Subgroups — #16845464

Order 3968.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#14520895	C₂	1	1	yes	maximal, characteristic
3	#14520803	C₂	1	4	yes	maximal
4	C₂×C₃₁×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₃₁	C₂²	1	2	yes	—
6	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₃₁	C₂²	1	2	yes	—
8	C₂²×C₃₁⋊C₈	C₂²	1	2	yes	—
9	C₃₁×#97	C₄	1	4	yes	complemented
10	C₃₁⋊#95	C₄	1	4	yes	—
11	C₄×C₃₁⋊C₈	C₄	1	4	yes	complemented
12	C₂²×C₄×C₃₁	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
14	C₂²×Dic₃₁	C₂×C₄	1	4	yes	—
15	C₂×C₈×C₃₁	—	2	4	no	—
16	C₂×C₈×C₃₁	C₂×C₄	1	4	yes	—
17	C₄²×C₃₁	C₂×C₄	1	2	yes	—
18	C₄²×C₃₁	C₂×C₄	1	2	yes	—
19	C₄×Dic₃₁	—	2	4	no	—
20	C₂×C₃₁⋊C₈	—	2	4	no	—
21	C₂×C₃₁⋊C₈	C₂×C₄	1	4	yes	—
22	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₃₁	—	2	4	no	—
24	C₂×C₄×C₃₁	C₄²	1	4	yes	—
25	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₃₁	#41	1	4	yes	—
28	C₂×Dic₃₁	—	2	4	no	—
29	C₂×Dic₃₁	—	2	8	no	—
30	C₈×C₃₁	—	2	4	no	—
31	C₃₁⋊C₈	—	2	4	no	—
32	#1746	—	31	1	no	maximal, Sylow
33	C₂²×C₃₁	C₂×C₄²	1	1	yes	characteristic
34	C₂²×C₃₁	#117	1	2	yes	—
35	C₂²×C₃₁	#131	1	4	yes	—
36	C₄×C₃₁	—	2	4	no	—
37	C₄×C₃₁	#117	1	2	yes	—
38	C₄×C₃₁	#117	1	2	yes	—
39	Dic₃₁	—	4	4	no	—
40	C₂×#97	D₃₁	1	1	yes	characteristic
41	C₂×C₄×C₈	—	31	1	no	—
42	#376	—	31	1	no	—
43	#336	—	31	4	no	—
44	C₂×C₃₁	#376	1	1	yes	characteristic
45	C₂×C₃₁	#405	1	2	yes	—
46	C₂×C₃₁	#433	1	4	yes	—
47	C₂²×C₈	—	31	2	no	—
48	C₂²×C₈	C₂×D₃₁	1	2	yes	—
49	C₂×C₄²	—	31	2	no	—
50	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
51	#97	Dic₃₁	1	4	yes	complemented
52	C₄×C₈	—	31	4	no	—
53	#95	—	31	4	no	—
54	C₃₁	#1746	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₄	—	31	4	no	—
56	C₂²×C₄	C₄×D₃₁	1	2	yes	—
57	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
58	C₂×C₈	—	2	4	no	—
59	C₂×C₈	—	31	4	no	—
60	C₂×C₈	—	62	4	no	—
61	C₂×C₈	C₂×Dic₃₁	1	4	yes	—
62	C₄²	—	62	4	no	—
63	C₄²	C₄×D₃₁	1	2	yes	—
64	C₄²	C₂×Dic₃₁	1	2	yes	—
65	C₂³	C₂×C₄×D₃₁	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	62	4	no	—
68	C₂×C₄	—	62	8	no	—
69	C₂×C₄	C₄×Dic₃₁	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
71	C₂×C₄	#92495	1	4	yes	—
72	C₂×C₄	C₂²×Dic₃₁	1	1	yes	characteristic
73	C₈	—	2	4	no	—
74	C₈	—	62	4	no	—
75	C₂²	#11758449	1	2	yes	—
76	C₂²	#11758484	1	4	yes	—
77	C₂²	C₂×C₄×Dic₃₁	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	124	4	no	—
80	C₄	#11758449	1	2	yes	—
81	C₄	#11758503	1	2	yes	—
82	C₂	#14520895	1	1	yes	characteristic
83	C₂	#14521007	1	2	yes	—
84	C₂	#14521111	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₁
commutator	C₂²×C₃₁	C₂×C₄²
Fitting	C₂×C₃₁×#97	C₂
socle, prime radical	C₂³×C₃₁	C₂²×C₄
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₂×#97	D₃₁
hypocenter	C₃₁	#1746
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
9. C₃₁×#97	C₄	semidirect
11. C₄×C₃₁⋊C₈	C₄	semidirect
51. #97	Dic₃₁	semidirect
54. C₃₁	#1746	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
#14520895	2
#14520803	2
C₂×C₃₁×#97	2
#1746	31