Subgroups — #16845467

Order 3968.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521007	C₂	1	3	yes	maximal
2	#14520806	C₂	1	3	yes	maximal
3	C₃₁×#338	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₃₁	C₂²	1	3	yes	—
5	#11758503	C₂²	1	3	yes	—
6	C₂²×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
7	#11758403	C₄	1	6	yes	complemented
8	C₈×Dic₃₁	C₄	1	6	yes	complemented
9	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
10	M₁₆×C₃₁	—	2	6	no	—
11	C₂×C₈×C₃₁	C₂×C₄	1	6	yes	—
12	C₂²⋊Dic₃₁	—	2	3	no	—
13	C₄⋊Dic₃₁	—	2	3	no	—
14	C₄×Dic₃₁	C₂×C₄	1	6	yes	—
15	C₂×C₃₁⋊C₈	C₂×C₄	1	3	yes	—
16	C₂×C₃₁⋊C₈	C₂×C₄	1	3	yes	—
17	C₂³×C₃₁	#41	1	1	yes	characteristic
18	C₂×C₄×C₃₁	C₂²×C₄	1	3	yes	—
19	C₂×C₄×C₃₁	#41	1	3	yes	—
20	C₂×Dic₃₁	—	2	6	no	—
21	C₈×C₃₁	—	2	6	no	—
22	C₃₁⋊C₈	C₄²	1	1	yes	characteristic
23	C₃₁⋊C₈	C₄²	1	3	yes	—
24	#1747	—	31	1	no	maximal, Sylow
25	C₂²×C₃₁	—	4	1	no	—
26	C₂²×C₃₁	#117	1	3	yes	—
27	C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
28	C₄×C₃₁	#117	1	3	yes	—
29	Dic₃₁	—	4	6	no	—
30	#405	—	31	3	no	—
31	#338	D₃₁	1	1	yes	characteristic
32	H(3,ℤ/4)	—	31	3	no	—
33	C₂×C₃₁	—	2	3	no	—
34	C₂×C₃₁	#376	1	1	yes	characteristic
35	C₂×M₁₆	C₂×D₃₁	1	3	yes	—
36	C₂²×C₈	—	31	1	no	—
37	#117	—	31	3	no	—
38	#97	—	31	6	no	—
39	C₄×C₈	—	31	6	no	—
40	C₃₁	#1747	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	31	3	no	—
44	C₂×C₈	—	31	3	no	—
45	C₂×C₈	C₄×D₃₁	1	6	yes	—
46	C₄⋊C₄	—	62	3	no	—
47	C₂²⋊C₄	—	62	3	no	—
48	C₄²	—	31	6	no	—
49	C₂³	#92499	1	1	yes	characteristic
50	C₂×C₄	—	62	6	no	—
51	C₂×C₄	C₂×C₄×D₃₁	1	3	yes	—
52	C₂×C₄	#92497	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	31	1	no	—
55	C₈	—	31	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#11758469	1	3	yes	—
58	C₄	—	124	6	no	—
59	C₄	C₄²×D₃₁	1	1	yes	characteristic
60	C₄	#11758454	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#14520894	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₃₁
commutator	C₄×C₃₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₃₁×#338	C₂
socle	C₂×C₃₁	#376
prime radical	C₂³×C₃₁	#41
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	#338	D₃₁
hypocenter	C₃₁	#1747
LCS	G ▷ C₄×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
7. #11758403	C₄	semidirect
8. C₈×Dic₃₁	C₄	semidirect
40. C₃₁	#1747	semidirect

Maximal subgroups

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

subgroup	index
#14521007	2
#14520806	2
C₃₁×#338	2
#1747	31