Subgroups — #49097577

Order 35968.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823867	C₂	1	2	yes	maximal
2	#31823289	C₂	1	1	yes	maximal, characteristic
3	#31823288	C₂	1	2	yes	maximal
4	C₁₆×Dic₂₈₁	C₂	1	1	yes	maximal, characteristic
5	#366×C₂₈₁	C₂	1	1	yes	maximal, characteristic
6	#22582878	—	2	2	no	—
7	C₂×#17985113	C₂²	1	1	yes	characteristic
8	#22582813	C₂²	1	2	yes	—
9	#22582812	—	2	2	no	—
10	C₈×Dic₂₈₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
12	#107×C₂₈₁	C₂²	1	2	yes	—
13	C₂×Dic₅₆₂	—	4	2	no	—
14	C₂×#14555886	D₄	1	1	yes	characteristic
15	C₄⋊Dic₂₈₁	—	2	2	no	—
16	#17985117	—	4	2	no	—
17	C₄×Dic₂₈₁	D₄	1	1	yes	characteristic
18	#17985113	Q₈	1	2	yes	complemented
19	C₂×C₈×C₂₈₁	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₂₈₁	—	2	2	no	—
21	C₁₆×C₂₈₁	Q₈	1	2	yes	complemented
22	Dic₅₆₂	—	8	4	no	—
23	C₂×Dic₂₈₁	—	4	2	no	—
24	C₂×Dic₂₈₁	D₈	1	1	yes	characteristic
25	C₂×Dic₂₈₁	D₈	1	1	yes	characteristic
26	#14555886	Q₁₆	1	2	yes	—
27	C₂×C₄×C₂₈₁	—	4	2	no	—
28	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
29	C₈×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
30	C₈×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₂₈₁	C₂×D₈	1	1	yes	characteristic
32	C₄×C₂₈₁	—	8	2	no	—
33	C₄×C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic
34	C₄×C₂₈₁	C₂×Q₁₆	1	1	yes	characteristic
35	Dic₂₈₁	—	8	2	no	—
36	Dic₂₈₁	D₁₆	1	2	yes	—
37	Dic₂₈₁	Q₃₂	1	2	yes	—
38	C₂×C₂₈₁	#500	1	1	yes	characteristic
39	C₂×C₂₈₁	C₂×D₁₆	1	1	yes	characteristic
40	C₂×C₂₈₁	C₂×Q₃₂	1	1	yes	characteristic
41	C₂₈₁	#2252	1	1	yes	characteristic, complemented, Sylow
42	#2252	—	281	1	no	maximal, Sylow
43	#500	—	281	2	no	—
44	#366	—	281	1	no	—
45	#366	—	281	2	no	—
46	#366	D₂₈₁	1	1	yes	characteristic
47	C₄×C₁₆	—	281	1	no	—
48	C₄⋊Q₈	—	562	2	no	—
49	C₂×C₁₆	—	281	1	no	—
50	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
51	#107	—	281	2	no	—
52	#107	—	562	2	no	—
53	#107	C₂×D₂₈₁	1	2	yes	—
54	C₄×C₈	—	281	1	no	—
55	C₂×Q₈	—	1124	2	no	—
56	C₂×C₈	—	281	1	no	—
57	C₂×C₈	C₂²×D₂₈₁	1	1	yes	characteristic
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	—	562	2	no	—
60	C₄⋊C₄	—	1124	2	no	—
61	C₄²	—	281	1	no	—
62	C₁₆	—	281	2	no	—
63	C₁₆	Dic₅₆₂	1	2	yes	complemented
64	Q₈	—	2248	4	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	281	1	no	—
67	C₂×C₄	—	281	1	no	—
68	C₂×C₄	—	1124	2	no	—
69	C₂×C₄	D₄×D₂₈₁	1	1	yes	characteristic
70	C₈	—	281	2	no	—
71	C₈	Q₈×D₂₈₁	1	1	yes	characteristic
72	C₈	C₂×Dic₅₆₂	1	1	yes	characteristic
73	C₂²	D₈×D₂₈₁	1	1	yes	characteristic
74	C₄	—	8	2	no	—
75	C₄	—	281	2	no	—
76	C₄	—	281	2	no	—
77	C₄	—	2248	2	no	—
78	C₄	#22582878	1	1	yes	characteristic
79	C₄	Q₁₆×D₂₈₁	1	1	yes	characteristic
80	C₂	#31823867	1	1	yes	characteristic
81	C₂	D₁₆×D₂₈₁	1	1	yes	characteristic
82	C₂	Q₃₂×D₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₂₈₁
commutator, cosocle	C₂×C₈×C₂₈₁	C₂³
Frattini	C₂×C₈	C₂²×D₂₈₁
Fitting	#366×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₂×D₈
hypercenter	#366	D₂₈₁
hypocenter	C₂₈₁	#2252
LCS	G ▷ C₂×C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
18. #17985113	Q₈	semidirect
21. C₁₆×C₂₈₁	Q₈	semidirect
41. C₂₈₁	#2252	semidirect
63. C₁₆	Dic₅₆₂	semidirect

Maximal subgroups

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

subgroup	index
#31823867	2
#31823289	2
#31823288	2
C₁₆×Dic₂₈₁	2
#366×C₂₈₁	2
#2252	281