Subgroups — C₃₁×#1425 #16841358

Order 3968.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#368	C₂	1	2	yes	maximal
3	C₂×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
4	C₃₁×#108	—	2	2	no	—
5	C₃₁×C₃₂	C₄	1	2	yes	—
6	M₁₆×C₃₁	—	4	2	no	—
7	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
8	C₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₃₁	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₃₁	D₈	1	1	yes	characteristic
11	C₈×C₃₁	—	8	2	no	—
12	C₈×C₃₁	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₃₁	Q₁₆	1	1	yes	characteristic
14	#1425	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₃₁	Q₃₂	1	1	yes	characteristic
16	C₄×C₃₁	#107	1	1	yes	characteristic
17	C₄×C₃₁	D₁₆	1	1	yes	characteristic
18	C₂×C₃₂	C₂×C₃₁	1	1	yes	characteristic
19	#368	C₂×C₃₁	1	2	yes	—
20	C₂×C₃₁	—	2	1	no	—
21	C₂×C₃₁	#366	1	1	yes	characteristic
22	C₂×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
23	#108	—	2	2	no	—
24	C₃₂	C₄×C₃₁	1	2	yes	—
25	C₃₁	#1425	1	1	yes	characteristic, direct product factor, Sylow
26	M₁₆	—	4	2	no	—
27	C₂×C₈	D₄×C₃₁	1	1	yes	characteristic
28	C₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
29	C₁₆	Q₈×C₃₁	1	1	yes	characteristic
30	C₂×C₄	D₈×C₃₁	1	1	yes	characteristic
31	C₈	—	8	2	no	—
32	C₈	C₄⋊C₄×C₃₁	1	1	yes	characteristic
33	C₈	Q₁₆×C₃₁	1	1	yes	characteristic
34	C₂²	C₃₁×Q₃₂	1	1	yes	characteristic
35	C₄	C₃₁×#107	1	1	yes	characteristic
36	C₄	C₃₁×D₁₆	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	C₃₁×#366	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	D₁₆
commutator	C₁₆	C₂×C₄×C₃₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₃₁
socle	C₂×C₃₁	#366
prime radical	C₂²×C₃₁	Q₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₈×C₃₁ ◁ C₂×C₁₆×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
14. #1425	C₃₁	direct (N × H)
25. C₃₁	#1425	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×C₃₂	2
C₃₁×#368	2
#1425	31

Subgroups — C31×#1425 #16841358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#1425 #16841358