Subgroups — C₂×#1273 #7847

Order 256.

491 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈	C₂	1	3	yes	maximal
2	#1273	C₂	1	4	yes	maximal, direct product factor
3	C₂³×C₈	C₄	1	6	yes	—
4	C₂²×C₄²	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₈	—	2	12	no	—
6	C₂×C₄×C₈	C₄	1	6	yes	—
7	C₂×C₄×C₈	C₂²	1	6	yes	—
8	C₂³×C₄	C₂×C₄	1	3	yes	—
9	C₂²×C₈	—	2	12	no	—
10	C₂²×C₈	—	2	12	no	—
11	C₂²×C₈	C₈	1	24	yes	complemented
12	C₂²×C₈	C₂×C₄	1	12	yes	—
13	C₂×C₄²	C₂×C₄	1	3	yes	—
14	C₂×C₄²	D₄	1	6	yes	—
15	C₂×C₄²	Q₈	1	2	yes	—
16	C₂×C₄²	C₂³	1	1	yes	characteristic
17	C₄×C₈	—	2	12	no	—
18	C₄×C₈	—	2	12	no	—
19	C₂⁴	C₄²	1	1	yes	characteristic
20	C₂²×C₄	C₄²	1	3	yes	—
21	C₂²×C₄	C₂²⋊C₄	1	6	yes	—
22	C₂²×C₄	C₄⋊C₄	1	6	yes	—
23	C₂²×C₄	C₂×C₈	1	12	yes	—
24	C₂²×C₄	M₁₆	1	12	yes	—
25	C₂²×C₄	C₂²×C₄	1	3	yes	—
26	C₂×C₈	—	2	48	no	—
27	C₂×C₈	—	2	12	no	—
28	C₂×C₈	—	2	12	no	—
29	C₂×C₈	C₂×C₈	1	24	yes	complemented
30	C₄²	C₂²⋊C₄	1	6	yes	—
31	C₄²	C₄⋊C₄	1	6	yes	—
32	C₄²	C₂×D₄	1	3	yes	—
33	C₄²	C₂×Q₈	1	1	yes	characteristic
34	C₂³	#95	1	2	yes	—
35	C₂³	C₄×C₈	1	6	yes	—
36	C₂³	#97	1	6	yes	—
37	C₂³	C₂×C₄²	1	1	yes	characteristic
38	C₂×C₄	#95	1	6	yes	—
39	C₂×C₄	C₄×C₈	1	6	yes	—
40	C₂×C₄	#97	1	6	yes	—
41	C₂×C₄	C₂²⋊C₈	1	24	yes	—
42	C₂×C₄	C₄⋊C₈	1	24	yes	—
43	C₂×C₄	C₂×C₂²⋊C₄	1	3	yes	—
44	C₂×C₄	C₂×C₄⋊C₄	1	3	yes	—
45	C₂×C₄	C₂²×C₈	1	6	yes	—
46	C₂×C₄	C₂×M₁₆	1	6	yes	—
47	C₈	—	2	24	no	—
48	C₂²	C₈²	1	4	yes	—
49	C₂²	#322	1	12	yes	—
50	C₂²	#336	1	12	yes	—
51	C₂²	C₂×#95	1	1	yes	characteristic
52	C₂²	C₂×C₄×C₈	1	3	yes	—
53	C₂²	C₂×#97	1	3	yes	—
54	C₄	#336	1	12	yes	—
55	C₄	C₂×C₂²⋊C₈	1	6	yes	—
56	C₄	C₂×C₄⋊C₈	1	6	yes	—
57	C₂	#1273	1	8	yes	direct product factor
58	C₂	C₂×C₈²	1	1	yes	characteristic
59	C₂	C₂×#322	1	3	yes	—
60	C₂	C₂×#336	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂²
commutator	C₂	C₂×C₈²
Frattini, cosocle	C₂×C₄²	C₂³
socle, prime radical	C₂⁴	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #1273	C₂	direct (N × H)
11. C₂²×C₈	C₈	semidirect
29. C₂×C₈	C₂×C₈	semidirect
57. C₂	#1273	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×C₄×C₈	2
#1273	2

Subgroups — C2×#1273 #7847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1273 #7847