Subgroups — C₂×#1425 #13635

Order 256.

91 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#368	C₂	1	2	yes	maximal
3	#1425	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆	C₂²	1	1	yes	characteristic
5	C₂×#108	—	2	2	no	—
6	C₂×C₃₂	C₄	1	2	yes	—
7	C₂×C₃₂	C₄	1	2	yes	—
8	C₂×C₃₂	C₂²	1	2	yes	—
9	#368	—	2	2	no	—
10	#368	C₂²	1	4	yes	—
11	C₂×M₁₆	—	4	2	no	—
12	C₂²×C₈	D₄	1	1	yes	characteristic
13	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆	D₄	1	1	yes	characteristic
16	C₂×C₁₆	Q₈	1	1	yes	characteristic
17	C₂×C₁₆	Q₈	1	1	yes	characteristic
18	C₂×C₁₆	C₂³	1	1	yes	characteristic
19	#108	—	2	4	no	—
20	#108	—	4	2	no	—
21	C₃₂	C₂×C₄	1	4	yes	—
22	C₂²×C₄	D₈	1	1	yes	characteristic
23	M₁₆	—	4	4	no	—
24	M₁₆	—	8	2	no	—
25	C₂×C₈	—	8	2	no	—
26	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₈	D₈	1	1	yes	characteristic
29	C₂×C₈	Q₁₆	1	1	yes	characteristic
30	C₂×C₈	Q₁₆	1	1	yes	characteristic
31	C₂×C₈	C₂×D₄	1	1	yes	characteristic
32	C₁₆	C₄⋊C₄	1	1	yes	characteristic
33	C₁₆	C₄⋊C₄	1	1	yes	characteristic
34	C₁₆	C₂²×C₄	1	1	yes	characteristic
35	C₁₆	C₂×Q₈	1	1	yes	characteristic
36	C₂³	Q₃₂	1	1	yes	characteristic
37	C₂×C₄	#107	1	1	yes	characteristic
38	C₂×C₄	#107	1	1	yes	characteristic
39	C₂×C₄	D₁₆	1	1	yes	characteristic
40	C₂×C₄	D₁₆	1	1	yes	characteristic
41	C₂×C₄	Q₃₂	1	1	yes	characteristic
42	C₂×C₄	C₂×D₈	1	1	yes	characteristic
43	C₈	—	8	4	no	—
44	C₈	#107	1	1	yes	characteristic
45	C₈	#107	1	1	yes	characteristic
46	C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₈	C₂×Q₁₆	1	1	yes	characteristic
48	C₂²	—	2	2	no	—
49	C₂²	#366	1	1	yes	characteristic
50	C₂²	#366	1	1	yes	characteristic
51	C₂²	C₂×Q₃₂	1	1	yes	characteristic
52	C₄	#366	1	1	yes	characteristic
53	C₄	#366	1	1	yes	characteristic
54	C₄	C₂×#107	1	1	yes	characteristic
55	C₄	C₂×D₁₆	1	1	yes	characteristic
56	C₂	—	2	1	no	—
57	C₂	—	2	1	no	—
58	C₂	#1425	1	2	yes	direct product factor
59	C₂	C₂×#366	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₆
commutator	C₁₆	C₂²×C₄
Frattini, cosocle	C₂×C₁₆	C₂³
socle	C₂²	#366
prime radical	C₂³	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ G
LECS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #1425	C₂	direct (N × H)
58. C₂	#1425	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×C₃₂	2
C₂×#368	2
#1425	2

Subgroups — C2×#1425 #13635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1425 #13635