Subgroups — #43244037

Order 28096.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28380766	C₂	1	2	yes	maximal, complemented
2	#28380686	C₂	1	2	yes	maximal, complemented
3	D₇₀₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₄₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₃₂×C₄₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#20296330	—	2	2	no	—
7	#20296316	—	2	2	no	—
8	D₃₅₁₂	C₂²	1	2	yes	—
9	C₈×D₄₃₉	C₂²	1	1	yes	characteristic
10	C₄₃₉⋊C₁₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₄₃₉	C₂²	1	2	yes	—
12	C₁₆×C₄₃₉	C₂²	1	1	yes	characteristic
13	D₁₇₅₆	—	2	2	no	—
14	D₁₇₅₆	—	4	2	no	—
15	C₄×D₄₃₉	—	4	2	no	—
16	C₄×D₄₃₉	D₄	1	1	yes	characteristic
17	C₄₃₉⋊C₈	D₄	1	1	yes	characteristic
18	Q₈×C₄₃₉	—	2	2	no	—
19	C₈×C₄₃₉	C₂³	1	1	yes	characteristic
20	C₂×D₄₃₉	—	4	2	no	—
21	C₂×D₄₃₉	D₈	1	1	yes	characteristic
22	C₄×C₄₃₉	—	4	2	no	—
23	C₄×C₄₃₉	C₂×D₄	1	1	yes	characteristic
24	Dic₄₃₉	D₈	1	1	yes	characteristic
25	C₂×C₄₃₉	C₂×D₈	1	1	yes	characteristic
26	D₄₃₉	—	2	1	no	—
27	D₄₃₉	—	8	2	no	—
28	C₄₃₉	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	439	1	no	maximal, Sylow
30	#135	—	439	2	no	—
31	Q₃₂	D₄₃₉	1	1	yes	characteristic, complemented
32	SD₃₂	—	439	2	no	—
33	D₁₆	—	439	1	no	—
34	C₂×C₁₆	—	439	1	no	—
35	#41	—	878	2	no	—
36	Q₁₆	C₂×D₄₃₉	1	2	yes	—
37	SD₁₆	—	878	2	no	—
38	D₈	—	439	2	no	—
39	C₂×C₈	—	439	1	no	—
40	C₁₆	—	439	1	no	—
41	C₁₆	C₂×D₄₃₉	1	1	yes	characteristic
42	Q₈	—	2	2	no	—
43	D₄	—	878	2	no	—
44	D₄	—	1756	2	no	—
45	C₂×C₄	—	439	1	no	—
46	C₂×C₄	—	1756	2	no	—
47	C₈	—	439	1	no	—
48	C₈	C₂²×D₄₃₉	1	1	yes	characteristic
49	C₂²	—	439	1	no	—
50	C₂²	—	1756	2	no	—
51	C₄	—	4	2	no	—
52	C₄	—	439	1	no	—
53	C₄	D₄×D₄₃₉	1	1	yes	characteristic
54	C₂	—	878	1	no	—
55	C₂	—	3512	2	no	—
56	C₂	D₈×D₄₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₃₉
commutator, cosocle	C₈×C₄₃₉	C₂³
Frattini	C₈	C₂²×D₄₃₉
Fitting	Q₃₂×C₄₃₉	C₂
socle	C₂×C₄₃₉	C₂×D₈
hypercenter	Q₃₂	D₄₃₉
hypocenter	C₄₃₉	#508
LCS	G ▷ C₈×C₄₃₉ ▷ C₄×C₄₃₉ ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #28380766	C₂	semidirect
2. #28380686	C₂	semidirect
3. D₇₀₂₄	C₂	semidirect
4. C₁₆×D₄₃₉	C₂	semidirect
5. Q₃₂×C₄₃₉	C₂	semidirect
28. C₄₃₉	#508	semidirect
31. Q₃₂	D₄₃₉	semidirect

Maximal subgroups

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

subgroup	index
#28380766	2
#28380686	2
D₇₀₂₄	2
C₁₆×D₄₃₉	2
Q₃₂×C₄₃₉	2
#508	439