Subgroups — C₂×#1839 #20770

Order 256.

567 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄³	C₂	1	1	yes	maximal, characteristic
2	#1839	C₂	1	8	yes	maximal, direct product factor
3	C₂×#336	C₂	1	6	yes	maximal
4	C₂³×C₈	C₂²	1	4	yes	—
5	C₂²×C₄²	C₄	1	3	yes	—
6	C₂²×C₄²	C₄	1	1	yes	characteristic
7	C₂²×C₄²	C₂²	1	3	yes	—
8	C₄³	C₄	1	4	yes	—
9	C₄³	C₂²	1	4	yes	—
10	#336	C₂²	1	24	yes	—
11	C₂³×C₄	C₂×C₄	1	3	yes	—
12	C₂³×C₄	C₂×C₄	1	3	yes	—
13	C₂³×C₄	C₂³	1	1	yes	characteristic
14	C₂²×C₈	—	2	24	no	—
15	C₂²×C₈	C₂³	1	8	yes	—
16	C₂×C₄²	—	2	12	no	—
17	C₂×C₄²	—	2	12	no	—
18	C₂×C₄²	C₈	1	8	yes	complemented
19	C₂×C₄²	C₂×C₄	1	6	yes	—
20	C₂×C₄²	C₂×C₄	1	12	yes	—
21	C₂×C₄²	C₂×C₄	1	4	yes	—
22	C₂×C₄²	C₂³	1	6	yes	—
23	C₂⁴	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₄	—	2	6	no	—
25	C₂²×C₄	—	2	6	no	—
26	C₂²×C₄	—	2	6	no	—
27	C₂²×C₄	—	2	6	no	—
28	C₂²×C₄	C₂×C₈	1	12	yes	—
29	C₂²×C₄	M₁₆	1	12	yes	—
30	C₂²×C₄	C₂²×C₄	1	6	yes	—
31	C₂²×C₄	C₂²×C₄	1	6	yes	—
32	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄	#41	1	12	yes	—
34	C₂²×C₄	C₂⁴	1	1	yes	characteristic
35	C₂×C₈	—	2	24	no	—
36	C₂×C₈	—	4	16	no	—
37	C₄²	—	2	12	no	—
38	C₄²	—	2	24	no	—
39	C₄²	—	2	12	no	—
40	C₄²	C₂×C₈	1	16	yes	complemented
41	C₂³	#117	1	6	yes	—
42	C₂³	C₂²×C₈	1	2	yes	—
43	C₂³	C₂×M₁₆	1	6	yes	—
44	C₂³	C₂³×C₄	1	1	yes	characteristic
45	C₂×C₄	—	2	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	—	2	6	no	—
48	C₂×C₄	—	2	6	no	—
49	C₂×C₄	—	2	24	no	—
50	C₂×C₄	—	2	24	no	—
51	C₂×C₄	#117	1	6	yes	—
52	C₂×C₄	#126	1	16	yes	—
53	C₂×C₄	C₂²×C₈	1	12	yes	—
54	C₂×C₄	C₂×M₁₆	1	12	yes	—
55	C₂×C₄	C₂×#41	1	6	yes	—
56	C₈	—	4	8	no	—
57	C₂²	#383	1	4	yes	—
58	C₂²	#431	1	12	yes	—
59	C₂²	#432	1	12	yes	—
60	C₂²	C₂×#117	1	3	yes	—
61	C₂²	C₂³×C₈	1	1	yes	characteristic
62	C₂²	C₂²×M₁₆	1	3	yes	—
63	C₄	—	2	12	no	—
64	C₄	—	2	12	no	—
65	C₄	#383	1	4	yes	—
66	C₄	C₂×#126	1	4	yes	—
67	C₂	#1839	1	8	yes	direct product factor
68	C₂	C₂×#383	1	1	yes	characteristic
69	C₂	C₂×#431	1	3	yes	—
70	C₂	C₂×#432	1	3	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂³
commutator	C₂²	C₂³×C₈
Frattini, cosocle	C₂²×C₄	C₂⁴
socle, prime radical	C₂⁴	C₂²×C₄
LCS	G ▷ C₂² ▷ 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
2. #1839	C₂	direct (N × H)
18. C₂×C₄²	C₈	semidirect
40. C₄²	C₂×C₈	semidirect
67. C₂	#1839	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×C₄³	2
#1839	2
C₂×#336	2

Subgroups — C2×#1839 #20770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1839 #20770