Subgroups — D₂₀₆₀₈ #72274591

Order 41216.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₃₀₄	C₂	1	2	yes	maximal, complemented
2	D₅₁₅₂	—	2	2	no	—
3	D₂₅₇₆	—	4	2	no	—
4	D₁₂₈₈	—	8	2	no	—
5	C₇×C₂₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×C₂₃×C₆₄	C₂²	1	1	yes	characteristic
7	C₇×C₂₃×C₃₂	D₄	1	1	yes	characteristic
8	C₇×C₁₆×C₂₃	D₈	1	1	yes	characteristic
9	D₂₉₄₄	—	7	1	no	maximal, Hall
10	D₁₄₇₂	—	7	2	no	—
11	C₂₃×C₁₂₈	D₇	1	1	yes	characteristic, complemented
12	D₈₉₆	—	23	1	no	maximal, Hall
13	D₇₃₆	—	14	2	no	—
14	C₂₃×C₆₄	C₂×D₇	1	1	yes	characteristic
15	D₆₄₄	—	16	2	no	—
16	C₇×C₈×C₂₃	D₁₆	1	1	yes	characteristic
17	D₄₄₈	—	23	2	no	—
18	C₇×C₁₂₈	D₂₃	1	1	yes	characteristic, complemented
19	D₃₆₈	—	28	2	no	—
20	C₂₃×C₃₂	D₂₈	1	1	yes	characteristic
21	C₂×D₁₆₁	—	32	2	no	—
22	C₄×C₇×C₂₃	D₃₂	1	1	yes	characteristic
23	D₂₂₄	—	46	2	no	—
24	C₇×C₆₄	C₂×D₂₃	1	1	yes	characteristic
25	D₁₈₄	—	56	2	no	—
26	C₁₆×C₂₃	D₅₆	1	1	yes	characteristic
27	C₂×C₇×C₂₃	D₆₄	1	1	yes	characteristic
28	D₁₆₁	—	64	2	no	—
29	D₁₂₈	—	161	1	no	Sylow
30	D₁₁₂	—	92	2	no	—
31	C₇×C₃₂	D₉₂	1	1	yes	characteristic
32	D₉₂	—	112	2	no	—
33	C₈×C₂₃	D₁₁₂	1	1	yes	characteristic
34	C₇×C₂₃	D₁₂₈	1	1	yes	characteristic, complemented, Hall
35	D₆₄	—	161	2	no	—
36	C₁₂₈	D₁₆₁	1	1	yes	characteristic, complemented
37	D₅₆	—	184	2	no	—
38	C₇×C₁₆	D₁₈₄	1	1	yes	characteristic
39	C₂×D₂₃	—	224	2	no	—
40	C₄×C₂₃	D₂₂₄	1	1	yes	characteristic
41	D₃₂	—	322	2	no	—
42	C₆₄	C₂×D₁₆₁	1	1	yes	characteristic
43	D₂₈	—	368	2	no	—
44	C₇×C₈	D₃₆₈	1	1	yes	characteristic
45	C₂×C₂₃	D₄₄₈	1	1	yes	characteristic
46	D₂₃	—	448	2	no	—
47	D₁₆	—	644	2	no	—
48	C₃₂	D₆₄₄	1	1	yes	characteristic
49	C₂×D₇	—	736	2	no	—
50	C₄×C₇	D₇₃₆	1	1	yes	characteristic
51	C₂₃	D₈₉₆	1	1	yes	characteristic, complemented, Sylow
52	D₈	—	1288	2	no	—
53	C₁₆	D₁₂₈₈	1	1	yes	characteristic
54	C₂×C₇	D₁₄₇₂	1	1	yes	characteristic
55	D₇	—	1472	2	no	—
56	D₄	—	2576	2	no	—
57	C₈	D₂₅₇₆	1	1	yes	characteristic
58	C₇	D₂₉₄₄	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	5152	2	no	—
60	C₄	D₅₁₅₂	1	1	yes	characteristic
61	C₂	—	10304	2	no	—
62	C₂	D₁₀₃₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₀₃₀₄
commutator, cosocle	C₇×C₂₃×C₆₄	C₂²
Frattini	C₆₄	C₂×D₁₆₁
Fitting	C₇×C₂₃×C₁₂₈	C₂
socle	C₂×C₇×C₂₃	D₆₄
hypercenter	C₁₂₈	D₁₆₁
hypocenter	C₇×C₂₃	D₁₂₈
LCS	G ▷ C₇×C₂₃×C₆₄ ▷ C₇×C₂₃×C₃₂ ▷ C₇×C₁₆×C₂₃ ▷ C₇×C₈×C₂₃ ▷ C₄×C₇×C₂₃ ▷ C₂×C₇×C₂₃ ▷ C₇×C₂₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ C₆₄ ◁ C₁₂₈

Complements

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

N	H ≅ G/N	type
1. D₁₀₃₀₄	C₂	semidirect
5. C₇×C₂₃×C₁₂₈	C₂	semidirect
11. C₂₃×C₁₂₈	D₇	semidirect
18. C₇×C₁₂₈	D₂₃	semidirect
34. C₇×C₂₃	D₁₂₈	semidirect
36. C₁₂₈	D₁₆₁	semidirect
51. C₂₃	D₈₉₆	semidirect
58. C₇	D₂₉₄₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₁₀₃₀₄	2
C₇×C₂₃×C₁₂₈	2
D₂₉₄₄	7
D₈₉₆	23

Subgroups — D20608 #72274591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₀₆₀₈ #72274591