Subgroups — C₂×Dic₂₅₁₂ #34102441

Order 20096.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₅₆	C₂	1	2	yes	maximal
2	Dic₂₅₁₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₁₅₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₆₂₈	—	2	2	no	—
5	Dic₁₂₅₆	—	2	2	no	—
6	Dic₁₂₅₆	C₂²	1	4	yes	—
7	C₂×C₁₆×C₁₅₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₅₇	C₂²	1	2	yes	—
9	C₂×Dic₃₁₄	—	4	2	no	—
10	Dic₆₂₈	—	2	4	no	—
11	Dic₆₂₈	—	4	2	no	—
12	C₂×C₈×C₁₅₇	D₄	1	1	yes	characteristic
13	C₁₆×C₁₅₇	D₄	1	1	yes	characteristic
14	C₁₆×C₁₅₇	C₂³	1	1	yes	characteristic
15	Dic₃₁₄	—	4	4	no	—
16	Dic₃₁₄	—	8	2	no	—
17	C₂×Dic₁₅₇	—	8	2	no	—
18	C₂×C₄×C₁₅₇	D₈	1	1	yes	characteristic
19	C₈×C₁₅₇	D₈	1	1	yes	characteristic
20	C₈×C₁₅₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₁₅₇	D₁₆	1	1	yes	characteristic
22	C₄×C₁₅₇	D₁₆	1	1	yes	characteristic
23	C₄×C₁₅₇	C₂×D₈	1	1	yes	characteristic
24	Dic₁₅₇	—	8	4	no	—
25	C₂×C₁₅₇	Q₆₄	1	2	yes	complemented
26	C₂×C₁₅₇	C₂×D₁₆	1	1	yes	characteristic
27	C₁₅₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₆₄	—	157	1	no	maximal, Sylow
29	C₂×Q₃₂	—	157	2	no	—
30	Q₆₄	—	157	4	no	—
31	C₂×C₃₂	D₁₅₇	1	1	yes	characteristic
32	C₂×Q₁₆	—	314	2	no	—
33	Q₃₂	—	314	2	no	—
34	Q₃₂	—	157	4	no	—
35	C₂×C₁₆	C₂×D₁₅₇	1	1	yes	characteristic
36	C₃₂	C₂×D₁₅₇	1	2	yes	—
37	C₂×Q₈	—	628	2	no	—
38	Q₁₆	—	314	4	no	—
39	Q₁₆	—	628	2	no	—
40	C₂×C₈	D₆₂₈	1	1	yes	characteristic
41	C₁₆	D₆₂₈	1	1	yes	characteristic
42	C₁₆	C₂²×D₁₅₇	1	1	yes	characteristic
43	Q₈	—	628	4	no	—
44	Q₈	—	1256	2	no	—
45	C₂×C₄	—	1256	2	no	—
46	C₂×C₄	D₁₂₅₆	1	1	yes	characteristic
47	C₈	D₁₂₅₆	1	1	yes	characteristic
48	C₈	C₂×D₆₂₈	1	1	yes	characteristic
49	C₂²	D₂₅₁₂	1	1	yes	characteristic
50	C₄	—	1256	4	no	—
51	C₄	D₂₅₁₂	1	1	yes	characteristic
52	C₄	C₂×D₁₂₅₆	1	1	yes	characteristic
53	C₂	Dic₂₅₁₂	1	2	yes	direct product factor
54	C₂	C₂×D₂₅₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₅₁₂
commutator, cosocle	C₁₆×C₁₅₇	C₂³
Frattini	C₁₆	C₂²×D₁₅₇
Fitting	C₂×C₃₂×C₁₅₇	C₂
socle, prime radical	C₂²×C₁₅₇	D₁₆
hypercenter	C₂×C₃₂	D₁₅₇
hypocenter	C₁₅₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₅₇ ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
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. Dic₂₅₁₂	C₂	direct (N × H)
25. C₂×C₁₅₇	Q₆₄	semidirect
27. C₁₅₇	C₂×Q₆₄	semidirect
53. C₂	Dic₂₅₁₂	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×Dic₁₂₅₆	2
Dic₂₅₁₂	2
C₂×C₃₂×C₁₅₇	2
C₂×Q₆₄	157

Subgroups — C2×Dic2512 #34102441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₂₅₁₂ #34102441