Subgroups — #16845460

Order 3968.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758391	C₂	1	2	yes	maximal
2	#14520804	C₂	1	4	yes	maximal
3	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₃₁	C₄	1	4	yes	—
5	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
6	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	C₂²×C₃₁⋊C₈	C₂²	1	4	yes	—
8	#11758391	C₄	1	8	yes	complemented
9	C₂²×C₄×C₃₁	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₃₁	C₂×C₄	1	4	yes	—
11	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
12	C₄²×C₃₁	—	2	8	no	—
13	C₄²×C₃₁	—	2	4	no	—
14	C₄²×C₃₁	C₂×C₄	1	4	yes	—
15	C₂×C₃₁⋊C₈	—	2	8	no	—
16	C₂×C₃₁⋊C₈	C₂×C₄	1	8	yes	—
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	4	no	—
21	C₂×C₄×C₃₁	C₄²	1	4	yes	—
22	C₂×C₄×C₃₁	M₁₆	1	8	yes	—
23	C₂×C₄×C₃₁	C₂²×C₄	1	2	yes	—
24	C₂×C₄×C₃₁	#41	1	4	yes	—
25	C₃₁⋊C₈	—	2	8	no	—
26	#1745	—	31	1	no	maximal, Sylow
27	C₂²×C₃₁	C₂×C₄²	1	1	yes	characteristic
28	C₂²×C₃₁	#117	1	2	yes	—
29	C₂²×C₃₁	C₂×M₁₆	1	4	yes	—
30	C₄×C₃₁	—	2	4	no	—
31	C₄×C₃₁	—	2	8	no	—
32	C₄×C₃₁	#117	1	4	yes	—
33	C₂×#97	—	31	2	no	—
34	C₄³	D₃₁	1	1	yes	characteristic
35	#336	—	31	4	no	—
36	C₂×C₃₁	#376	1	1	yes	characteristic
37	C₂×C₃₁	C₄×M₁₆	1	2	yes	—
38	C₂×C₃₁	#432	1	4	yes	—
39	C₂²×C₈	—	31	4	no	—
40	C₂×C₄²	Dic₃₁	1	4	yes	—
41	C₂×C₄²	C₂×D₃₁	1	2	yes	—
42	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
43	#97	—	31	8	no	—
44	C₃₁	#1745	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₄	C₂×Dic₃₁	1	4	yes	—
46	C₂²×C₄	C₂×Dic₃₁	1	2	yes	—
47	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
48	C₂×C₈	—	31	8	no	—
49	C₂×C₈	—	62	8	no	—
50	C₄²	—	2	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	C₄×D₃₁	1	4	yes	—
53	C₂³	C₂²×Dic₃₁	1	1	yes	characteristic
54	C₂×C₄	—	2	4	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	#92474	1	8	yes	—
58	C₂×C₄	C₄×Dic₃₁	1	4	yes	—
59	C₂×C₄	C₂×C₄×D₃₁	1	2	yes	—
60	C₂×C₄	#92495	1	4	yes	—
61	C₈	—	62	8	no	—
62	C₂²	C₂×#92474	1	4	yes	—
63	C₂²	C₂×C₄×Dic₃₁	1	1	yes	characteristic
64	C₂²	#11758503	1	2	yes	—
65	C₄	—	2	8	no	—
66	C₄	—	2	4	no	—
67	C₄	#11758449	1	4	yes	—
68	C₂	#14520895	1	1	yes	characteristic
69	C₂	C₄×#92474	1	2	yes	—
70	C₂	#14521106	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₁
commutator	C₂²×C₃₁	C₂×C₄²
Fitting	C₄³×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂²×C₄
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₄³	D₃₁
hypocenter	C₃₁	#1745
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
8. #11758391	C₄	semidirect
44. C₃₁	#1745	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758391	2
#14520804	2
C₄³×C₃₁	2
#1745	31