #3133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#490 #3133