Subgroups — #16843694

Order 3968.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521179	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#346	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₆₂	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₃₁	—	2	1	no	—
6	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	#11758403	—	2	1	no	—
8	Dic₃₁⋊C₈	—	2	1	no	—
9	C₂×C₃₁⋊C₁₆	—	2	1	no	—
10	C₄⋊(C₃₁⋊C₈)	C₄	1	1	yes	characteristic
11	C₂×Dic₆₂	C₈	1	1	yes	characteristic
12	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
14	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₃₁	C₈	1	1	yes	characteristic
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	—	2	1	no	—
18	C₂×C₃₁⋊C₈	—	2	1	no	—
19	C₁₆×C₃₁	—	2	2	no	—
20	C₃₁⋊C₁₆	—	4	1	no	—
21	C₂×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₃₁	M₁₆	1	1	yes	characteristic
24	C₂×Dic₃₁	—	2	1	no	—
25	C₂×Dic₃₁	—	2	1	no	—
26	Dic₆₂	—	4	1	no	—
27	C₈×C₃₁	—	2	1	no	—
28	C₈×C₃₁	SD₁₆	1	1	yes	characteristic
29	C₈×C₃₁	Q₁₆	1	1	yes	characteristic
30	C₃₁⋊C₈	—	4	1	no	—
31	#1338	—	31	1	no	maximal, Sylow
32	C₂²×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₃₁	—	2	1	no	—
34	C₄×C₃₁	—	2	1	no	—
35	C₄×C₃₁	#103	1	1	yes	characteristic
36	C₄×C₃₁	#104	1	1	yes	characteristic
37	Dic₃₁	—	4	1	no	—
38	Dic₃₁	—	4	1	no	—
39	#446	—	31	1	no	—
40	C₄⋊C₁₆	—	31	1	no	—
41	#346	D₃₁	1	1	yes	characteristic
42	C₂×C₃₁	Q₈⋊C₈	1	1	yes	characteristic
43	C₂×C₃₁	#349	1	1	yes	characteristic
44	C₂×C₃₁	#350	1	1	yes	characteristic
45	C₄×Q₈	—	31	1	no	—
46	C₂×C₁₆	—	2	1	no	—
47	C₂×C₁₆	—	62	1	no	—
48	C₄⋊C₈	—	31	1	no	—
49	C₄⋊C₈	—	62	1	no	—
50	#97	—	62	1	no	—
51	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
52	C₃₁	#1338	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₈	—	31	1	no	—
54	C₂×C₈	—	62	1	no	—
55	C₂×C₈	D₁₂₄	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₃₁	1	1	yes	characteristic
57	C₄⋊C₄	—	31	1	no	—
58	C₄⋊C₄	—	62	1	no	—
59	C₄²	—	62	1	no	—
60	C₄²	C₄×D₃₁	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₆	—	124	1	no	—
63	Q₈	—	124	1	no	—
64	C₂×C₄	—	62	1	no	—
65	C₂×C₄	—	62	1	no	—
66	C₂×C₄	C₈×D₃₁	1	1	yes	characteristic
67	C₂×C₄	#92469	1	1	yes	characteristic
68	C₂×C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	124	1	no	—
71	C₈	#92470	1	1	yes	characteristic
72	C₈	Dic₁₂₄	1	1	yes	characteristic
73	C₂²	(C₂×D₃₁)⋊C₈	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	124	1	no	—
77	C₄	—	124	1	no	—
78	C₄	#11758393	1	1	yes	characteristic
79	C₄	#11758404	1	1	yes	characteristic
80	C₂	#14520781	1	1	yes	characteristic
81	C₂	#14520830	1	1	yes	characteristic
82	C₂	#14520834	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₃₁)⋊C₄
commutator	C₂×C₄×C₃₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₁
Fitting	C₃₁×#346	C₂
socle, prime radical	C₂²×C₃₁	C₂²⋊C₈
cosocle	C₄×C₈×C₃₁	C₂²
hypercenter	#346	D₃₁
hypocenter	C₃₁	#1338
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
52. C₃₁	#1338	semidirect

Maximal subgroups

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

subgroup	index
#14521179	2
C₄⋊(C₃₁⋊C₁₆)	2
C₃₁×#346	2
#1338	31