Subgroups — C₂×#1454 #17322

Order 256.

401 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#431	C₂	1	3	yes	maximal
2	#1454	C₂	1	8	yes	maximal, direct product factor
3	C₂×#322	C₂	1	3	yes	maximal, complemented
4	C₂×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄²	C₂²	1	1	yes	characteristic
6	#431	C₄	1	12	yes	—
7	#431	C₂²	1	12	yes	—
8	C₂×C₄⋊C₈	C₄	1	6	yes	—
9	C₂×C₂²⋊C₈	C₄	1	6	yes	—
10	C₂×C₄×C₈	C₂²	1	3	yes	—
11	C₂×C₄×C₈	C₂²	1	3	yes	—
12	#322	C₂²	1	12	yes	complemented
13	C₈²	C₂²	1	4	yes	complemented
14	C₂³×C₄	C₂×C₄	1	3	yes	—
15	C₂²×C₈	C₂×C₄	1	6	yes	—
16	C₂²×C₈	C₂×C₄	1	6	yes	—
17	C₂×C₄²	C₂×C₄	1	3	yes	—
18	C₂×C₄²	C₂×C₄	1	6	yes	—
19	C₂×C₄²	C₂³	1	2	yes	—
20	C₂×C₄²	C₂³	1	1	yes	characteristic
21	C₄⋊C₈	C₂×C₄	1	24	yes	—
22	C₂²⋊C₈	C₂×C₄	1	24	yes	—
23	C₄×C₈	C₂×C₄	1	6	yes	—
24	C₄×C₈	C₂×C₄	1	6	yes	—
25	C₄×C₈	C₂³	1	6	yes	—
26	C₄×C₈	C₂³	1	6	yes	—
27	C₂⁴	C₄²	1	1	yes	characteristic
28	C₂²×C₄	—	2	12	no	—
29	C₂²×C₄	C₄²	1	3	yes	—
30	C₂²×C₄	C₄²	1	6	yes	—
31	C₂²×C₄	C₂²×C₄	1	6	yes	—
32	C₂²×C₄	C₂²×C₄	1	3	yes	—
33	C₂×C₈	—	2	12	no	—
34	C₂×C₈	—	2	12	no	—
35	C₂×C₈	C₂²×C₄	1	12	yes	—
36	C₂×C₈	C₂²×C₄	1	12	yes	—
37	C₄²	C₄²	1	6	yes	—
38	C₄²	C₂²×C₄	1	3	yes	—
39	C₄²	C₂²×C₄	1	6	yes	—
40	C₄²	C₂⁴	1	1	yes	characteristic
41	C₂³	—	2	6	no	—
42	C₂³	C₂×C₄²	1	2	yes	—
43	C₂³	C₂×C₄²	1	1	yes	characteristic
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	2	12	no	—
46	C₂×C₄	—	2	12	no	—
47	C₂×C₄	C₂×C₄²	1	6	yes	—
48	C₂×C₄	C₂×C₄²	1	3	yes	—
49	C₂×C₄	#131	1	12	yes	—
50	C₂×C₄	C₂³×C₄	1	3	yes	—
51	C₈	—	2	12	no	—
52	C₈	—	2	12	no	—
53	C₂²	—	2	6	no	—
54	C₂²	—	4	4	no	—
55	C₂²	#405	1	6	yes	—
56	C₂²	C₂²×C₄²	1	1	yes	characteristic
57	C₄	—	2	6	no	—
58	C₄	#405	1	6	yes	—
59	C₄	C₂×#131	1	6	yes	—
60	C₂	—	4	2	no	—
61	C₂	#1454	1	4	yes	direct product factor
62	C₂	C₂×#405	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂³
commutator	C₂²	C₂²×C₄²
Frattini, cosocle	C₄²	C₂⁴
socle	C₂³	C₂×C₄²
prime radical	C₂⁴	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #1454	C₂	direct (N × H)
3. C₂×#322	C₂	semidirect
4. C₂×C₈²	C₂	semidirect
12. #322	C₂²	semidirect
13. C₈²	C₂²	semidirect
61. C₂	#1454	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×#431	2
#1454	2
C₂×#322	2
C₂×C₈²	2

Subgroups — C2×#1454 #17322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1454 #17322