Subgroups — #46834567

Order 34688.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#31773727	C₂	1	1	yes	maximal, characteristic
3	#368×C₂₇₁	C₂	1	1	yes	maximal, characteristic
4	#22576096	—	2	1	no	—
5	C₂₇₁⋊C₃₂	C₄	1	2	yes	—
6	C₂×C₁₆×C₂₇₁	C₂²	1	1	yes	characteristic
7	#108×C₂₇₁	—	2	1	no	—
8	#16864638	—	4	1	no	—
9	M₁₆×C₂₇₁	—	4	1	no	—
10	C₂×C₈×C₂₇₁	D₄	1	1	yes	characteristic
11	C₁₆×C₂₇₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₇₁	Q₈	1	1	yes	characteristic
13	C₂₇₁⋊C₈	—	8	1	no	—
14	C₂×C₄×C₂₇₁	D₈	1	1	yes	characteristic
15	C₈×C₂₇₁	—	8	1	no	—
16	C₈×C₂₇₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₇₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₇₁	Q₃₂	1	1	yes	characteristic
19	C₄×C₂₇₁	#107	1	1	yes	characteristic
20	C₄×C₂₇₁	D₁₆	1	1	yes	characteristic
21	C₂×C₂₇₁	—	2	1	no	—
22	C₂×C₂₇₁	#366	1	1	yes	characteristic
23	C₂₇₁	#1425	1	1	yes	characteristic, complemented, Sylow
24	#1425	—	271	1	no	maximal, Sylow
25	C₂×C₃₂	—	271	1	no	—
26	#368	—	271	1	no	—
27	#368	D₂₇₁	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₂₇₁	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	542	1	no	—
31	C₃₂	—	271	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	1084	1	no	—
34	C₂×C₈	C₂²⋊D₂₇₁	1	1	yes	characteristic
35	C₁₆	C₄×D₂₇₁	1	1	yes	characteristic
36	C₁₆	Dic₅₄₂	1	1	yes	characteristic
37	C₂×C₄	#16864639	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	2168	1	no	—
40	C₈	Dic₂₇₁⋊C₄	1	1	yes	characteristic
41	C₈	#16864644	1	1	yes	characteristic
42	C₂²	#22576106	1	1	yes	characteristic
43	C₄	#22576093	1	1	yes	characteristic
44	C₄	#22576101	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#31773722	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22576101
commutator	C₁₆×C₂₇₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₇₁
Fitting	#368×C₂₇₁	C₂
socle	C₂×C₂₇₁	#366
prime radical	C₂²×C₂₇₁	Q₃₂
cosocle	C₂×C₁₆×C₂₇₁	C₂²
hypercenter	#368	D₂₇₁
hypocenter	C₂₇₁	#1425
LCS	G ▷ C₁₆×C₂₇₁ ▷ C₈×C₂₇₁ ▷ C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
23. C₂₇₁	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₇₁⋊C₃₂	2
#31773727	2
#368×C₂₇₁	2
#1425	271