Subgroups — #22587952

Order 9088.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986350	C₂	1	3	yes	maximal, complemented
2	#17986346	C₂	1	3	yes	maximal
3	C₈²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#14556128	C₂²	1	3	yes	—
5	#14556125	C₂²	1	1	yes	characteristic
6	#14556053	—	2	6	no	—
7	#14556050	—	2	6	no	—
8	C₄×C₈×C₇₁	C₂²	1	3	yes	—
9	C₂×Dic₁₄₂	—	2	3	no	—
10	C₂×D₂₈₄	—	2	3	no	—
11	C₄⋊Dic₇₁	—	2	3	no	—
12	C₄⋊Dic₇₁	—	2	3	no	—
13	C₂×C₈×C₇₁	D₄	1	6	yes	—
14	C₄²×C₇₁	C₂³	1	1	yes	characteristic
15	C₂²×D₇₁	—	4	1	no	—
16	C₂×C₄×C₇₁	C₂×D₄	1	3	yes	—
17	C₂×Dic₇₁	—	4	3	no	—
18	D₂₈₄	—	4	6	no	—
19	Dic₁₄₂	—	4	6	no	—
20	C₈×C₇₁	—	2	6	no	—
21	C₂²×C₇₁	#127	1	1	yes	characteristic
22	C₂×D₇₁	—	8	3	no	—
23	C₄×C₇₁	#135	1	6	yes	—
24	Dic₇₁	—	8	3	no	—
25	C₂×C₇₁	#495	1	3	yes	—
26	D₇₁	—	16	1	no	—
27	#1711	—	71	1	no	maximal, Sylow
28	C₇₁	#1711	1	1	yes	characteristic, complemented, Sylow
29	#487	—	71	3	no	—
30	#486	—	71	3	no	—
31	C₈²	D₇₁	1	1	yes	characteristic, complemented
32	C₄⋊Q₈	—	71	3	no	—
33	#127	—	71	1	no	—
34	#103	—	142	6	no	—
35	#102	—	142	6	no	—
36	C₄×C₈	C₂×D₇₁	1	3	yes	—
37	C₂×Q₈	—	142	3	no	—
38	C₂×D₄	—	142	3	no	—
39	C₂×C₈	D₂₈₄	1	6	yes	—
40	C₄⋊C₄	—	142	3	no	—
41	C₄⋊C₄	—	142	3	no	—
42	C₄²	C₂²×D₇₁	1	1	yes	characteristic
43	C₂³	—	284	1	no	—
44	Q₈	—	284	6	no	—
45	D₄	—	284	6	no	—
46	C₂×C₄	—	284	3	no	—
47	C₂×C₄	C₂×D₂₈₄	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	568	3	no	—
50	C₂²	#14556125	1	1	yes	characteristic
51	C₄	—	568	3	no	—
52	C₄	#14556150	1	6	yes	—
53	C₂	—	1136	1	no	—
54	C₂	#17986383	1	3	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	#1711
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
1. #17986350	C₂	semidirect
3. C₈²×C₇₁	C₂	semidirect
28. C₇₁	#1711	semidirect
31. C₈²	D₇₁	semidirect