Subgroups — C₂×#1842 #20789

Order 256.

735 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×C₄³	C₂	1	1	yes	maximal, characteristic
3	#1842	C₂	1	8	yes	maximal, direct product factor
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	C₂×C₄⋊C₈	—	2	24	no	—
9	C₂×C₄⋊C₈	C₂²	1	24	yes	—
10	C₄³	C₄	1	4	yes	—
11	C₄³	C₂²	1	4	yes	—
12	C₂³×C₄	C₂×C₄	1	3	yes	—
13	C₂³×C₄	C₂×C₄	1	3	yes	—
14	C₂³×C₄	C₂³	1	1	yes	characteristic
15	C₂²×C₈	—	2	24	no	—
16	C₂²×C₈	C₂³	1	8	yes	—
17	C₂×C₄²	—	2	12	no	—
18	C₂×C₄²	C₈	1	8	yes	complemented
19	C₂×C₄²	C₂×C₄	1	12	yes	—
20	C₂×C₄²	C₂×C₄	1	6	yes	—
21	C₂×C₄²	C₂×C₄	1	4	yes	—
22	C₂×C₄²	D₄	1	12	yes	—
23	C₂×C₄²	Q₈	1	12	yes	—
24	C₂×C₄²	C₂³	1	6	yes	—
25	C₄⋊C₈	—	2	48	no	—
26	C₂⁴	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄	—	2	12	no	—
28	C₂²×C₄	C₄⋊C₄	1	12	yes	—
29	C₂²×C₄	C₄⋊C₄	1	12	yes	—
30	C₂²×C₄	C₂×C₈	1	12	yes	—
31	C₂²×C₄	M₁₆	1	12	yes	—
32	C₂²×C₄	C₂²×C₄	1	6	yes	—
33	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄	C₂²×C₄	1	6	yes	—
35	C₂²×C₄	C₂×D₄	1	6	yes	—
36	C₂²×C₄	C₂×Q₈	1	6	yes	—
37	C₂²×C₄	C₂⁴	1	1	yes	characteristic
38	C₂×C₈	—	2	24	no	—
39	C₂×C₈	—	4	16	no	—
40	C₄²	—	2	24	no	—
41	C₄²	C₄⋊C₄	1	24	yes	—
42	C₄²	C₂×C₈	1	16	yes	complemented
43	C₄²	C₂×D₄	1	12	yes	—
44	C₄²	C₂×Q₈	1	12	yes	—
45	C₂³	C₂×C₄⋊C₄	1	6	yes	—
46	C₂³	C₂²×C₈	1	2	yes	—
47	C₂³	C₂×M₁₆	1	6	yes	—
48	C₂³	C₂³×C₄	1	1	yes	characteristic
49	C₂×C₄	—	2	12	no	—
50	C₂×C₄	—	2	24	no	—
51	C₂×C₄	C₄⋊C₈	1	48	yes	complemented
52	C₂×C₄	C₂×C₄⋊C₄	1	12	yes	—
53	C₂×C₄	C₂×C₄⋊C₄	1	6	yes	—
54	C₂×C₄	C₂×C₄⋊C₄	1	12	yes	—
55	C₂×C₄	#127	1	4	yes	—
56	C₂×C₄	C₄⋊Q₈	1	12	yes	—
57	C₂×C₄	C₂²×C₈	1	12	yes	—
58	C₂×C₄	C₂×M₁₆	1	12	yes	—
59	C₂×C₄	C₂²×D₄	1	3	yes	—
60	C₂×C₄	C₂²×Q₈	1	3	yes	—
61	C₈	—	4	8	no	—
62	C₂²	#384	1	4	yes	—
63	C₂²	C₂×C₄⋊C₈	1	12	yes	—
64	C₂²	#423	1	12	yes	—
65	C₂²	C₂²×C₄⋊C₄	1	3	yes	—
66	C₂²	C₂³×C₈	1	1	yes	characteristic
67	C₂²	C₂²×M₁₆	1	3	yes	—
68	C₄	—	2	12	no	—
69	C₄	#384	1	4	yes	—
70	C₄	C₂×C₄⋊C₈	1	24	yes	complemented
71	C₄	C₂×#127	1	1	yes	characteristic
72	C₄	C₂×C₄⋊Q₈	1	3	yes	—
73	C₂	#1842	1	8	yes	direct product factor
74	C₂	C₂×#384	1	1	yes	characteristic
75	C₂	C₂²×C₄⋊C₈	1	3	yes	—
76	C₂	C₂×#423	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
3. #1842	C₂	direct (N × H)
18. C₂×C₄²	C₈	semidirect
42. C₄²	C₂×C₈	semidirect
51. C₂×C₄	C₄⋊C₈	semidirect
70. C₄	C₂×C₄⋊C₈	semidirect
73. C₂	#1842	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×C₄³	2
#1842	2

Subgroups — C2×#1842 #20789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1842 #20789