Subgroups — #16847495

Order 3968.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521087	C₂	1	2	yes	maximal
2	#14520877	C₂	1	2	yes	maximal, complemented
3	#14520875	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
6	#11758503	—	2	2	no	—
7	C₂×C₁₆×C₃₁	C₄	1	4	yes	complemented
8	C₂×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
10	#11758406	C₂²	1	4	yes	—
11	#11758405	—	2	2	no	—
12	C₂²×C₄×C₃₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₃₁	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₁	Q₈	1	2	yes	—
16	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
17	C₂²⋊Dic₃₁	—	4	2	no	—
18	C₄⋊Dic₃₁	—	2	4	no	—
19	C₄×Dic₃₁	—	4	2	no	—
20	C₁₆×C₃₁	C₂×C₄	1	2	yes	—
21	C₁₆×C₃₁	C₂×C₄	1	2	yes	—
22	C₂³×C₃₁	D₈	1	1	yes	characteristic
23	C₂×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₃₁	D₈	1	1	yes	characteristic
25	C₂×C₄×C₃₁	Q₁₆	1	2	yes	—
26	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₃₁	—	4	4	no	—
28	C₈×C₃₁	C₄⋊C₄	1	2	yes	—
29	C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₃₁	C₂×Q₈	1	1	yes	characteristic
31	#2158	—	31	1	no	maximal, Sylow
32	C₂²×C₃₁	—	2	2	no	—
33	C₂²×C₃₁	#107	1	2	yes	—
34	C₂²×C₃₁	C₂×D₈	1	1	yes	characteristic
35	C₄×C₃₁	#107	1	2	yes	—
36	C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₄×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
38	Dic₃₁	—	8	4	no	—
39	C₂²×C₁₆	D₃₁	1	1	yes	characteristic
40	#427	—	31	2	no	—
41	#367	—	31	2	no	—
42	#366	—	31	2	no	—
43	C₂×C₃₁	—	2	2	no	—
44	C₂×C₃₁	C₂×#107	1	1	yes	characteristic
45	C₂×C₃₁	#508	1	2	yes	—
46	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic
47	#117	—	62	2	no	—
48	C₂×C₁₆	Dic₃₁	1	4	yes	complemented
49	C₂×C₁₆	C₂×D₃₁	1	1	yes	characteristic
50	C₂×C₁₆	C₂×D₃₁	1	1	yes	characteristic
51	#107	—	31	4	no	—
52	#106	—	62	2	no	—
53	C₃₁	#2158	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	D₁₂₄	1	1	yes	characteristic
55	C₂×C₈	Dic₆₂	1	2	yes	—
56	C₂×C₈	D₁₂₄	1	1	yes	characteristic
57	C₂×C₈	C₂×Dic₃₁	1	2	yes	—
58	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
59	C₄⋊C₄	—	62	4	no	—
60	C₂²⋊C₄	—	124	2	no	—
61	C₄²	—	124	2	no	—
62	C₁₆	C₂×Dic₃₁	1	2	yes	—
63	C₁₆	C₂×Dic₃₁	1	2	yes	—
64	C₂³	D₂₄₈	1	1	yes	characteristic
65	C₂×C₄	—	124	4	no	—
66	C₂×C₄	D₂₄₈	1	1	yes	characteristic
67	C₂×C₄	Dic₁₂₄	1	2	yes	—
68	C₂×C₄	C₄⋊Dic₃₁	1	2	yes	—
69	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
70	C₈	C₄⋊Dic₃₁	1	2	yes	—
71	C₈	C₂×Dic₆₂	1	1	yes	characteristic
72	C₈	C₂²×Dic₃₁	1	1	yes	characteristic
73	C₂²	—	2	2	no	—
74	C₂²	#11758406	1	2	yes	—
75	C₂²	C₂×D₂₄₈	1	1	yes	characteristic
76	C₄	—	248	4	no	—
77	C₄	#11758406	1	2	yes	—
78	C₄	C₂×Dic₁₂₄	1	1	yes	characteristic
79	C₄	C₂×C₄⋊Dic₃₁	1	1	yes	characteristic
80	C₂	—	2	2	no	—
81	C₂	C₂×#11758406	1	1	yes	characteristic
82	C₂	#14521481	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₂₄₈
commutator	C₈×C₃₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₁
Fitting	C₂²×C₁₆×C₃₁	C₂
socle	C₂²×C₃₁	C₂×D₈
prime radical	C₂³×C₃₁	D₈
cosocle	C₂×C₈×C₃₁	C₂³
hypercenter	C₂²×C₁₆	D₃₁
hypocenter	C₃₁	#2158
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14520877	C₂	semidirect
3. #14520875	C₂	semidirect
7. C₂×C₁₆×C₃₁	C₄	semidirect
48. C₂×C₁₆	Dic₃₁	semidirect
53. C₃₁	#2158	semidirect

Maximal subgroups

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

subgroup	index
#14521087	2
#14520877	2
#14520875	2
C₂²×C₁₆×C₃₁	2
#2158	31