Subgroups — C₂×#1843 #20790

Order 256.

615 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈	C₂	1	6	yes	maximal
2	C₂×#376	C₂	1	1	yes	maximal, characteristic
3	#1843	C₂	1	8	yes	maximal, direct product factor
4	C₂³×C₈	C₂²	1	4	yes	—
5	C₂²×C₄²	C₂²	1	3	yes	—
6	C₂×C₄⋊C₈	—	2	24	no	—
7	C₂×C₄⋊C₈	C₂²	1	24	yes	—
8	#376	C₄	1	4	yes	—
9	#376	C₂²	1	4	yes	—
10	C₂×#95	C₄	1	4	yes	—
11	C₂³×C₄	C₂×C₄	1	6	yes	—
12	C₂³×C₄	C₂³	1	1	yes	characteristic
13	C₂²×C₈	—	2	24	no	—
14	C₂²×C₈	C₂³	1	8	yes	—
15	C₂×C₄²	C₂×C₄	1	6	yes	—
16	C₂×C₄²	D₄	1	12	yes	—
17	C₂×C₄²	Q₈	1	12	yes	—
18	C₂×C₄²	C₂³	1	6	yes	—
19	C₄⋊C₈	—	2	48	no	—
20	#95	C₂×C₄	1	16	yes	—
21	C₂⁴	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄	—	2	24	no	—
23	C₂²×C₄	C₄⋊C₄	1	24	yes	—
24	C₂²×C₄	C₂²×C₄	1	12	yes	—
25	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄	C₂×D₄	1	6	yes	—
27	C₂²×C₄	C₂×Q₈	1	6	yes	—
28	C₂²×C₄	C₂⁴	1	1	yes	characteristic
29	C₂×C₈	—	2	24	no	—
30	C₂×C₈	—	4	16	no	—
31	C₄²	C₄⋊C₄	1	24	yes	—
32	C₄²	C₂×D₄	1	12	yes	—
33	C₄²	C₂×Q₈	1	12	yes	—
34	C₂³	C₂×C₄⋊C₄	1	6	yes	—
35	C₂³	#131	1	8	yes	—
36	C₂³	C₂³×C₄	1	1	yes	characteristic
37	C₂×C₄	—	2	24	no	—
38	C₂×C₄	—	2	48	no	—
39	C₂×C₄	C₂×C₄⋊C₄	1	24	yes	—
40	C₂×C₄	C₂×C₄⋊C₄	1	6	yes	—
41	C₂×C₄	#127	1	4	yes	—
42	C₂×C₄	C₄⋊Q₈	1	12	yes	—
43	C₂×C₄	C₂²×D₄	1	3	yes	—
44	C₂×C₄	C₂²×Q₈	1	3	yes	—
45	C₈	—	4	8	no	—
46	C₂²	#384	1	4	yes	—
47	C₂²	#424	1	24	yes	—
48	C₂²	C₂²×C₄⋊C₄	1	3	yes	—
49	C₂²	C₂×#131	1	4	yes	—
50	C₄	—	2	24	no	—
51	C₄	#384	1	4	yes	—
52	C₄	C₂×#127	1	1	yes	characteristic
53	C₄	C₂×C₄⋊Q₈	1	3	yes	—
54	C₂	#1843	1	8	yes	direct product factor
55	C₂	C₂×#384	1	1	yes	characteristic
56	C₂	C₂×#424	1	6	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂³
commutator	C₂³	C₂³×C₄
Frattini, cosocle	C₂²×C₄	C₂⁴
socle, prime radical	C₂⁴	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #1843	C₂	direct (N × H)
54. C₂	#1843	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
C₂×#376	2
#1843	2

Subgroups — C2×#1843 #20790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1843 #20790