Subgroups — #49094921

Order 35968.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823868	C₂	1	4	yes	maximal
2	#31823843	C₂	1	2	yes	maximal
3	C₈²×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₂₄	—	2	4	no	—
5	#22582879	C₂²	1	4	yes	—
6	#22582813	—	2	8	no	—
7	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₂₈₁	C₂²	1	2	yes	—
9	C₂×Dic₅₆₂	—	2	4	no	—
10	Dic₁₁₂₄	—	4	8	no	—
11	C₄⋊Dic₂₈₁	—	2	8	no	—
12	C₂×C₈×C₂₈₁	D₄	1	2	yes	—
13	C₂×C₈×C₂₈₁	D₄	1	4	yes	—
14	C₄²×C₂₈₁	C₂³	1	1	yes	characteristic
15	Dic₅₆₂	—	4	8	no	—
16	C₂×Dic₂₈₁	—	4	4	no	—
17	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₈₁	C₂×D₄	1	2	yes	—
19	C₈×C₂₈₁	D₈	1	4	yes	—
20	C₈×C₂₈₁	Q₁₆	1	8	yes	complemented
21	C₂²×C₂₈₁	#127	1	1	yes	characteristic
22	C₄×C₂₈₁	C₂×D₈	1	2	yes	—
23	C₄×C₂₈₁	C₂×Q₁₆	1	4	yes	—
24	Dic₂₈₁	—	8	4	no	—
25	C₂×C₂₈₁	#493	1	1	yes	characteristic
26	C₂×C₂₈₁	#494	1	2	yes	—
27	C₂₈₁	#1713	1	1	yes	characteristic, complemented, Sylow
28	#1713	—	281	1	no	maximal, Sylow
29	#500	—	281	4	no	—
30	#494	—	281	2	no	—
31	C₈²	D₂₈₁	1	1	yes	characteristic
32	C₂×Q₁₆	—	562	4	no	—
33	C₄⋊Q₈	—	281	4	no	—
34	#107	—	562	8	no	—
35	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
36	C₄×C₈	C₂×D₂₈₁	1	2	yes	—
37	C₂×Q₈	—	562	4	no	—
38	Q₁₆	—	1124	8	no	—
39	C₂×C₈	D₁₁₂₄	1	2	yes	—
40	C₂×C₈	D₁₁₂₄	1	4	yes	—
41	C₄⋊C₄	—	562	8	no	—
42	C₄²	C₂²×D₂₈₁	1	1	yes	characteristic
43	Q₈	—	1124	8	no	—
44	C₂×C₄	—	1124	4	no	—
45	C₂×C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
46	C₂×C₄	C₂×D₁₁₂₄	1	2	yes	—
47	C₈	D₂₂₄₈	1	4	yes	—
48	C₈	Dic₁₁₂₄	1	8	yes	complemented
49	C₂²	#22582876	1	1	yes	characteristic
50	C₄	—	2248	4	no	—
51	C₄	C₂×D₂₂₄₈	1	2	yes	—
52	C₄	C₂×Dic₁₁₂₄	1	4	yes	—
53	C₂	#31823840	1	1	yes	characteristic
54	C₂	#31823843	1	2	yes	—

	subgroup	G/H
center	C₂²	#22582876
commutator, cosocle	C₄²×C₂₈₁	C₂³
Frattini	C₄²	C₂²×D₂₈₁
Fitting	C₈²×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	#127
hypercenter	C₈²	D₂₈₁
hypocenter	C₂₈₁	#1713
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
20. C₈×C₂₈₁	Q₁₆	semidirect
27. C₂₈₁	#1713	semidirect
48. C₈	Dic₁₁₂₄	semidirect

Maximal subgroups

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

subgroup	index
#31823868	2
#31823843	2
C₈²×C₂₈₁	2
#1713	281