Subgroups — #16843768

Order 3968.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521454	C₂	1	1	yes	maximal, characteristic
2	#14520802	C₂	1	1	yes	maximal, characteristic
3	C₃₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#11758446	—	2	1	no	—
5	C₂×C₁₆×C₃₁	—	2	1	no	—
6	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	#11758406	—	2	1	no	—
8	#11758406	C₄	1	2	yes	—
9	C₄⋊(C₃₁⋊C₈)	—	2	1	no	—
10	C₂×Dic₆₂	—	4	1	no	—
11	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
13	C₄²×C₃₁	D₄	1	1	yes	characteristic
14	C₄⋊Dic₃₁	—	2	2	no	—
15	C₄⋊Dic₃₁	—	4	1	no	—
16	C₂×C₃₁⋊C₈	—	4	1	no	—
17	C₁₆×C₃₁	—	4	1	no	—
18	C₂×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₃₁	D₈	1	1	yes	characteristic
20	C₂×C₄×C₃₁	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₃₁	—	4	2	no	—
22	Dic₆₂	—	8	2	no	—
23	C₈×C₃₁	—	2	1	no	—
24	C₈×C₃₁	SD₁₆	1	1	yes	characteristic
25	C₈×C₃₁	Q₁₆	1	1	yes	characteristic
26	C₃₁⋊C₈	—	8	1	no	—
27	#1365	—	31	1	no	maximal, Sylow
28	C₂²×C₃₁	#102	1	1	yes	characteristic
29	C₄×C₃₁	—	2	1	no	—
30	C₄×C₃₁	#101	1	1	yes	characteristic
31	C₄×C₃₁	#103	1	1	yes	characteristic
32	C₄×C₃₁	SD₃₂	1	1	yes	characteristic
33	C₄×C₃₁	Q₃₂	1	1	yes	characteristic
34	Dic₃₁	—	8	2	no	—
35	#500	—	31	1	no	—
36	C₄⋊C₁₆	D₃₁	1	1	yes	characteristic
37	#335	—	31	1	no	—
38	C₂×C₃₁	#332	1	1	yes	characteristic
39	C₂×C₃₁	#358	1	1	yes	characteristic
40	C₂×C₃₁	#361	1	1	yes	characteristic
41	C₄⋊Q₈	—	62	1	no	—
42	C₂×C₁₆	—	2	1	no	—
43	#107	—	31	2	no	—
44	#107	—	62	1	no	—
45	C₄⋊C₈	—	62	1	no	—
46	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
47	C₃₁	#1365	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	124	1	no	—
49	C₂×C₈	—	124	1	no	—
50	C₂×C₈	C₄×D₃₁	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₃₁	1	1	yes	characteristic
52	C₄⋊C₄	—	62	2	no	—
53	C₄⋊C₄	—	124	1	no	—
54	C₄²	D₁₂₄	1	1	yes	characteristic
55	C₁₆	—	4	1	no	—
56	Q₈	—	248	2	no	—
57	C₂×C₄	—	124	2	no	—
58	C₂×C₄	#92470	1	1	yes	characteristic
59	C₂×C₄	D₂₄₈	1	1	yes	characteristic
60	C₂×C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	248	1	no	—
63	C₈	#92480	1	1	yes	characteristic
64	C₈	#92482	1	1	yes	characteristic
65	C₂²	#11758409	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	248	2	no	—
68	C₄	#11758388	1	1	yes	characteristic
69	C₄	Dic₂₄₈	1	1	yes	characteristic
70	C₄	#11758398	1	1	yes	characteristic
71	C₄	#11758412	1	1	yes	characteristic
72	C₂	#14520794	1	1	yes	characteristic
73	C₂	#14520854	1	1	yes	characteristic
74	C₂	#14520863	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11758409
commutator	C₂×C₈×C₃₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₃₁
Fitting	C₃₁×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₃₁	#102
cosocle	C₄×C₈×C₃₁	C₂²
hypercenter	C₄⋊C₁₆	D₃₁
hypocenter	C₃₁	#1365
LCS	G ▷ C₂×C₈×C₃₁ ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
47. C₃₁	#1365	semidirect

Maximal subgroups

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

subgroup	index
#14521454	2
#14520802	2
C₃₁×C₄⋊C₁₆	2
#1365	31