Subgroups — #43243431

Order 28096.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#28380677	C₂	1	1	yes	maximal, characteristic
3	#107×C₄₃₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₄₃₉	—	2	1	no	—
5	C₄₃₉⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₄₃₉	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₄₃₉	—	2	1	no	—
8	C₂×Dic₄₃₉	—	4	1	no	—
9	C₂×C₄×C₄₃₉	—	4	1	no	—
10	C₂×C₄×C₄₃₉	D₄	1	1	yes	characteristic
11	C₈×C₄₃₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₃₉	Q₈	1	1	yes	characteristic
13	C₂²×C₄₃₉	D₈	1	1	yes	characteristic
14	C₄×C₄₃₉	—	8	1	no	—
15	C₄×C₄₃₉	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₄₃₉	Q₁₆	1	1	yes	characteristic
17	Dic₄₃₉	—	8	1	no	—
18	C₂×C₄₃₉	#107	1	1	yes	characteristic
19	C₂×C₄₃₉	SD₃₂	1	1	yes	characteristic
20	C₂×C₄₃₉	SD₃₂	1	1	yes	characteristic
21	C₄₃₉	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	439	1	no	maximal, Sylow
23	C₂×C₁₆	—	439	1	no	—
24	#107	—	439	1	no	—
25	#107	D₄₃₉	1	1	yes	characteristic
26	C₂×C₈	C₂×D₄₃₉	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	878	1	no	—
29	C₁₆	—	439	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	1756	1	no	—
32	C₂×C₄	C₂²⋊D₄₃₉	1	1	yes	characteristic
33	C₈	C₄×D₄₃₉	1	1	yes	characteristic
34	C₈	Dic₈₇₈	1	1	yes	characteristic
35	C₂²	#20296314	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	3512	1	no	—
38	C₄	Dic₄₃₉⋊C₄	1	1	yes	characteristic
39	C₄	#20296319	1	1	yes	characteristic
40	C₂	#28380676	1	1	yes	characteristic
41	C₂	#28380686	1	1	yes	characteristic
42	C₂	#28380687	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#20296314
commutator	C₈×C₄₃₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₃₉
Fitting	#107×C₄₃₉	C₂
socle, prime radical	C₂²×C₄₃₉	D₈
cosocle	C₂×C₈×C₄₃₉	C₂²
hypercenter	#107	D₄₃₉
hypocenter	C₄₃₉	#367
LCS	G ▷ C₈×C₄₃₉ ▷ C₄×C₄₃₉ ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₄₃₉⋊C₁₆	C₄	semidirect
21. C₄₃₉	#367	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃₉⋊C₁₆	2
#28380677	2
#107×C₄₃₉	2
#367	439