Subgroups — #49095475

Order 35968.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22582815	C₂	1	4	yes	maximal
2	#31823487	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985122	C₂²	1	4	yes	—
5	#22582815	—	2	8	no	—
6	C₄⋊#14555886	—	2	4	no	—
7	C₂²×C₈×C₂₈₁	C₂²	1	2	yes	—
8	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₂₈₁	C₄	1	2	yes	—
10	C₄×C₈×C₂₈₁	C₄	1	2	yes	—
11	#17985122	—	2	8	no	—
12	C₂×#14555886	—	2	4	no	—
13	C₂²×C₄×C₂₈₁	Q₈	1	2	yes	—
14	C₂²×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₂₈₁	C₂×C₄	1	4	yes	—
16	C₂×C₈×C₂₈₁	D₄	1	4	yes	—
17	C₂×C₈×C₂₈₁	Q₈	1	4	yes	—
18	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₂₈₁	D₄	1	2	yes	—
21	#14555886	—	4	4	no	—
22	C₂³×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
23	C₂×C₄×C₂₈₁	—	2	4	no	—
24	C₂×C₄×C₂₈₁	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₂₈₁	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₈₁	C₂×D₄	1	2	yes	—
28	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₂₈₁	C₂×Q₈	1	2	yes	—
30	C₈×C₂₈₁	C₄⋊C₄	1	8	yes	—
31	C₂²×C₂₈₁	—	2	2	no	—
32	C₂²×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₂₈₁	C₄⋊Q₈	1	2	yes	—
34	C₄×C₂₈₁	—	2	2	no	—
35	C₄×C₂₈₁	#108	1	4	yes	complemented
36	C₄×C₂₈₁	C₂×C₄⋊C₄	1	2	yes	—
37	C₄×C₂₈₁	#127	1	1	yes	characteristic
38	C₄×C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₂₈₁	—	2	2	no	—
40	C₂×C₂₈₁	#384	1	1	yes	characteristic
41	C₂×C₂₈₁	C₂×#108	1	2	yes	—
42	C₂₈₁	#1848	1	1	yes	characteristic, complemented, Sylow
43	#1848	—	281	1	no	maximal, Sylow
44	C₂×#108	—	281	4	no	—
45	#423	—	281	2	no	—
46	C₂×C₄×C₈	D₂₈₁	1	1	yes	characteristic
47	C₂×M₁₆	—	281	4	no	—
48	C₂²×C₈	C₂×D₂₈₁	1	2	yes	—
49	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
50	#108	—	562	8	no	—
51	C₄⋊C₈	—	562	4	no	—
52	C₄×C₈	Dic₂₈₁	1	2	yes	—
53	C₄×C₈	Dic₂₈₁	1	2	yes	—
54	C₂²×C₄	Dic₅₆₂	1	2	yes	—
55	C₂²×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
56	M₁₆	—	562	8	no	—
57	C₂×C₈	—	562	4	no	—
58	C₂×C₈	C₂×Dic₂₈₁	1	4	yes	—
59	C₂×C₈	D₁₁₂₄	1	4	yes	—
60	C₂×C₈	Dic₅₆₂	1	4	yes	—
61	C₄²	C₂×Dic₂₈₁	1	1	yes	characteristic
62	C₄²	C₂×Dic₂₈₁	1	1	yes	characteristic
63	C₄²	D₁₁₂₄	1	2	yes	—
64	C₂³	C₂×Dic₅₆₂	1	1	yes	characteristic
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₄⋊Dic₂₈₁	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₂₈₁	1	2	yes	—
68	C₂×C₄	C₂²×Dic₂₈₁	1	1	yes	characteristic
69	C₂×C₄	C₂×D₁₁₂₄	1	2	yes	—
70	C₂×C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
71	C₂×C₄	C₂×Dic₅₆₂	1	2	yes	—
72	C₈	—	1124	4	no	—
73	C₈	C₄⋊Dic₂₈₁	1	8	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	C₂×C₄⋊Dic₂₈₁	1	1	yes	characteristic
76	C₂²	#22582879	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	#22582815	1	4	yes	complemented
79	C₄	C₂×C₄⋊Dic₂₈₁	1	2	yes	—
80	C₄	#22582876	1	1	yes	characteristic
81	C₄	#22582879	1	1	yes	characteristic
82	C₂	—	2	2	no	—
83	C₂	#31823333	1	1	yes	characteristic
84	C₂	C₂×#22582815	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁₂₄
commutator	C₂×C₄×C₂₈₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₈₁
Fitting	C₂×C₄×C₈×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂×C₄⋊C₄
prime radical	C₂³×C₂₈₁	C₂×Q₈
cosocle	C₂²×C₄×C₂₈₁	C₂³
hypercenter	C₂×C₄×C₈	D₂₈₁
hypocenter	C₂₈₁	#1848
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
35. C₄×C₂₈₁	#108	semidirect
42. C₂₈₁	#1848	semidirect
78. C₄	#22582815	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22582815	2
#31823487	2
C₂×C₄×C₈×C₂₈₁	2
#1848	281