Subgroups — Dic₄₄₀₀ #72215871

Order 17600.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₂₀₀	C₂	1	2	yes	maximal
2	Dic₁₁₀₀	—	2	2	no	—
3	Dic₈₈₀	—	5	1	no	maximal
4	Dic₅₅₀	—	4	2	no	—
5	C₁₁×C₂₅×C₃₂	C₂	1	1	yes	maximal, characteristic
6	C₁₁×C₁₆×C₂₅	C₂²	1	1	yes	characteristic
7	C₈×C₁₁×C₂₅	D₄	1	1	yes	characteristic
8	Dic₄₄₀	—	5	2	no	—
9	C₅×C₁₁×C₃₂	D₅	1	1	yes	characteristic
10	Dic₄₀₀	—	11	1	no	maximal, Hall
11	C₄×C₁₁×C₂₅	D₈	1	1	yes	characteristic
12	Dic₂₇₅	—	8	2	no	—
13	Dic₂₂₀	—	10	2	no	—
14	C₅×C₁₁×C₁₆	C₂×D₅	1	1	yes	characteristic
15	Dic₂₀₀	—	11	2	no	—
16	C₂₅×C₃₂	D₁₁	1	1	yes	characteristic
17	Dic₁₇₆	—	25	1	no	Hall
18	C₂×C₁₁×C₂₅	D₁₆	1	1	yes	characteristic
19	Dic₁₁₀	—	20	2	no	—
20	C₅×C₈×C₁₁	D₂₀	1	1	yes	characteristic
21	Dic₁₀₀	—	22	2	no	—
22	C₁₆×C₂₅	C₂×D₁₁	1	1	yes	characteristic
23	Dic₈₈	—	25	2	no	—
24	C₁₁×C₃₂	D₂₅	1	1	yes	characteristic
25	Dic₈₀	—	55	1	no	—
26	C₁₁×C₂₅	Q₆₄	1	1	yes	characteristic, complemented, Hall
27	C₄×C₅×C₁₁	D₄₀	1	1	yes	characteristic
28	Dic₅₅	—	40	2	no	—
29	Dic₅₀	—	44	2	no	—
30	C₈×C₂₅	D₄₄	1	1	yes	characteristic
31	Dic₄₄	—	50	2	no	—
32	C₁₁×C₁₆	C₂×D₂₅	1	1	yes	characteristic
33	Dic₄₀	—	55	2	no	—
34	C₅×C₃₂	D₅₅	1	1	yes	characteristic
35	C₂×C₅×C₁₁	D₈₀	1	1	yes	characteristic
36	C₄×C₂₅	D₈₈	1	1	yes	characteristic
37	Dic₂₅	—	88	2	no	—
38	Dic₂₂	—	100	2	no	—
39	C₈×C₁₁	D₁₀₀	1	1	yes	characteristic
40	Dic₂₀	—	110	2	no	—
41	C₅×C₁₆	C₂×D₅₅	1	1	yes	characteristic
42	Q₆₄	—	275	1	no	Sylow
43	C₅×C₁₁	Dic₈₀	1	1	yes	characteristic
44	C₂×C₂₅	D₁₇₆	1	1	yes	characteristic
45	C₄×C₁₁	D₂₀₀	1	1	yes	characteristic
46	Dic₁₁	—	200	2	no	—
47	Dic₁₀	—	220	2	no	—
48	C₅×C₈	D₂₂₀	1	1	yes	characteristic
49	Q₃₂	—	275	2	no	—
50	C₃₂	D₂₇₅	1	1	yes	characteristic
51	C₂₅	Dic₁₇₆	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₁₁	D₄₀₀	1	1	yes	characteristic
53	C₄×C₅	D₄₄₀	1	1	yes	characteristic
54	Dic₅	—	440	2	no	—
55	Q₁₆	—	550	2	no	—
56	C₁₆	C₂×D₂₇₅	1	1	yes	characteristic
57	C₁₁	Dic₄₀₀	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₅	D₈₈₀	1	1	yes	characteristic
59	Q₈	—	1100	2	no	—
60	C₈	D₁₁₀₀	1	1	yes	characteristic
61	C₅	Dic₈₈₀	1	1	yes	characteristic
62	C₄	—	2200	2	no	—
63	C₄	D₂₂₀₀	1	1	yes	characteristic
64	C₂	D₄₄₀₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄₄₀₀
commutator, cosocle	C₁₁×C₁₆×C₂₅	C₂²
Frattini	C₅×C₁₆	C₂×D₅₅
Fitting	C₁₁×C₂₅×C₃₂	C₂
socle, prime radical	C₂×C₅×C₁₁	D₈₀
hypercenter	C₃₂	D₂₇₅
hypocenter	C₁₁×C₂₅	Q₆₄
LCS	G ▷ C₁₁×C₁₆×C₂₅ ▷ C₈×C₁₁×C₂₅ ▷ C₄×C₁₁×C₂₅ ▷ C₂×C₁₁×C₂₅ ▷ C₁₁×C₂₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
26. C₁₁×C₂₅	Q₆₄	semidirect
51. C₂₅	Dic₁₇₆	semidirect
57. C₁₁	Dic₄₀₀	semidirect

Maximal subgroups

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

subgroup	index
Dic₂₂₀₀	2
Dic₈₈₀	5
C₁₁×C₂₅×C₃₂	2
Dic₄₀₀	11

Subgroups — Dic4400 #72215871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₄₄₀₀ #72215871