Subgroups — C₂×Dic₁₇₁₂ #28338766

Order 13696.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₅₆	C₂	1	2	yes	maximal
2	Dic₁₇₁₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₂₈	—	2	2	no	—
5	Dic₈₅₆	—	2	2	no	—
6	Dic₈₅₆	C₂²	1	4	yes	—
7	C₂×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₀₇	C₂²	1	2	yes	—
9	C₂×Dic₂₁₄	—	4	2	no	—
10	Dic₄₂₈	—	2	4	no	—
11	Dic₄₂₈	—	4	2	no	—
12	C₂×C₈×C₁₀₇	D₄	1	1	yes	characteristic
13	C₁₆×C₁₀₇	D₄	1	1	yes	characteristic
14	C₁₆×C₁₀₇	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₁₀₇	D₈	1	1	yes	characteristic
16	C₂×Dic₁₀₇	—	8	2	no	—
17	Dic₂₁₄	—	4	4	no	—
18	Dic₂₁₄	—	8	2	no	—
19	C₈×C₁₀₇	D₈	1	1	yes	characteristic
20	C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₁₀₇	D₁₆	1	1	yes	characteristic
22	C₄×C₁₀₇	D₁₆	1	1	yes	characteristic
23	C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
24	Dic₁₀₇	—	8	4	no	—
25	C₂×C₁₀₇	Q₆₄	1	2	yes	complemented
26	C₂×C₁₀₇	C₂×D₁₆	1	1	yes	characteristic
27	C₂×Q₆₄	—	107	1	no	maximal, Sylow
28	C₁₀₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₃₂	—	107	2	no	—
30	Q₆₄	—	107	4	no	—
31	C₂×C₃₂	D₁₀₇	1	1	yes	characteristic
32	C₂×Q₁₆	—	214	2	no	—
33	Q₃₂	—	107	4	no	—
34	Q₃₂	—	214	2	no	—
35	C₂×C₁₆	C₂×D₁₀₇	1	1	yes	characteristic
36	C₃₂	C₂×D₁₀₇	1	2	yes	—
37	C₂×Q₈	—	428	2	no	—
38	Q₁₆	—	428	2	no	—
39	Q₁₆	—	214	4	no	—
40	C₂×C₈	D₄₂₈	1	1	yes	characteristic
41	C₁₆	D₄₂₈	1	1	yes	characteristic
42	C₁₆	C₂²×D₁₀₇	1	1	yes	characteristic
43	Q₈	—	856	2	no	—
44	Q₈	—	428	4	no	—
45	C₂×C₄	—	856	2	no	—
46	C₂×C₄	D₈₅₆	1	1	yes	characteristic
47	C₈	D₈₅₆	1	1	yes	characteristic
48	C₈	C₂×D₄₂₈	1	1	yes	characteristic
49	C₂²	D₁₇₁₂	1	1	yes	characteristic
50	C₄	—	856	4	no	—
51	C₄	D₁₇₁₂	1	1	yes	characteristic
52	C₄	C₂×D₈₅₆	1	1	yes	characteristic
53	C₂	Dic₁₇₁₂	1	2	yes	direct product factor
54	C₂	C₂×D₁₇₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₇₁₂
commutator, cosocle	C₁₆×C₁₀₇	C₂³
Frattini	C₁₆	C₂²×D₁₀₇
Fitting	C₂×C₃₂×C₁₀₇	C₂
socle, prime radical	C₂²×C₁₀₇	D₁₆
hypercenter	C₂×C₃₂	D₁₀₇
hypocenter	C₁₀₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₀₇ ▷ C₈×C₁₀₇ ▷ C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
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. Dic₁₇₁₂	C₂	direct (N × H)
25. C₂×C₁₀₇	Q₆₄	semidirect
28. C₁₀₇	C₂×Q₆₄	semidirect
53. C₂	Dic₁₇₁₂	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×Dic₈₅₆	2
Dic₁₇₁₂	2
C₂×C₃₂×C₁₀₇	2
C₂×Q₆₄	107

Subgroups — C2×Dic1712 #28338766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₁₇₁₂ #28338766