Subgroups — C₂×C₄×Q₁₆ #2938

Order 128.

244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈	C₂	1	2	yes	maximal
3	C₄×Q₁₆	C₂	1	8	yes	maximal, direct product factor
4	C₂×#107	C₂	1	1	yes	maximal, characteristic
5	C₂×#103	C₂	1	2	yes	maximal
6	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈	C₂²	1	2	yes	—
8	C₂×Q₁₆	C₄	1	8	yes	direct product factor
9	C₂×Q₁₆	C₂²	1	4	yes	—
10	C₂²×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₈	C₂²	1	1	yes	characteristic
12	C₄×Q₈	—	2	4	no	—
13	C₄×Q₈	C₂²	1	8	yes	—
14	C₂×C₄⋊C₄	—	2	2	no	—
15	C₂×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₄²	—	2	2	no	—
17	C₂×C₄²	C₂²	1	1	yes	characteristic
18	#107	C₂²	1	4	yes	—
19	#103	C₂²	1	8	yes	—
20	C₄×C₈	C₂²	1	4	yes	—
21	C₂×Q₈	—	2	2	no	—
22	C₂×Q₈	—	2	4	no	—
23	C₂×Q₈	C₂×C₄	1	8	yes	—
24	C₂×Q₈	C₂³	1	4	yes	—
25	C₂²×C₄	—	2	2	no	—
26	C₂²×C₄	—	2	2	no	—
27	C₂²×C₄	D₄	1	1	yes	characteristic
28	C₂²×C₄	D₄	1	1	yes	characteristic
29	C₂²×C₄	C₂³	1	1	yes	characteristic
30	Q₁₆	C₂×C₄	1	16	yes	direct product factor
31	C₂×C₈	—	2	2	no	—
32	C₂×C₈	C₂×C₄	1	4	yes	—
33	C₂×C₈	C₂³	1	2	yes	—
34	C₂×C₈	C₂³	1	2	yes	—
35	C₄⋊C₄	—	2	8	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	C₂³	1	4	yes	—
38	C₄²	—	2	8	no	—
39	C₄²	D₄	1	2	yes	—
40	C₄²	C₂³	1	2	yes	—
41	C₂³	C₂×D₄	1	1	yes	characteristic
42	Q₈	—	2	8	no	—
43	Q₈	—	2	4	no	—
44	Q₈	C₂²×C₄	1	8	yes	—
45	C₂×C₄	—	2	8	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	2	4	no	—
48	C₂×C₄	—	2	4	no	—
49	C₂×C₄	—	4	4	no	—
50	C₂×C₄	Q₁₆	1	4	yes	direct product factor
51	C₂×C₄	C₂²×C₄	1	2	yes	—
52	C₂×C₄	C₂×D₄	1	2	yes	—
53	C₂×C₄	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄	C₂×D₄	1	2	yes	—
55	C₂×C₄	#41	1	2	yes	—
56	C₂×C₄	C₂⁴	1	1	yes	characteristic
57	C₈	—	2	2	no	—
58	C₈	C₂²×C₄	1	4	yes	—
59	C₂²	C₄×D₄	1	2	yes	—
60	C₂²	C₂×Q₁₆	1	2	yes	—
61	C₂²	#135	1	2	yes	—
62	C₂²	C₂²×D₄	1	1	yes	characteristic
63	C₄	—	2	8	no	—
64	C₄	—	2	2	no	—
65	C₄	—	4	4	no	—
66	C₄	C₄×D₄	1	2	yes	—
67	C₄	C₂×Q₁₆	1	4	yes	direct product factor
68	C₄	C₂³×C₄	1	1	yes	characteristic
69	C₄	C₂×#41	1	1	yes	characteristic
70	C₂	C₄×Q₁₆	1	4	yes	direct product factor
71	C₂	C₂×C₄×D₄	1	1	yes	characteristic
72	C₂	C₂²×Q₁₆	1	1	yes	characteristic
73	C₂	C₂×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄
commutator	C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
socle, prime radical	C₂³	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ 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×Q₁₆	C₂	direct (N × H)
8. C₂×Q₁₆	C₄	direct (N × H)
30. Q₁₆	C₂×C₄	direct (N × H)
50. C₂×C₄	Q₁₆	direct (N × H)
67. C₄	C₂×Q₁₆	direct (N × H)
70. C₂	C₄×Q₁₆	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×Q₁₆	2
C₂×C₄×Q₈	2
C₄×Q₁₆	2
C₂×#107	2
C₂×#103	2
C₂×C₄×C₈	2

Subgroups — C2×C4×Q16 #2938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Q₁₆ #2938