Subgroups — C₂×#1424 #13632

Order 256.

103 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×#366	C₂	1	2	yes	maximal
3	#1424	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆	C₂²	1	1	yes	characteristic
5	C₂×#107	—	2	2	no	—
6	C₂×C₃₂	C₄	1	4	yes	complemented
7	C₂×C₃₂	C₂²	1	2	yes	—
8	#366	—	2	2	no	—
9	#366	C₂²	1	4	yes	—
10	C₂²×C₈	D₄	1	1	yes	characteristic
11	C₂×C₄⋊C₄	—	4	2	no	—
12	C₂×C₁₆	C₂×C₄	1	2	yes	—
13	C₂×C₁₆	D₄	1	1	yes	characteristic
14	C₂×C₁₆	Q₈	1	2	yes	—
15	C₂×C₁₆	C₂³	1	1	yes	characteristic
16	#107	—	2	4	no	—
17	#107	—	4	2	no	—
18	C₃₂	C₂×C₄	1	4	yes	complemented
19	C₂²×C₄	—	8	2	no	—
20	C₂²×C₄	D₈	1	1	yes	characteristic
21	C₂×C₈	C₄⋊C₄	1	2	yes	—
22	C₂×C₈	D₈	1	1	yes	characteristic
23	C₂×C₈	Q₁₆	1	2	yes	—
24	C₂×C₈	C₂×D₄	1	1	yes	characteristic
25	C₄⋊C₄	—	4	4	no	—
26	C₄⋊C₄	—	8	2	no	—
27	C₁₆	C₄⋊C₄	1	2	yes	—
28	C₁₆	C₂²×C₄	1	1	yes	characteristic
29	C₁₆	C₂×Q₈	1	1	yes	characteristic
30	C₂³	D₁₆	1	1	yes	characteristic
31	C₂×C₄	—	8	4	no	—
32	C₂×C₄	—	16	4	no	—
33	C₂×C₄	#107	1	2	yes	—
34	C₂×C₄	D₁₆	1	1	yes	characteristic
35	C₂×C₄	Q₃₂	1	2	yes	—
36	C₂×C₄	C₂×D₈	1	1	yes	characteristic
37	C₈	#107	1	2	yes	—
38	C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₈	C₂×Q₁₆	1	1	yes	characteristic
40	C₂²	#366	1	2	yes	—
41	C₂²	SD₆₄	1	4	yes	—
42	C₂²	C₂×D₁₆	1	1	yes	characteristic
43	C₄	—	16	4	no	—
44	C₄	#366	1	2	yes	—
45	C₄	C₂×#107	1	1	yes	characteristic
46	C₄	C₂×Q₃₂	1	1	yes	characteristic
47	C₂	#1424	1	4	yes	direct product factor
48	C₂	C₂×#366	1	1	yes	characteristic
49	C₂	C₂×SD₆₄	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³	D₁₆
commutator	C₁₆	C₂²×C₄
Frattini, cosocle	C₂×C₁₆	C₂³
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ 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. #1424	C₂	direct (N × H)
6. C₂×C₃₂	C₄	semidirect
18. C₃₂	C₂×C₄	semidirect
47. C₂	#1424	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×#366	2
#1424	2

Subgroups — C2×#1424 #13632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1424 #13632