Subgroups — #16845865

Order 3968.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₃₁⋊C₈)	C₂	1	6	yes	maximal
2	C₃₁×#376	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₃₁	C₂²	1	3	yes	—
4	C₂²×C₃₁⋊C₈	C₂²	1	4	yes	—
5	C₃₁×#95	C₄	1	4	yes	—
6	C₄⋊(C₃₁⋊C₈)	—	2	12	no	—
7	C₂²×C₄×C₃₁	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
9	C₄²×C₃₁	D₄	1	6	yes	—
10	C₄²×C₃₁	Q₈	1	6	yes	—
11	C₂×C₃₁⋊C₈	—	2	12	no	—
12	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₃₁	—	2	12	no	—
14	C₂×C₄×C₃₁	C₄⋊C₄	1	12	yes	—
15	C₂×C₄×C₃₁	C₂×D₄	1	3	yes	—
16	C₂×C₄×C₃₁	C₂×Q₈	1	3	yes	—
17	C₃₁⋊C₈	—	4	4	no	—
18	#1843	—	31	1	no	maximal, Sylow
19	C₂²×C₃₁	C₂×C₄⋊C₄	1	3	yes	—
20	C₂²×C₃₁	#131	1	4	yes	—
21	C₄×C₃₁	—	2	12	no	—
22	C₄×C₃₁	#127	1	1	yes	characteristic
23	C₄×C₃₁	C₄⋊Q₈	1	3	yes	—
24	C₂×C₄⋊C₈	—	31	6	no	—
25	#376	D₃₁	1	1	yes	characteristic
26	C₂×C₃₁	#384	1	1	yes	characteristic
27	C₂×C₃₁	#424	1	6	yes	—
28	C₂²×C₈	—	31	4	no	—
29	C₂×C₄²	C₂×D₃₁	1	3	yes	—
30	C₄⋊C₈	—	62	12	no	—
31	#95	Dic₃₁	1	4	yes	—
32	C₃₁	#1843	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄	C₂×Dic₃₁	1	6	yes	—
34	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
35	C₂×C₈	—	62	12	no	—
36	C₄²	Dic₆₂	1	6	yes	—
37	C₄²	D₁₂₄	1	6	yes	—
38	C₂³	C₂²×Dic₃₁	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₃₁	1	12	yes	—
41	C₂×C₄	C₂×Dic₆₂	1	3	yes	—
42	C₂×C₄	C₂×D₁₂₄	1	3	yes	—
43	C₈	—	124	4	no	—
44	C₂²	C₂×C₄⋊Dic₃₁	1	3	yes	—
45	C₂²	#11758525	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#11758446	1	3	yes	—
48	C₄	#11758451	1	1	yes	characteristic
49	C₂	#14520919	1	1	yes	characteristic
50	C₂	#14521076	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₁
commutator, socle, prime radical	C₂³×C₃₁	C₂²×C₄
Fitting	C₃₁×#376	C₂
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	#376	D₃₁
hypocenter	C₃₁	#1843
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
32. C₃₁	#1843	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₃₁⋊C₈)	2
C₃₁×#376	2
#1843	31