Subgroups — #49094890

Order 35968.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823861	C₂	1	3	yes	maximal, complemented
2	#31823836	C₂	1	3	yes	maximal
3	C₈²×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17985127	—	2	6	no	—
5	#22582879	C₂²	1	3	yes	—
6	#22582876	C₂²	1	1	yes	characteristic
7	#22582811	—	2	6	no	—
8	C₄×C₈×C₂₈₁	C₂²	1	3	yes	—
9	C₂×Dic₅₆₂	—	2	3	no	—
10	C₂×D₁₁₂₄	—	2	3	no	—
11	#17985127	—	4	12	no	—
12	C₄⋊Dic₂₈₁	—	2	6	no	—
13	C₂×C₈×C₂₈₁	D₄	1	6	yes	—
14	C₄²×C₂₈₁	C₂³	1	1	yes	characteristic
15	C₂²×D₂₈₁	—	4	1	no	—
16	Dic₅₆₂	—	4	6	no	—
17	D₁₁₂₄	—	4	6	no	—
18	C₂×Dic₂₈₁	—	4	3	no	—
19	C₂×C₄×C₂₈₁	C₂×D₄	1	3	yes	—
20	C₈×C₂₈₁	SD₁₆	1	12	yes	complemented
21	C₂²×C₂₈₁	#127	1	1	yes	characteristic
22	C₂×D₂₈₁	—	8	3	no	—
23	C₄×C₂₈₁	C₂×SD₁₆	1	6	yes	—
24	Dic₂₈₁	—	8	3	no	—
25	C₂×C₂₈₁	#492	1	3	yes	—
26	D₂₈₁	—	16	1	no	—
27	C₂₈₁	#1705	1	1	yes	characteristic, complemented, Sylow
28	#1705	—	281	1	no	maximal, Sylow
29	#498	—	281	3	no	—
30	#492	—	281	3	no	—
31	C₈²	D₂₈₁	1	1	yes	characteristic, complemented
32	C₂×SD₁₆	—	562	6	no	—
33	C₄⋊Q₈	—	281	3	no	—
34	#127	—	281	1	no	—
35	#106	—	562	6	no	—
36	C₄×C₈	C₂×D₂₈₁	1	3	yes	—
37	C₂×Q₈	—	562	3	no	—
38	C₂×D₄	—	562	3	no	—
39	SD₁₆	—	1124	12	no	—
40	C₂×C₈	D₁₁₂₄	1	6	yes	—
41	C₄⋊C₄	—	562	6	no	—
42	C₄²	C₂²×D₂₈₁	1	1	yes	characteristic
43	C₂³	—	1124	1	no	—
44	Q₈	—	1124	6	no	—
45	D₄	—	1124	6	no	—
46	C₂×C₄	—	1124	3	no	—
47	C₂×C₄	C₂×D₁₁₂₄	1	3	yes	—
48	C₈	#17985127	1	12	yes	complemented
49	C₂²	—	2248	3	no	—
50	C₂²	#22582876	1	1	yes	characteristic
51	C₄	—	2248	3	no	—
52	C₄	C₂×#17985127	1	6	yes	—
53	C₂	—	4496	1	no	—
54	C₂	#31823836	1	3	yes	—

	subgroup	G/H
center	C₂²	#22582876
commutator, cosocle	C₄²×C₂₈₁	C₂³
Frattini	C₄²	C₂²×D₂₈₁
Fitting	C₈²×C₂₈₁	C₂
socle	C₂²×C₂₈₁	#127
prime radical	#22582876	C₂²
hypercenter	C₈²	D₂₈₁
hypocenter	C₂₈₁	#1705
LCS	G ▷ C₄²×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #31823861	C₂	semidirect
3. C₈²×C₂₈₁	C₂	semidirect
20. C₈×C₂₈₁	SD₁₆	semidirect
27. C₂₈₁	#1705	semidirect
31. C₈²	D₂₈₁	semidirect
48. C₈	#17985127	semidirect

Maximal subgroups

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

subgroup	index
#31823861	2
#31823836	2
C₈²×C₂₈₁	2
#1705	281