Subgroups — #16845831

Order 3968.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₃₁⋊C₈)	C₂	1	2	yes	maximal
2	#14520804	C₂	1	4	yes	maximal
3	C₃₁×#376	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
5	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
6	C₂²×C₃₁⋊C₈	C₂²	1	4	yes	—
7	C₃₁×#95	C₄	1	4	yes	—
8	C₄⋊(C₃₁⋊C₈)	—	2	4	no	—
9	C₂²×C₄×C₃₁	C₂×C₄	1	4	yes	—
10	C₂²×C₄×C₃₁	C₂×C₄	1	2	yes	—
11	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
12	C₄²×C₃₁	—	2	4	no	—
13	C₄²×C₃₁	D₄	1	2	yes	—
14	C₄²×C₃₁	Q₈	1	2	yes	—
15	C₂×C₃₁⋊C₈	—	2	4	no	—
16	C₂×C₃₁⋊C₈	—	2	8	no	—
17	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁	—	2	4	no	—
19	C₂×C₄×C₃₁	—	2	4	no	—
20	C₂×C₄×C₃₁	—	2	8	no	—
21	C₂×C₄×C₃₁	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₃₁	#41	1	4	yes	—
25	C₃₁⋊C₈	—	4	4	no	—
26	#1832	—	31	1	no	maximal, Sylow
27	C₂²×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₃₁	#117	1	2	yes	—
29	C₂²×C₃₁	#131	1	4	yes	—
30	C₄×C₃₁	—	2	4	no	—
31	C₄×C₃₁	—	4	4	no	—
32	C₄×C₃₁	#124	1	2	yes	—
33	C₄×C₃₁	#125	1	2	yes	—
34	C₂×C₄⋊C₈	—	31	2	no	—
35	#376	D₃₁	1	1	yes	characteristic
36	#336	—	31	4	no	—
37	C₂×C₃₁	#382	1	1	yes	characteristic
38	C₂×C₃₁	#424	1	2	yes	—
39	C₂×C₃₁	#433	1	4	yes	—
40	C₂²×C₈	—	31	4	no	—
41	C₂×C₄²	C₂×D₃₁	1	2	yes	—
42	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
43	C₄⋊C₈	—	62	4	no	—
44	#95	Dic₃₁	1	4	yes	—
45	C₃₁	#1832	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	C₂×Dic₃₁	1	4	yes	—
47	C₂²×C₄	C₂×Dic₃₁	1	2	yes	—
48	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
49	C₂×C₈	—	62	4	no	—
50	C₂×C₈	—	62	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	Dic₆₂	1	2	yes	—
53	C₄²	D₁₂₄	1	2	yes	—
54	C₂³	C₂²×Dic₃₁	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	8	no	—
58	C₂×C₄	C₄⋊Dic₃₁	1	4	yes	—
59	C₂×C₄	C₂×Dic₆₂	1	1	yes	characteristic
60	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
61	C₂×C₄	#92495	1	4	yes	—
62	C₈	—	124	4	no	—
63	C₂²	C₂×C₄⋊Dic₃₁	1	1	yes	characteristic
64	C₂²	#11758503	1	2	yes	—
65	C₂²	#11758525	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	4	4	no	—
68	C₄	#11758447	1	2	yes	—
69	C₄	#11758452	1	2	yes	—
70	C₂	#14520915	1	1	yes	characteristic
71	C₂	#14521076	1	2	yes	—
72	C₂	#14521110	1	4	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	#1832
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
45. C₃₁	#1832	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
#14520804	2
C₃₁×#376	2
#1832	31