Subgroups — #16845329

Order 3968.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521454	C₂	1	4	yes	maximal
2	#14521429	C₂	1	2	yes	maximal
3	C₈²×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₂₄	—	2	4	no	—
5	#11758446	C₂²	1	4	yes	—
6	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₃₁	C₂²	1	2	yes	—
8	#11758406	—	2	8	no	—
9	C₂×Dic₆₂	—	2	4	no	—
10	C₂×C₈×C₃₁	D₄	1	2	yes	—
11	C₂×C₈×C₃₁	D₄	1	4	yes	—
12	C₄²×C₃₁	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₃₁	—	2	8	no	—
14	Dic₁₂₄	—	4	8	no	—
15	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
17	C₂×Dic₃₁	—	4	4	no	—
18	Dic₆₂	—	4	8	no	—
19	C₈×C₃₁	D₈	1	4	yes	—
20	C₈×C₃₁	Q₁₆	1	8	yes	complemented
21	#1713	—	31	1	no	maximal, Sylow
22	C₂²×C₃₁	#127	1	1	yes	characteristic
23	C₄×C₃₁	C₂×D₈	1	2	yes	—
24	C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
25	Dic₃₁	—	8	4	no	—
26	#500	—	31	4	no	—
27	#494	—	31	2	no	—
28	C₈²	D₃₁	1	1	yes	characteristic
29	C₂×C₃₁	#493	1	1	yes	characteristic
30	C₂×C₃₁	#494	1	2	yes	—
31	C₂×Q₁₆	—	62	4	no	—
32	C₄⋊Q₈	—	31	4	no	—
33	#107	—	62	8	no	—
34	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
35	C₄×C₈	C₂×D₃₁	1	2	yes	—
36	C₃₁	#1713	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	62	4	no	—
38	Q₁₆	—	124	8	no	—
39	C₂×C₈	D₁₂₄	1	2	yes	—
40	C₂×C₈	D₁₂₄	1	4	yes	—
41	C₄⋊C₄	—	62	8	no	—
42	C₄²	C₂²×D₃₁	1	1	yes	characteristic
43	Q₈	—	124	8	no	—
44	C₂×C₄	—	124	4	no	—
45	C₂×C₄	C₂×D₁₂₄	1	1	yes	characteristic
46	C₂×C₄	C₂×D₁₂₄	1	2	yes	—
47	C₈	D₂₄₈	1	4	yes	—
48	C₈	Dic₁₂₄	1	8	yes	complemented
49	C₂²	#11758451	1	1	yes	characteristic
50	C₄	—	248	4	no	—
51	C₄	C₂×D₂₄₈	1	2	yes	—
52	C₄	C₂×Dic₁₂₄	1	4	yes	—
53	C₂	#14521426	1	1	yes	characteristic
54	C₂	#14521429	1	2	yes	—

	subgroup	G/H
center	C₂²	#11758451
commutator, cosocle	C₄²×C₃₁	C₂³
Frattini	C₄²	C₂²×D₃₁
Fitting	C₈²×C₃₁	C₂
socle, prime radical	C₂²×C₃₁	#127
hypercenter	C₈²	D₃₁
hypocenter	C₃₁	#1713
LCS	G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₃₁	Q₁₆	semidirect
36. C₃₁	#1713	semidirect
48. C₈	Dic₁₂₄	semidirect

Maximal subgroups

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

subgroup	index
#14521454	2
#14521429	2
C₈²×C₃₁	2
#1713	31