Subgroups — C₂×#1370 #12003

Order 256.

143 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₁₆	C₂	1	2	yes	maximal
2	C₂×C₈²	C₂	1	1	yes	maximal, characteristic
3	#1370	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆	—	2	2	no	—
5	C₂×C₄×C₈	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
8	C₄⋊C₁₆	—	2	2	no	—
9	C₄⋊C₁₆	C₂²	1	4	yes	—
10	C₈²	C₄	1	2	yes	—
11	C₈²	C₂²	1	2	yes	—
12	C₂²×C₈	—	2	1	no	—
13	C₂²×C₈	C₈	1	1	yes	characteristic
14	C₂²×C₈	C₈	1	1	yes	characteristic
15	C₂²×C₈	D₄	1	1	yes	characteristic
16	C₂²×C₈	Q₈	1	1	yes	characteristic
17	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆	—	2	4	no	—
19	C₂×C₁₆	—	4	4	no	—
20	C₄×C₈	—	2	1	no	—
21	C₄×C₈	C₈	1	2	yes	—
22	C₄×C₈	C₂×C₄	1	2	yes	—
23	C₄×C₈	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈	C₂×C₄	1	2	yes	—
25	C₄×C₈	D₄	1	1	yes	characteristic
26	C₄×C₈	Q₈	1	1	yes	characteristic
27	C₄×C₈	C₂³	1	1	yes	characteristic
28	C₂²×C₄	C₄⋊C₄	1	1	yes	characteristic
29	C₂²×C₄	C₂×C₈	1	1	yes	characteristic
30	C₂²×C₄	M₁₆	1	1	yes	characteristic
31	C₂×C₈	—	2	4	no	—
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	—	2	2	no	—
34	C₂×C₈	—	2	2	no	—
35	C₂×C₈	C₁₆	1	4	yes	complemented
36	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈	C₂×C₈	1	2	yes	—
39	C₂×C₈	C₂×C₈	1	2	yes	—
40	C₂×C₈	D₈	1	2	yes	—
41	C₂×C₈	Q₁₆	1	2	yes	—
42	C₂×C₈	C₂×D₄	1	1	yes	characteristic
43	C₂×C₈	C₂×Q₈	1	1	yes	characteristic
44	C₄²	C₄⋊C₄	1	1	yes	characteristic
45	C₄²	C₂×C₈	1	1	yes	characteristic
46	C₄²	M₁₆	1	1	yes	characteristic
47	C₄²	C₂²×C₄	1	1	yes	characteristic
48	C₁₆	—	4	4	no	—
49	C₂³	C₄⋊C₈	1	1	yes	characteristic
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₄	C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₄	C₄⋊C₈	1	1	yes	characteristic
54	C₂×C₄	#107	1	2	yes	—
55	C₂×C₄	#108	1	2	yes	—
56	C₂×C₄	C₂×C₁₆	1	2	yes	—
57	C₂×C₄	M₃₂	1	2	yes	—
58	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
60	C₂×C₄	C₂×M₁₆	1	1	yes	characteristic
61	C₈	—	2	4	no	—
62	C₈	—	2	1	no	—
63	C₈	—	2	1	no	—
64	C₈	—	2	2	no	—
65	C₈	#107	1	2	yes	—
66	C₈	C₂×C₁₆	1	4	yes	complemented
67	C₈	C₂×D₈	1	1	yes	characteristic
68	C₈	C₂×Q₁₆	1	1	yes	characteristic
69	C₂²	#335	1	2	yes	—
70	C₂²	C₄⋊C₁₆	1	2	yes	—
71	C₂²	#364	1	2	yes	—
72	C₂²	C₂×C₄⋊C₈	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	2	1	no	—
75	C₄	#335	1	2	yes	—
76	C₄	C₄⋊C₁₆	1	2	yes	—
77	C₄	C₂×#107	1	1	yes	characteristic
78	C₄	C₂×#108	1	1	yes	characteristic
79	C₄	C₂²×C₁₆	1	1	yes	characteristic
80	C₄	C₂×M₃₂	1	1	yes	characteristic
81	C₂	#1370	1	4	yes	direct product factor
82	C₂	C₂×#335	1	1	yes	characteristic
83	C₂	C₂×C₄⋊C₁₆	1	1	yes	characteristic
84	C₂	C₂×#364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	D₄
commutator	C₄	C₂²×C₁₆
Frattini, cosocle	C₄×C₈	C₂³
socle, prime radical	C₂³	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #1370	C₂	direct (N × H)
35. C₂×C₈	C₁₆	semidirect
66. C₈	C₂×C₁₆	semidirect
81. C₂	#1370	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×C₄⋊C₁₆	2
C₂×C₈²	2
#1370	2

Subgroups — C2×#1370 #12003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1370 #12003