Subgroups — C₂×Dic₄₃₃₆ #46838669

Order 34688.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₁₆₈	C₂	1	2	yes	maximal
2	Dic₄₃₃₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₂₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₈₄	—	2	2	no	—
5	Dic₂₁₆₈	—	2	2	no	—
6	Dic₂₁₆₈	C₂²	1	4	yes	—
7	C₂×C₁₆×C₂₇₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₂₇₁	C₂²	1	2	yes	—
9	C₂×Dic₅₄₂	—	4	2	no	—
10	Dic₁₀₈₄	—	2	4	no	—
11	Dic₁₀₈₄	—	4	2	no	—
12	C₂×C₈×C₂₇₁	D₄	1	1	yes	characteristic
13	C₁₆×C₂₇₁	D₄	1	1	yes	characteristic
14	C₁₆×C₂₇₁	C₂³	1	1	yes	characteristic
15	Dic₅₄₂	—	4	4	no	—
16	Dic₅₄₂	—	8	2	no	—
17	C₂×Dic₂₇₁	—	8	2	no	—
18	C₂×C₄×C₂₇₁	D₈	1	1	yes	characteristic
19	C₈×C₂₇₁	D₈	1	1	yes	characteristic
20	C₈×C₂₇₁	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₂₇₁	D₁₆	1	1	yes	characteristic
22	C₄×C₂₇₁	D₁₆	1	1	yes	characteristic
23	C₄×C₂₇₁	C₂×D₈	1	1	yes	characteristic
24	Dic₂₇₁	—	8	4	no	—
25	C₂×C₂₇₁	Q₆₄	1	2	yes	complemented
26	C₂×C₂₇₁	C₂×D₁₆	1	1	yes	characteristic
27	C₂₇₁	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₆₄	—	271	1	no	maximal, Sylow
29	C₂×Q₃₂	—	271	2	no	—
30	Q₆₄	—	271	4	no	—
31	C₂×C₃₂	D₂₇₁	1	1	yes	characteristic
32	C₂×Q₁₆	—	542	2	no	—
33	Q₃₂	—	271	4	no	—
34	Q₃₂	—	542	2	no	—
35	C₂×C₁₆	C₂×D₂₇₁	1	1	yes	characteristic
36	C₃₂	C₂×D₂₇₁	1	2	yes	—
37	C₂×Q₈	—	1084	2	no	—
38	Q₁₆	—	542	4	no	—
39	Q₁₆	—	1084	2	no	—
40	C₂×C₈	D₁₀₈₄	1	1	yes	characteristic
41	C₁₆	D₁₀₈₄	1	1	yes	characteristic
42	C₁₆	C₂²×D₂₇₁	1	1	yes	characteristic
43	Q₈	—	1084	4	no	—
44	Q₈	—	2168	2	no	—
45	C₂×C₄	—	2168	2	no	—
46	C₂×C₄	D₂₁₆₈	1	1	yes	characteristic
47	C₈	D₂₁₆₈	1	1	yes	characteristic
48	C₈	C₂×D₁₀₈₄	1	1	yes	characteristic
49	C₂²	D₄₃₃₆	1	1	yes	characteristic
50	C₄	—	2168	4	no	—
51	C₄	D₄₃₃₆	1	1	yes	characteristic
52	C₄	C₂×D₂₁₆₈	1	1	yes	characteristic
53	C₂	Dic₄₃₃₆	1	2	yes	direct product factor
54	C₂	C₂×D₄₃₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₃₃₆
commutator, cosocle	C₁₆×C₂₇₁	C₂³
Frattini	C₁₆	C₂²×D₂₇₁
Fitting	C₂×C₃₂×C₂₇₁	C₂
socle, prime radical	C₂²×C₂₇₁	D₁₆
hypercenter	C₂×C₃₂	D₂₇₁
hypocenter	C₂₇₁	C₂×Q₆₄
LCS	G ▷ C₁₆×C₂₇₁ ▷ C₈×C₂₇₁ ▷ C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₄₃₃₆	C₂	direct (N × H)
25. C₂×C₂₇₁	Q₆₄	semidirect
27. C₂₇₁	C₂×Q₆₄	semidirect
53. C₂	Dic₄₃₃₆	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×Dic₂₁₆₈	2
Dic₄₃₃₆	2
C₂×C₃₂×C₂₇₁	2
C₂×Q₆₄	271

Subgroups — C2×Dic4336 #46838669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₄₃₃₆ #46838669