Subgroups — C₂×Dic₂₅₂₈ #34209319

Order 20224.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₆₄	C₂	1	2	yes	maximal
2	Dic₂₅₂₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₆₃₂	—	2	2	no	—
5	Dic₁₂₆₄	—	2	2	no	—
6	Dic₁₂₆₄	C₂²	1	4	yes	—
7	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
8	C₆₄×C₇₉	C₂²	1	2	yes	—
9	C₂×Dic₃₁₆	—	4	2	no	—
10	Dic₆₃₂	—	2	4	no	—
11	Dic₆₃₂	—	4	2	no	—
12	C₂×C₁₆×C₇₉	D₄	1	1	yes	characteristic
13	C₃₂×C₇₉	D₄	1	1	yes	characteristic
14	C₃₂×C₇₉	C₂³	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	8	2	no	—
16	Dic₃₁₆	—	4	4	no	—
17	Dic₃₁₆	—	8	2	no	—
18	C₂×C₈×C₇₉	D₈	1	1	yes	characteristic
19	C₁₆×C₇₉	D₈	1	1	yes	characteristic
20	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
21	C₂×C₄×C₇₉	D₁₆	1	1	yes	characteristic
22	C₂×Dic₇₉	—	16	2	no	—
23	Dic₁₅₈	—	8	4	no	—
24	Dic₁₅₈	—	16	2	no	—
25	C₈×C₇₉	D₁₆	1	1	yes	characteristic
26	C₈×C₇₉	C₂×D₈	1	1	yes	characteristic
27	C₂²×C₇₉	D₃₂	1	1	yes	characteristic
28	C₄×C₇₉	D₃₂	1	1	yes	characteristic
29	C₄×C₇₉	C₂×D₁₆	1	1	yes	characteristic
30	Dic₇₉	—	16	4	no	—
31	C₂×Q₁₂₈	—	79	1	no	maximal, Sylow
32	C₂×C₇₉	Q₁₂₈	1	2	yes	complemented
33	C₂×C₇₉	C₂×D₃₂	1	1	yes	characteristic
34	C₂×Q₆₄	—	79	2	no	—
35	Q₁₂₈	—	79	4	no	—
36	C₂×C₆₄	D₇₉	1	1	yes	characteristic
37	C₇₉	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
38	C₂×Q₃₂	—	158	2	no	—
39	Q₆₄	—	79	4	no	—
40	Q₆₄	—	158	2	no	—
41	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
42	C₆₄	C₂×D₇₉	1	2	yes	—
43	C₂×Q₁₆	—	316	2	no	—
44	Q₃₂	—	316	2	no	—
45	Q₃₂	—	158	4	no	—
46	C₂×C₁₆	D₃₁₆	1	1	yes	characteristic
47	C₃₂	D₃₁₆	1	1	yes	characteristic
48	C₃₂	C₂²×D₇₉	1	1	yes	characteristic
49	C₂×Q₈	—	632	2	no	—
50	Q₁₆	—	316	4	no	—
51	Q₁₆	—	632	2	no	—
52	C₂×C₈	D₆₃₂	1	1	yes	characteristic
53	C₁₆	D₆₃₂	1	1	yes	characteristic
54	C₁₆	C₂×D₃₁₆	1	1	yes	characteristic
55	Q₈	—	632	4	no	—
56	Q₈	—	1264	2	no	—
57	C₂×C₄	—	1264	2	no	—
58	C₂×C₄	D₁₂₆₄	1	1	yes	characteristic
59	C₈	D₁₂₆₄	1	1	yes	characteristic
60	C₈	C₂×D₆₃₂	1	1	yes	characteristic
61	C₂²	D₂₅₂₈	1	1	yes	characteristic
62	C₄	—	1264	4	no	—
63	C₄	D₂₅₂₈	1	1	yes	characteristic
64	C₄	C₂×D₁₂₆₄	1	1	yes	characteristic
65	C₂	Dic₂₅₂₈	1	2	yes	direct product factor
66	C₂	C₂×D₂₅₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₅₂₈
commutator, cosocle	C₃₂×C₇₉	C₂³
Frattini	C₃₂	C₂²×D₇₉
Fitting	C₂×C₆₄×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	D₃₂
hypercenter	C₂×C₆₄	D₇₉
hypocenter	C₇₉	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₂₅₂₈	C₂	direct (N × H)
32. C₂×C₇₉	Q₁₂₈	semidirect
37. C₇₉	C₂×Q₁₂₈	semidirect
65. C₂	Dic₂₅₂₈	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×Dic₁₂₆₄	2
Dic₂₅₂₈	2
C₂×C₆₄×C₇₉	2
C₂×Q₁₂₈	79

Subgroups — C2×Dic2528 #34209319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₂₅₂₈ #34209319