Subgroups — #22587950

Order 9088.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986404	C₂	1	2	yes	maximal
2	#17986350	C₂	1	4	yes	maximal
3	C₈²×C₇₁	C₂	1	1	yes	maximal, characteristic
4	#14556128	C₂²	1	4	yes	—
5	#14556062	—	2	4	no	—
6	#14556053	—	2	8	no	—
7	C₄×C₈×C₇₁	C₂²	1	2	yes	—
8	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₄₂	—	2	4	no	—
10	C₄⋊Dic₇₁	—	2	4	no	—
11	C₄⋊Dic₇₁	—	2	4	no	—
12	C₂×C₈×C₇₁	D₄	1	4	yes	—
13	C₂×C₈×C₇₁	D₄	1	2	yes	—
14	C₄²×C₇₁	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₇₁	C₂×D₄	1	2	yes	—
17	C₂×Dic₇₁	—	4	4	no	—
18	Dic₁₄₂	—	4	8	no	—
19	C₈×C₇₁	—	2	4	no	—
20	C₈×C₇₁	Q₁₆	1	4	yes	—
21	C₂²×C₇₁	#127	1	1	yes	characteristic
22	C₄×C₇₁	C₂×Q₁₆	1	2	yes	—
23	C₄×C₇₁	#135	1	4	yes	—
24	Dic₇₁	—	8	4	no	—
25	C₂×C₇₁	#494	1	1	yes	characteristic
26	C₂×C₇₁	#495	1	2	yes	—
27	#1710	—	71	1	no	maximal, Sylow
28	C₇₁	#1710	1	1	yes	characteristic, complemented, Sylow
29	#500	—	71	2	no	—
30	#487	—	71	4	no	—
31	C₈²	D₇₁	1	1	yes	characteristic
32	C₄⋊Q₈	—	71	4	no	—
33	#107	—	142	4	no	—
34	#103	—	142	8	no	—
35	C₄×C₈	C₂×D₇₁	1	2	yes	—
36	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
37	C₂×Q₈	—	142	4	no	—
38	C₂×C₈	D₂₈₄	1	4	yes	—
39	C₂×C₈	D₂₈₄	1	2	yes	—
40	C₄⋊C₄	—	142	4	no	—
41	C₄⋊C₄	—	142	4	no	—
42	C₄²	C₂²×D₇₁	1	1	yes	characteristic
43	Q₈	—	284	8	no	—
44	C₂×C₄	—	284	4	no	—
45	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
46	C₂×C₄	C₂×D₂₈₄	1	2	yes	—
47	C₈	—	2	4	no	—
48	C₈	Dic₂₈₄	1	4	yes	—
49	C₂²	#14556125	1	1	yes	characteristic
50	C₄	—	568	4	no	—
51	C₄	C₂×Dic₂₈₄	1	2	yes	—
52	C₄	#14556150	1	4	yes	—
53	C₂	#17986379	1	1	yes	characteristic
54	C₂	#17986383	1	2	yes	—

	subgroup	G/H
center	C₂²	#14556125
commutator	C₄²×C₇₁	C₂³
Frattini	C₄²	C₂²×D₇₁
Fitting	C₈²×C₇₁	C₂
socle	C₂²×C₇₁	#127
hypercenter	C₈²	D₇₁
hypocenter	C₇₁	#1710
LCS	G ▷ C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
28. C₇₁	#1710	semidirect