Subgroups — #43243402

Order 28096.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28380741	C₂	1	1	yes	maximal, characteristic
2	#28380662	C₂	1	1	yes	maximal, characteristic
3	#101×C₄₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₇₈	C₄	1	1	yes	characteristic
5	#20296313	—	2	1	no	—
6	Dic₄₃₉⋊C₄	—	2	1	no	—
7	Dic₄₃₉⋊C₄	—	2	1	no	—
8	C₄×Dic₄₃₉	C₄	1	1	yes	characteristic
9	C₂×Q₈×C₄₃₉	C₂²	1	1	yes	characteristic
10	M₁₆×C₄₃₉	—	2	1	no	—
11	Dic₈₇₈	—	4	1	no	—
12	C₂×Dic₄₃₉	—	2	1	no	—
13	C₂×Dic₄₃₉	—	2	1	no	—
14	C₄₃₉⋊C₈	—	4	1	no	—
15	Q₈×C₄₃₉	—	4	1	no	—
16	C₂×C₄×C₄₃₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃₉	D₄	1	1	yes	characteristic
19	C₈×C₄₃₉	—	4	1	no	—
20	C₂²×C₄₃₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₃₉	—	2	1	no	—
22	C₄×C₄₃₉	—	2	1	no	—
23	C₄×C₄₃₉	—	2	1	no	—
24	Dic₄₃₉	—	2	2	no	—
25	Dic₄₃₉	—	4	1	no	—
26	C₂×C₄₃₉	—	2	1	no	—
27	C₂×C₄₃₉	#99	1	1	yes	characteristic
28	C₄₃₉	#356	1	1	yes	characteristic, complemented, Sylow
29	#356	—	439	1	no	maximal, Sylow
30	C₄⋊Q₈	—	439	1	no	—
31	#101	—	439	1	no	—
32	#101	D₄₃₉	1	1	yes	characteristic
33	C₂×Q₈	—	439	1	no	—
34	C₂×Q₈	C₂×D₄₃₉	1	1	yes	characteristic
35	M₁₆	—	2	1	no	—
36	M₁₆	—	878	1	no	—
37	C₄⋊C₄	—	878	1	no	—
38	C₄⋊C₄	—	878	1	no	—
39	C₄²	—	439	1	no	—
40	Q₈	—	4	1	no	—
41	Q₈	—	1756	1	no	—
42	C₂×C₄	—	878	1	no	—
43	C₂×C₄	—	878	1	no	—
44	C₂×C₄	C₄×D₄₃₉	1	1	yes	characteristic
45	C₂×C₄	C₂²⋊D₄₃₉	1	1	yes	characteristic
46	C₂×C₄	D₁₇₅₆	1	1	yes	characteristic
47	C₈	—	4	1	no	—
48	C₈	—	1756	1	no	—
49	C₂²	(C₂×D₄₃₉)⋊C₄	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	878	2	no	—
54	C₄	—	1756	1	no	—
55	C₂	—	2	1	no	—
56	C₂	#28380657	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28380657
commutator	C₂×C₄×C₄₃₉	C₂×C₄
Frattini	C₂×Q₈	C₂×D₄₃₉
Fitting	#101×C₄₃₉	C₂
socle	C₂×C₄₃₉	#99
prime radical	C₂²×C₄₃₉	C₂²⋊C₄
cosocle	C₂×Q₈×C₄₃₉	C₂²
hypercenter	#101	D₄₃₉
hypocenter	C₄₃₉	#356
LCS	G ▷ C₂×C₄×C₄₃₉ ▷ C₂²×C₄₃₉ ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
28. C₄₃₉	#356	semidirect

Maximal subgroups

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

subgroup	index
#28380741	2
#28380662	2
#101×C₄₃₉	2
#356	439