Subgroups — #43243409

Order 28096.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₇₅₆	C₂	1	1	yes	maximal, characteristic
2	#28380677	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₄₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₇₈	—	2	1	no	—
5	Dic₁₇₅₆	—	2	1	no	—
6	Dic₁₇₅₆	C₄	1	2	yes	complemented
7	C₄⋊Dic₄₃₉	—	2	1	no	—
8	C₂×C₈×C₄₃₉	C₂²	1	1	yes	characteristic
9	C₁₆×C₄₃₉	—	2	1	no	—
10	Dic₈₇₈	—	2	2	no	—
11	Dic₈₇₈	—	4	1	no	—
12	C₂×Dic₄₃₉	—	4	1	no	—
13	C₂×Dic₄₃₉	—	4	1	no	—
14	C₂×C₄×C₄₃₉	D₄	1	1	yes	characteristic
15	C₈×C₄₃₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₄₃₉	D₄	1	1	yes	characteristic
17	C₂²×C₄₃₉	D₈	1	1	yes	characteristic
18	C₄×C₄₃₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₄₃₉	SD₁₆	1	1	yes	characteristic
20	Dic₄₃₉	—	4	2	no	—
21	Dic₄₃₉	—	8	1	no	—
22	C₂×C₄₃₉	#102	1	1	yes	characteristic
23	C₂×C₄₃₉	SD₃₂	1	1	yes	characteristic
24	C₂×C₄₃₉	Q₃₂	1	1	yes	characteristic
25	C₄₃₉	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	439	1	no	maximal, Sylow
27	C₂×Q₁₆	—	439	1	no	—
28	C₂×C₁₆	D₄₃₉	1	1	yes	characteristic
29	#107	—	439	1	no	—
30	C₂×Q₈	—	878	1	no	—
31	Q₁₆	—	878	1	no	—
32	Q₁₆	—	439	2	no	—
33	C₂×C₈	C₂×D₄₃₉	1	1	yes	characteristic
34	C₄⋊C₄	—	878	1	no	—
35	C₁₆	—	2	1	no	—
36	Q₈	—	878	2	no	—
37	Q₈	—	1756	1	no	—
38	C₂×C₄	—	1756	1	no	—
39	C₂×C₄	—	1756	1	no	—
40	C₂×C₄	D₁₇₅₆	1	1	yes	characteristic
41	C₈	C₄×D₄₃₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₄₃₉	1	1	yes	characteristic
43	C₂²	D₃₅₁₂	1	1	yes	characteristic
44	C₄	—	3512	1	no	—
45	C₄	—	1756	2	no	—
46	C₄	(C₂×D₄₃₉)⋊C₄	1	1	yes	characteristic
47	C₄	#20296318	1	1	yes	characteristic
48	C₂	#28380665	1	1	yes	characteristic
49	C₂	#28380688	1	1	yes	characteristic
50	C₂	Dic₃₅₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₅₁₂
commutator	C₈×C₄₃₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₃₉
Fitting	C₂×C₁₆×C₄₃₉	C₂
socle, prime radical	C₂²×C₄₃₉	D₈
cosocle	C₂×C₈×C₄₃₉	C₂²
hypercenter	C₂×C₁₆	D₄₃₉
hypocenter	C₄₃₉	#358
LCS	G ▷ C₈×C₄₃₉ ▷ C₄×C₄₃₉ ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. Dic₁₇₅₆	C₄	semidirect
25. C₄₃₉	#358	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₇₅₆	2
#28380677	2
C₂×C₁₆×C₄₃₉	2
#358	439