Subgroups — D₁₈₉₈₄ #72273807

Order 37968.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₄₉₂	C₂	1	2	yes	maximal, complemented
2	D₆₃₂₈	—	3	1	no	maximal, Hall
3	D₃₁₆₄	—	3	2	no	—
4	D₂₇₁₂	—	7	1	no	maximal, Hall
5	D₁₃₅₆	—	7	2	no	—
6	C₃×C₇×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×C₈×C₁₁₃	D₃	1	1	yes	characteristic, complemented
8	C₃×C₈×C₁₁₃	D₇	1	1	yes	characteristic, complemented
9	C₂×D₂₃₇₃	—	2	2	no	—
10	C₃×C₄×C₇×C₁₁₃	C₂²	1	1	yes	characteristic
11	D₂₃₇₃	—	4	2	no	—
12	C₂×C₃×C₇×C₁₁₃	D₄	1	1	yes	characteristic
13	C₂×D₇₉₁	—	6	2	no	—
14	C₄×C₇×C₁₁₃	C₂×D₃	1	1	yes	characteristic
15	C₃×C₇×C₁₁₃	D₈	1	1	yes	characteristic, complemented, Hall
16	D₉₀₄	—	21	1	no	Hall
17	C₂×C₇×C₁₁₃	D₁₂	1	1	yes	characteristic
18	D₇₉₁	—	12	2	no	—
19	C₂×D₃₃₉	—	14	2	no	—
20	C₃×C₄×C₁₁₃	C₂×D₇	1	1	yes	characteristic
21	D₄₅₂	—	21	2	no	—
22	C₈×C₁₁₃	D₂₁	1	1	yes	characteristic, complemented
23	C₇×C₁₁₃	D₂₄	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₁₁₃	D₂₈	1	1	yes	characteristic
25	D₃₃₉	—	28	2	no	—
26	C₂×D₁₁₃	—	42	2	no	—
27	C₄×C₁₁₃	C₂×D₂₁	1	1	yes	characteristic
28	C₃×C₁₁₃	D₅₆	1	1	yes	characteristic, complemented, Hall
29	D₁₆₈	—	113	1	no	maximal, Hall
30	C₂×C₁₁₃	D₈₄	1	1	yes	characteristic
31	D₁₁₃	—	84	2	no	—
32	D₈₄	—	113	2	no	—
33	C₃×C₇×C₈	D₁₁₃	1	1	yes	characteristic, complemented
34	C₁₁₃	D₁₆₈	1	1	yes	characteristic, complemented, Sylow
35	D₅₆	—	339	1	no	Hall
36	C₂×D₂₁	—	226	2	no	—
37	C₃×C₄×C₇	C₂×D₁₁₃	1	1	yes	characteristic
38	D₂₈	—	339	2	no	—
39	C₇×C₈	D₃₃₉	1	1	yes	characteristic, complemented
40	D₂₄	—	791	1	no	Hall
41	C₂×C₃×C₇	D₄₅₂	1	1	yes	characteristic
42	D₂₁	—	452	2	no	—
43	C₂×D₇	—	678	2	no	—
44	C₄×C₇	C₂×D₃₃₉	1	1	yes	characteristic
45	D₁₂	—	791	2	no	—
46	C₃×C₈	D₇₉₁	1	1	yes	characteristic, complemented
47	C₃×C₇	D₉₀₄	1	1	yes	characteristic, complemented, Hall
48	D₈	—	2373	1	no	Sylow
49	C₂×C₇	D₁₃₅₆	1	1	yes	characteristic
50	D₇	—	1356	2	no	—
51	C₂×D₃	—	1582	2	no	—
52	C₃×C₄	C₂×D₇₉₁	1	1	yes	characteristic
53	D₄	—	2373	2	no	—
54	C₈	D₂₃₇₃	1	1	yes	characteristic, complemented
55	C₇	D₂₇₁₂	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	D₃₁₆₄	1	1	yes	characteristic
57	D₃	—	3164	2	no	—
58	C₂²	—	4746	2	no	—
59	C₄	C₂×D₂₃₇₃	1	1	yes	characteristic
60	C₃	D₆₃₂₈	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	9492	2	no	—
62	C₂	D₉₄₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₉₄₉₂
commutator, cosocle	C₃×C₄×C₇×C₁₁₃	C₂²
Frattini	C₄	C₂×D₂₃₇₃
Fitting	C₃×C₇×C₈×C₁₁₃	C₂
socle	C₂×C₃×C₇×C₁₁₃	D₄
hypercenter	C₈	D₂₃₇₃
hypocenter	C₃×C₇×C₁₁₃	D₈
LCS	G ▷ C₃×C₄×C₇×C₁₁₃ ▷ C₂×C₃×C₇×C₁₁₃ ▷ C₃×C₇×C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. D₉₄₉₂	C₂	semidirect
6. C₃×C₇×C₈×C₁₁₃	C₂	semidirect
7. C₇×C₈×C₁₁₃	D₃	semidirect
8. C₃×C₈×C₁₁₃	D₇	semidirect
15. C₃×C₇×C₁₁₃	D₈	semidirect
22. C₈×C₁₁₃	D₂₁	semidirect
23. C₇×C₁₁₃	D₂₄	semidirect
28. C₃×C₁₁₃	D₅₆	semidirect
33. C₃×C₇×C₈	D₁₁₃	semidirect
34. C₁₁₃	D₁₆₈	semidirect
39. C₇×C₈	D₃₃₉	semidirect
46. C₃×C₈	D₇₉₁	semidirect
47. C₃×C₇	D₉₀₄	semidirect
54. C₈	D₂₃₇₃	semidirect
55. C₇	D₂₇₁₂	semidirect
60. C₃	D₆₃₂₈	semidirect

Maximal subgroups

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

subgroup	index
D₉₄₉₂	2
D₆₃₂₈	3
D₂₇₁₂	7
C₃×C₇×C₈×C₁₁₃	2
D₁₆₈	113

Subgroups — D18984 #72273807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₈₉₈₄ #72273807