Subgroups — #43243414

Order 28096.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28380683	C₂	1	1	yes	maximal, characteristic, complemented
2	#28380675	C₂	1	1	yes	maximal, characteristic, complemented
3	#135×C₄₃₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₄₃₉	—	2	1	no	—
5	C₄₃₉⋊C₁₆	—	2	1	no	—
6	#41×C₄₃₉	—	2	1	no	—
7	Q₁₆×C₄₃₉	C₄	1	1	yes	characteristic, complemented
8	SD₁₆×C₄₃₉	—	2	1	no	—
9	D₈×C₄₃₉	C₄	1	1	yes	characteristic, complemented
10	C₂×C₈×C₄₃₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₃₉	—	4	1	no	—
12	Q₈×C₄₃₉	—	2	1	no	—
13	D₄×C₄₃₉	—	2	1	no	—
14	D₄×C₄₃₉	—	4	1	no	—
15	C₂×C₄×C₄₃₉	—	4	1	no	—
16	C₂×C₄×C₄₃₉	D₄	1	1	yes	characteristic
17	C₈×C₄₃₉	C₂×C₄	1	1	yes	characteristic
18	C₈×C₄₃₉	D₄	1	1	yes	characteristic
19	C₂²×C₄₃₉	—	4	1	no	—
20	C₂²×C₄₃₉	D₈	1	1	yes	characteristic
21	C₄×C₄₃₉	—	4	1	no	—
22	C₄×C₄₃₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₄₃₉	SD₁₆	1	1	yes	characteristic
24	Dic₄₃₉	—	8	1	no	—
25	C₂×C₄₃₉	—	2	1	no	—
26	C₂×C₄₃₉	—	8	1	no	—
27	C₂×C₄₃₉	#102	1	1	yes	characteristic
28	C₄₃₉	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	439	1	no	maximal, Sylow
30	#135	D₄₃₉	1	1	yes	characteristic
31	M₃₂	—	439	1	no	—
32	#106	—	439	1	no	—
33	#41	—	2	1	no	—
34	Q₁₆	Dic₄₃₉	1	1	yes	characteristic, complemented
35	SD₁₆	—	2	1	no	—
36	D₈	Dic₄₃₉	1	1	yes	characteristic, complemented
37	C₂×C₈	C₂×D₄₃₉	1	1	yes	characteristic
38	C₄⋊C₄	—	878	1	no	—
39	C₁₆	—	878	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	2	1	no	—
42	D₄	—	4	1	no	—
43	C₂×C₄	—	4	1	no	—
44	C₂×C₄	—	1756	1	no	—
45	C₂×C₄	C₂²⋊D₄₃₉	1	1	yes	characteristic
46	C₈	C₂×Dic₄₃₉	1	1	yes	characteristic
47	C₈	C₂²⋊D₄₃₉	1	1	yes	characteristic
48	C₂²	—	4	1	no	—
49	C₂²	#20296314	1	1	yes	characteristic
50	C₄	—	4	1	no	—
51	C₄	—	3512	1	no	—
52	C₄	C₂²⋊Dic₄₃₉	1	1	yes	characteristic
53	C₄	#20296317	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	8	1	no	—
56	C₂	#28380664	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28380664
commutator	C₈×C₄₃₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₃₉
Fitting, prime radical	#135×C₄₃₉	C₂
socle	C₂×C₄₃₉	#102
cosocle	C₂×C₈×C₄₃₉	C₂²
hypercenter	#135	D₄₃₉
hypocenter	C₄₃₉	#360
LCS	G ▷ C₈×C₄₃₉ ▷ C₄×C₄₃₉ ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #28380683	C₂	semidirect
2. #28380675	C₂	semidirect
7. Q₁₆×C₄₃₉	C₄	semidirect
9. D₈×C₄₃₉	C₄	semidirect
28. C₄₃₉	#360	semidirect
34. Q₁₆	Dic₄₃₉	semidirect
36. D₈	Dic₄₃₉	semidirect

Maximal subgroups

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

subgroup	index
#28380683	2
#28380675	2
#135×C₄₃₉	2
#360	439