Subgroups — C₂×C₄×M₁₆ #2871

Order 128.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₁₆	C₂	1	2	yes	maximal
2	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆	C₂	1	8	yes	maximal, direct product factor
4	C₂×#97	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₈	C₂	1	2	yes	maximal, complemented
6	C₂³×C₄	C₄	1	2	yes	—
7	C₂³×C₄	C₂²	1	1	yes	characteristic
8	C₂×M₁₆	C₄	1	16	yes	direct product factor
9	C₂×M₁₆	C₂²	1	8	yes	—
10	C₂²×C₈	C₂²	1	4	yes	—
11	C₂×C₄²	C₄	1	2	yes	—
12	C₂×C₄²	C₄	1	4	yes	—
13	C₂×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₄²	C₂²	1	4	yes	—
15	C₂×C₄²	C₂²	1	1	yes	characteristic
16	#97	C₂²	1	8	yes	complemented
17	C₄×C₈	C₂²	1	8	yes	complemented
18	C₂⁴	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄	—	2	8	no	—
20	C₂²×C₄	C₂×C₄	1	2	yes	—
21	C₂²×C₄	C₂×C₄	1	8	yes	—
22	C₂²×C₄	C₂×C₄	1	2	yes	—
23	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄	C₂×C₄	1	8	yes	—
25	C₂²×C₄	C₂×C₄	1	2	yes	—
26	C₂²×C₄	C₂³	1	2	yes	—
27	C₂²×C₄	C₂³	1	1	yes	characteristic
28	M₁₆	C₂×C₄	1	32	yes	direct product factor
29	C₂×C₈	C₂×C₄	1	16	yes	complemented
30	C₂×C₈	C₂³	1	8	yes	—
31	C₄²	C₂×C₄	1	2	yes	—
32	C₄²	C₂×C₄	1	8	yes	—
33	C₄²	C₂×C₄	1	2	yes	—
34	C₄²	C₂³	1	2	yes	—
35	C₄²	C₂³	1	2	yes	—
36	C₂³	—	2	4	no	—
37	C₂³	C₄²	1	4	yes	—
38	C₂³	C₂²×C₄	1	2	yes	—
39	C₂³	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	—	2	16	no	—
42	C₂×C₄	C₄²	1	8	yes	—
43	C₂×C₄	C₄²	1	4	yes	—
44	C₂×C₄	M₁₆	1	8	yes	direct product factor
45	C₂×C₄	C₂²×C₄	1	4	yes	—
46	C₂×C₄	C₂²×C₄	1	2	yes	—
47	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄	C₂²×C₄	1	4	yes	—
49	C₂×C₄	C₂²×C₄	1	8	yes	—
50	C₂×C₄	C₂²×C₄	1	4	yes	—
51	C₂×C₄	C₂⁴	1	1	yes	characteristic
52	C₈	C₂²×C₄	1	16	yes	complemented
53	C₂²	—	2	4	no	—
54	C₂²	—	2	8	no	—
55	C₂²	C₂×C₄²	1	4	yes	—
56	C₂²	C₂×C₄²	1	2	yes	—
57	C₂²	C₂×M₁₆	1	4	yes	—
58	C₂²	C₂³×C₄	1	1	yes	characteristic
59	C₄	—	2	4	no	—
60	C₄	C₂×C₄²	1	2	yes	—
61	C₄	C₂×C₄²	1	4	yes	—
62	C₄	C₂×M₁₆	1	8	yes	direct product factor
63	C₄	C₂³×C₄	1	2	yes	—
64	C₂	—	2	4	no	—
65	C₂	C₄×M₁₆	1	4	yes	direct product factor
66	C₂	C₂²×C₄²	1	1	yes	characteristic
67	C₂	C₂²×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²
commutator	C₂	C₂²×C₄²
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂³	C₂²×C₄
prime radical	C₂⁴	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₄×M₁₆	C₂	direct (N × H)
4. C₂×#97	C₂	semidirect
5. C₂×C₄×C₈	C₂	semidirect
8. C₂×M₁₆	C₄	direct (N × H)
16. #97	C₂²	semidirect
17. C₄×C₈	C₂²	semidirect
28. M₁₆	C₂×C₄	direct (N × H)
29. C₂×C₈	C₂×C₄	semidirect
44. C₂×C₄	M₁₆	direct (N × H)
52. C₈	C₂²×C₄	semidirect
62. C₄	C₂×M₁₆	direct (N × H)
65. C₂	C₄×M₁₆	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×M₁₆	2
C₂²×C₄²	2
C₄×M₁₆	2
C₂×#97	2
C₂×C₄×C₈	2

Subgroups — C2×C4×M16 #2871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×M₁₆ #2871