Subgroups — D₁₆₆₉₂ #72272811

Order 33384.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₅₆₄	—	3	1	no	maximal, Hall
2	D₁₂₈₄	—	13	1	no	maximal, Hall
3	C₂×D₄₁₇₃	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×C₁₃×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄₁₇₃	—	2	2	no	—
6	C₂×C₃×C₁₃×C₁₀₇	C₂²	1	1	yes	characteristic
7	C₂×D₁₃₉₁	—	3	2	no	—
8	C₄×C₁₃×C₁₀₇	D₃	1	1	yes	characteristic, complemented
9	C₃×C₁₃×C₁₀₇	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃×C₁₀₇	C₂×D₃	1	1	yes	characteristic
11	D₁₃₉₁	—	6	2	no	—
12	C₁₃×C₁₀₇	D₁₂	1	1	yes	characteristic, complemented, Hall
13	C₂×D₃₂₁	—	13	2	no	—
14	C₃×C₄×C₁₀₇	D₁₃	1	1	yes	characteristic, complemented
15	D₄₂₈	—	39	1	no	Hall
16	C₂×C₃×C₁₀₇	C₂×D₁₃	1	1	yes	characteristic
17	D₃₂₁	—	26	2	no	—
18	C₂×D₁₀₇	—	39	2	no	—
19	C₄×C₁₀₇	D₃₉	1	1	yes	characteristic, complemented
20	C₃×C₁₀₇	D₅₂	1	1	yes	characteristic, complemented, Hall
21	D₁₅₆	—	107	1	no	maximal, Hall
22	C₂×C₁₀₇	C₂×D₃₉	1	1	yes	characteristic
23	D₁₀₇	—	78	2	no	—
24	C₂×D₃₉	—	107	2	no	—
25	C₃×C₄×C₁₃	D₁₀₇	1	1	yes	characteristic, complemented
26	C₁₀₇	D₁₅₆	1	1	yes	characteristic, complemented, Sylow
27	D₅₂	—	321	1	no	Hall
28	C₂×C₃×C₁₃	C₂×D₁₀₇	1	1	yes	characteristic
29	D₃₉	—	214	2	no	—
30	C₂×D₁₃	—	321	2	no	—
31	C₄×C₁₃	D₃₂₁	1	1	yes	characteristic, complemented
32	C₃×C₁₃	D₄₂₈	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₃	C₂×D₃₂₁	1	1	yes	characteristic
34	D₁₃	—	642	2	no	—
35	D₁₂	—	1391	1	no	Hall
36	C₁₃	D₁₂₈₄	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₃	—	1391	2	no	—
38	C₃×C₄	D₁₃₉₁	1	1	yes	characteristic, complemented
39	D₄	—	4173	1	no	Sylow
40	C₂×C₃	C₂×D₁₃₉₁	1	1	yes	characteristic
41	D₃	—	2782	2	no	—
42	C₂²	—	4173	2	no	—
43	C₄	D₄₁₇₃	1	1	yes	characteristic, complemented
44	C₃	D₅₅₆₄	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	8346	2	no	—
46	C₂	C₂×D₄₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₄₁₇₃
commutator, socle, cosocle	C₂×C₃×C₁₃×C₁₀₇	C₂²
Fitting	C₃×C₄×C₁₃×C₁₀₇	C₂
hypercenter	C₄	D₄₁₇₃
hypocenter	C₃×C₁₃×C₁₀₇	D₄
LCS	G ▷ C₂×C₃×C₁₃×C₁₀₇ ▷ C₃×C₁₃×C₁₀₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
3. C₂×D₄₁₇₃	C₂	semidirect
4. C₃×C₄×C₁₃×C₁₀₇	C₂	semidirect
8. C₄×C₁₃×C₁₀₇	D₃	semidirect
9. C₃×C₁₃×C₁₀₇	D₄	semidirect
12. C₁₃×C₁₀₇	D₁₂	semidirect
14. C₃×C₄×C₁₀₇	D₁₃	semidirect
19. C₄×C₁₀₇	D₃₉	semidirect
20. C₃×C₁₀₇	D₅₂	semidirect
25. C₃×C₄×C₁₃	D₁₀₇	semidirect
26. C₁₀₇	D₁₅₆	semidirect
31. C₄×C₁₃	D₃₂₁	semidirect
32. C₃×C₁₃	D₄₂₈	semidirect
36. C₁₃	D₁₂₈₄	semidirect
38. C₃×C₄	D₁₃₉₁	semidirect
43. C₄	D₄₁₇₃	semidirect
44. C₃	D₅₅₆₄	semidirect

Maximal subgroups

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

subgroup	index
D₅₅₆₄	3
D₁₂₈₄	13
C₂×D₄₁₇₃	2
C₃×C₄×C₁₃×C₁₀₇	2
D₁₅₆	107

Subgroups — D16692 #72272811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆₆₉₂ #72272811