Subgroups — #16843767

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	C₄⋊(C₃₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#335	C₂	1	1	yes	maximal, characteristic
4	#11758446	—	2	1	no	—
5	C₃₁×C₄⋊C₈	—	2	1	no	—
6	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	#11758406	—	2	1	no	—
8	#11758406	C₄	1	2	yes	—
9	C₂×C₃₁⋊C₁₆	—	2	1	no	—
10	C₂×Dic₆₂	—	4	1	no	—
11	C₂×C₈×C₃₁	—	4	1	no	—
12	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
14	C₄²×C₃₁	D₄	1	1	yes	characteristic
15	C₄⋊Dic₃₁	—	2	2	no	—
16	C₄⋊Dic₃₁	—	4	1	no	—
17	C₃₁⋊C₁₆	—	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	1	no	—
23	Dic₆₂	—	8	1	no	—
24	C₈×C₃₁	—	2	1	no	—
25	C₈×C₃₁	—	8	1	no	—
26	C₈×C₃₁	SD₁₆	1	1	yes	characteristic
27	C₈×C₃₁	Q₁₆	1	1	yes	characteristic
28	#1364	—	31	1	no	maximal, Sylow
29	C₂²×C₃₁	#102	1	1	yes	characteristic
30	C₄×C₃₁	—	2	1	no	—
31	C₄×C₃₁	#101	1	1	yes	characteristic
32	C₄×C₃₁	#103	1	1	yes	characteristic
33	C₄×C₃₁	D₁₆	1	1	yes	characteristic
34	C₄×C₃₁	SD₃₂	1	1	yes	characteristic
35	Dic₃₁	—	8	2	no	—
36	#500	—	31	1	no	—
37	C₄⋊C₁₆	—	31	1	no	—
38	#335	D₃₁	1	1	yes	characteristic
39	C₂×C₃₁	#332	1	1	yes	characteristic
40	C₂×C₃₁	#357	1	1	yes	characteristic
41	C₂×C₃₁	#362	1	1	yes	characteristic
42	C₄⋊Q₈	—	62	1	no	—
43	C₂×C₁₆	—	62	1	no	—
44	#107	—	31	2	no	—
45	#107	—	62	1	no	—
46	C₄⋊C₈	—	2	1	no	—
47	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
48	C₃₁	#1364	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₈	—	124	1	no	—
50	C₂×C₈	—	4	1	no	—
51	C₂×C₈	C₄×D₃₁	1	1	yes	characteristic
52	C₂×C₈	D₁₂₄	1	1	yes	characteristic
53	C₄⋊C₄	—	62	2	no	—
54	C₄⋊C₄	—	124	1	no	—
55	C₄²	C₂²⋊D₃₁	1	1	yes	characteristic
56	C₁₆	—	124	1	no	—
57	Q₈	—	248	1	no	—
58	Q₈	—	248	1	no	—
59	C₂×C₄	—	124	2	no	—
60	C₂×C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
61	C₂×C₄	#92479	1	1	yes	characteristic
62	C₂×C₄	#92481	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	8	1	no	—
65	C₈	#92470	1	1	yes	characteristic
66	C₈	Dic₁₂₄	1	1	yes	characteristic
67	C₂²	#11758397	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	248	2	no	—
70	C₄	#11758404	1	1	yes	characteristic
71	C₄	#11758412	1	1	yes	characteristic
72	C₄	#11758414	1	1	yes	characteristic
73	C₄	#11758416	1	1	yes	characteristic
74	C₂	#14520796	1	1	yes	characteristic
75	C₂	#14520849	1	1	yes	characteristic
76	C₂	#14520864	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11758397
commutator	C₂×C₈×C₃₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₃₁
Fitting	C₃₁×#335	C₂
socle, prime radical	C₂²×C₃₁	#102
cosocle	C₄×C₈×C₃₁	C₂²
hypercenter	#335	D₃₁
hypocenter	C₃₁	#1364
LCS	G ▷ C₂×C₈×C₃₁ ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
48. C₃₁	#1364	semidirect

Maximal subgroups

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

subgroup	index
#14521454	2
C₄⋊(C₃₁⋊C₁₆)	2
C₃₁×#335	2
#1364	31