Subgroups — #49097613

Order 35968.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823896	C₂	1	2	yes	maximal, complemented
2	#31823300	C₂	1	2	yes	maximal, complemented
3	D₈₉₉₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₆₄×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#22582902	—	2	2	no	—
7	#22582822	—	2	2	no	—
8	D₄₄₉₆	C₂²	1	2	yes	—
9	C₁₆×D₂₈₁	C₂²	1	1	yes	characteristic
10	#22582785	C₂²	1	1	yes	characteristic
11	Q₃₂×C₂₈₁	C₂²	1	2	yes	—
12	C₃₂×C₂₈₁	C₂²	1	1	yes	characteristic
13	#17985139	—	4	2	no	—
14	#17985125	—	4	2	no	—
15	D₂₂₄₈	—	2	2	no	—
16	C₈×D₂₈₁	D₄	1	1	yes	characteristic
17	#17985113	D₄	1	1	yes	characteristic
18	Q₁₆×C₂₈₁	—	2	2	no	—
19	C₁₆×C₂₈₁	C₂³	1	1	yes	characteristic
20	D₁₁₂₄	—	4	2	no	—
21	D₁₁₂₄	—	8	2	no	—
22	C₄×D₂₈₁	—	8	2	no	—
23	C₄×D₂₈₁	D₈	1	1	yes	characteristic
24	#14555886	D₈	1	1	yes	characteristic
25	Q₈×C₂₈₁	—	4	2	no	—
26	C₈×C₂₈₁	C₂×D₄	1	1	yes	characteristic
27	C₂×D₂₈₁	—	8	2	no	—
28	C₂×D₂₈₁	D₁₆	1	1	yes	characteristic
29	C₄×C₂₈₁	—	8	2	no	—
30	C₄×C₂₈₁	C₂×D₈	1	1	yes	characteristic
31	Dic₂₈₁	D₁₆	1	1	yes	characteristic
32	C₂×C₂₈₁	C₂×D₁₆	1	1	yes	characteristic
33	D₂₈₁	—	2	1	no	—
34	D₂₈₁	—	16	2	no	—
35	C₂₈₁	#2262	1	1	yes	characteristic, complemented, Sylow
36	#2262	—	281	1	no	maximal, Sylow
37	#508	—	281	2	no	—
38	Q₆₄	D₂₈₁	1	1	yes	characteristic, complemented
39	SD₆₄	—	281	2	no	—
40	D₃₂	—	281	1	no	—
41	C₂×C₃₂	—	281	1	no	—
42	#135	—	562	2	no	—
43	Q₃₂	C₂×D₂₈₁	1	2	yes	—
44	SD₃₂	—	562	2	no	—
45	D₁₆	—	281	2	no	—
46	C₂×C₁₆	—	281	1	no	—
47	C₃₂	—	281	1	no	—
48	C₃₂	C₂×D₂₈₁	1	1	yes	characteristic
49	#41	—	1124	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	1124	2	no	—
52	D₈	—	562	2	no	—
53	C₂×C₈	—	281	1	no	—
54	C₁₆	—	281	1	no	—
55	C₁₆	C₂²×D₂₈₁	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	1124	2	no	—
58	D₄	—	2248	2	no	—
59	C₂×C₄	—	281	1	no	—
60	C₂×C₄	—	2248	2	no	—
61	C₈	—	281	1	no	—
62	C₈	D₄×D₂₈₁	1	1	yes	characteristic
63	C₂²	—	281	1	no	—
64	C₂²	—	2248	2	no	—
65	C₄	—	8	2	no	—
66	C₄	—	281	1	no	—
67	C₄	D₈×D₂₈₁	1	1	yes	characteristic
68	C₂	—	562	1	no	—
69	C₂	—	4496	2	no	—
70	C₂	D₁₆×D₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₂₈₁
commutator, cosocle	C₁₆×C₂₈₁	C₂³
Frattini	C₁₆	C₂²×D₂₈₁
Fitting	Q₆₄×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₂×D₁₆
hypercenter	Q₆₄	D₂₈₁
hypocenter	C₂₈₁	#2262
LCS	G ▷ C₁₆×C₂₈₁ ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #31823896	C₂	semidirect
2. #31823300	C₂	semidirect
3. D₈₉₉₂	C₂	semidirect
4. C₃₂×D₂₈₁	C₂	semidirect
5. Q₆₄×C₂₈₁	C₂	semidirect
35. C₂₈₁	#2262	semidirect
38. Q₆₄	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823896	2
#31823300	2
D₈₉₉₂	2
C₃₂×D₂₈₁	2
Q₆₄×C₂₈₁	2
#2262	281