Subgroups — C₂×Dic₂₇₂ #14531089

Order 2176.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₆	C₂	1	2	yes	maximal
2	Dic₂₇₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₆₈	—	2	2	no	—
5	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
6	Dic₁₃₆	—	2	2	no	—
7	Dic₁₃₆	C₂²	1	4	yes	—
8	C₁₇×C₃₂	C₂²	1	2	yes	—
9	C₂×Dic₃₄	—	4	2	no	—
10	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
11	Dic₆₈	—	2	4	no	—
12	Dic₆₈	—	4	2	no	—
13	C₁₆×C₁₇	D₄	1	1	yes	characteristic
14	C₁₆×C₁₇	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
16	C₂×Dic₁₇	—	8	2	no	—
17	Dic₃₄	—	4	4	no	—
18	Dic₃₄	—	8	2	no	—
19	C₈×C₁₇	D₈	1	1	yes	characteristic
20	C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
21	C₂×Q₆₄	—	17	1	no	maximal, Sylow
22	C₂²×C₁₇	D₁₆	1	1	yes	characteristic
23	C₄×C₁₇	D₁₆	1	1	yes	characteristic
24	C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
25	Dic₁₇	—	8	4	no	—
26	C₂×Q₃₂	—	17	2	no	—
27	Q₆₄	—	17	4	no	—
28	C₂×C₃₂	D₁₇	1	1	yes	characteristic
29	C₂×C₁₇	Q₆₄	1	2	yes	complemented
30	C₂×C₁₇	C₂×D₁₆	1	1	yes	characteristic
31	C₂×Q₁₆	—	34	2	no	—
32	Q₃₂	—	17	4	no	—
33	Q₃₂	—	34	2	no	—
34	C₂×C₁₆	C₂×D₁₇	1	1	yes	characteristic
35	C₃₂	C₂×D₁₇	1	2	yes	—
36	C₁₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	68	2	no	—
38	Q₁₆	—	34	4	no	—
39	Q₁₆	—	68	2	no	—
40	C₂×C₈	D₆₈	1	1	yes	characteristic
41	C₁₆	D₆₈	1	1	yes	characteristic
42	C₁₆	C₂²×D₁₇	1	1	yes	characteristic
43	Q₈	—	68	4	no	—
44	Q₈	—	136	2	no	—
45	C₂×C₄	—	136	2	no	—
46	C₂×C₄	D₁₃₆	1	1	yes	characteristic
47	C₈	D₁₃₆	1	1	yes	characteristic
48	C₈	C₂×D₆₈	1	1	yes	characteristic
49	C₂²	D₂₇₂	1	1	yes	characteristic
50	C₄	—	136	4	no	—
51	C₄	D₂₇₂	1	1	yes	characteristic
52	C₄	C₂×D₁₃₆	1	1	yes	characteristic
53	C₂	Dic₂₇₂	1	2	yes	direct product factor
54	C₂	C₂×D₂₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₇₂
commutator, cosocle	C₁₆×C₁₇	C₂³
Frattini	C₁₆	C₂²×D₁₇
Fitting	C₂×C₁₇×C₃₂	C₂
socle, prime radical	C₂²×C₁₇	D₁₆
hypercenter	C₂×C₃₂	D₁₇
hypocenter	C₁₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
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. Dic₂₇₂	C₂	direct (N × H)
29. C₂×C₁₇	Q₆₄	semidirect
36. C₁₇	C₂×Q₆₄	semidirect
53. C₂	Dic₂₇₂	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×Dic₁₃₆	2
Dic₂₇₂	2
C₂×C₁₇×C₃₂	2
C₂×Q₆₄	17

Subgroups — C2×Dic272 #14531089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₂₇₂ #14531089