Subgroups — #16854098

Order 3968.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14520947	C₂	1	4	yes	maximal
2	#14520933	C₂	1	8	yes	maximal
3	#14520915	C₂	1	2	yes	maximal
4	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄²×C₃₁	C₂²	1	4	yes	—
6	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₃₁	C₂²	1	4	yes	—
9	C₂×Dic₃₁⋊C₄	C₂²	1	8	yes	—
10	C₃₁⋊#95	C₂²	1	8	yes	—
11	C₃₁⋊#95	C₂²	1	8	yes	—
12	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
13	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
14	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
15	C₂²×Dic₃₁	C₂³	1	8	yes	—
16	C₄²×C₃₁	—	2	8	no	—
17	C₄²×C₃₁	—	2	4	no	—
18	C₄²×C₃₁	Q₈	1	4	yes	—
19	C₄⋊Dic₃₁	—	2	8	no	—
20	Dic₃₁⋊C₄	—	2	16	no	—
21	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
22	C₂×C₄×C₃₁	—	2	4	no	—
23	C₂×C₄×C₃₁	—	2	4	no	—
24	C₂×C₄×C₃₁	—	2	4	no	—
25	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
26	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
27	C₂×C₄×C₃₁	#41	1	8	yes	—
28	C₂×C₄×C₃₁	#41	1	4	yes	—
29	C₂×Dic₃₁	—	2	16	no	—
30	C₂×Dic₃₁	—	2	8	no	—
31	#2864	—	31	1	no	maximal, Sylow
32	C₂²×C₃₁	C₂²×Q₈	1	1	yes	characteristic
33	C₂²×C₃₁	C₂×#41	1	2	yes	—
34	C₂²×C₃₁	C₂×#41	1	4	yes	—
35	C₄×C₃₁	—	2	8	no	—
36	C₄×C₃₁	—	2	4	no	—
37	C₄×C₃₁	#125	1	4	yes	—
38	Dic₃₁	—	4	8	no	—
39	#389	—	31	4	no	—
40	#387	—	31	8	no	—
41	#382	—	31	2	no	—
42	C₄³	D₃₁	1	1	yes	characteristic
43	C₂×C₃₁	C₂×#125	1	1	yes	characteristic
44	C₂×C₃₁	#529	1	4	yes	—
45	C₂×C₃₁	#533	1	2	yes	—
46	C₂×C₄⋊C₄	—	31	4	no	—
47	C₂×C₄⋊C₄	—	31	8	no	—
48	C₂×C₄²	C₂×D₃₁	1	4	yes	—
49	C₂×C₄²	C₂×D₃₁	1	2	yes	—
50	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
51	#95	—	31	8	no	—
52	#95	—	31	8	no	—
53	C₃₁	#2864	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	—	31	8	no	—
55	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
56	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
57	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
58	C₄⋊C₄	—	62	16	no	—
59	C₄⋊C₄	—	62	8	no	—
60	C₄²	—	2	8	no	—
61	C₄²	—	2	4	no	—
62	C₄²	Dic₆₂	1	4	yes	—
63	C₂³	C₂³×D₃₁	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	62	16	no	—
68	C₂×C₄	—	62	8	no	—
69	C₂×C₄	C₂×Dic₆₂	1	4	yes	—
70	C₂×C₄	C₂×Dic₆₂	1	2	yes	—
71	C₂×C₄	#92495	1	8	yes	—
72	C₂×C₄	#92495	1	4	yes	—
73	C₂²	C₂²×Dic₆₂	1	1	yes	characteristic
74	C₂²	C₂×#92495	1	4	yes	—
75	C₂²	C₂×#92495	1	2	yes	—
76	C₄	—	2	4	no	—
77	C₄	—	2	8	no	—
78	C₄	—	124	8	no	—
79	C₄	#11758447	1	4	yes	—
80	C₂	C₂×#11758447	1	1	yes	characteristic
81	C₂	#14521583	1	4	yes	—
82	C₂	#14521606	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator, socle, prime radical, cosocle	C₂³×C₃₁	C₂⁴
Fitting	C₄³×C₃₁	C₂
hypercenter	C₄³	D₃₁
hypocenter	C₃₁	#2864
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
53. C₃₁	#2864	semidirect

Maximal subgroups

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

subgroup	index
#14520947	2
#14520933	2
#14520915	2
C₄³×C₃₁	2
#2864	31