Subgroups — C₂×#17985867 #22590730

Order 9088.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985867	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₇₁⋊#95	C₂	1	6	yes	maximal
3	C₂²×C₄²×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₇₁	C₂²	1	4	yes	—
5	C₇₁⋊#95	C₂²	1	24	yes	—
6	C₂³×C₄×C₇₁	C₂²	1	3	yes	—
7	C₂×C₄²×C₇₁	C₄	1	8	yes	complemented
8	C₂×C₄²×C₇₁	C₂²	1	4	yes	—
9	C₂²×Dic₇₁	—	2	24	no	—
10	C₂²×Dic₇₁	C₂³	1	8	yes	—
11	C₂⁴×C₇₁	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₇₁	—	2	12	no	—
13	C₂²×C₄×C₇₁	C₂×C₄	1	12	yes	—
14	C₂²×C₄×C₇₁	C₂³	1	6	yes	—
15	C₄²×C₇₁	C₂×C₄	1	16	yes	complemented
16	C₂³×C₇₁	C₂²×C₄	1	2	yes	—
17	C₂³×C₇₁	#41	1	12	yes	—
18	C₂³×C₇₁	C₂⁴	1	1	yes	characteristic
19	C₂×C₄×C₇₁	—	2	24	no	—
20	C₂×C₄×C₇₁	—	2	12	no	—
21	C₂×C₄×C₇₁	C₂²×C₄	1	12	yes	—
22	C₂×Dic₇₁	—	2	24	no	—
23	C₂×Dic₇₁	—	4	16	no	—
24	C₂²×C₇₁	#117	1	12	yes	—
25	C₂²×C₇₁	#126	1	16	yes	—
26	C₂²×C₇₁	C₂³×C₄	1	1	yes	characteristic
27	C₂²×C₇₁	C₂×#41	1	6	yes	—
28	C₄×C₇₁	—	2	12	no	—
29	Dic₇₁	—	4	8	no	—
30	C₂×C₇₁	#383	1	8	yes	complemented
31	C₂×C₇₁	C₂×#117	1	3	yes	—
32	C₂×C₇₁	C₂×#126	1	4	yes	—
33	C₂×#383	—	71	1	no	maximal, Sylow
34	C₇₁	C₂×#383	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₄²	D₇₁	1	1	yes	characteristic
36	#383	—	71	8	no	—
37	C₂×#95	—	71	6	no	—
38	C₂³×C₄	—	71	4	no	—
39	C₂³×C₄	C₂×D₇₁	1	3	yes	—
40	C₂×C₄²	Dic₇₁	1	8	yes	complemented
41	C₂×C₄²	C₂×D₇₁	1	4	yes	—
42	#95	—	71	24	no	—
43	C₂⁴	C₂²×D₇₁	1	1	yes	characteristic
44	C₂²×C₄	—	2	12	no	—
45	C₂²×C₄	—	71	8	no	—
46	C₂²×C₄	—	142	24	no	—
47	C₂²×C₄	C₂×Dic₇₁	1	12	yes	—
48	C₂²×C₄	C₂²×D₇₁	1	6	yes	—
49	C₄²	C₂×Dic₇₁	1	16	yes	complemented
50	C₂³	C₂²×Dic₇₁	1	2	yes	—
51	C₂³	#11765865	1	12	yes	—
52	C₂³	C₂³×D₇₁	1	1	yes	characteristic
53	C₂×C₄	—	2	12	no	—
54	C₂×C₄	—	2	24	no	—
55	C₂×C₄	—	284	16	no	—
56	C₂×C₄	—	142	24	no	—
57	C₂×C₄	C₂²×Dic₇₁	1	12	yes	—
58	C₂²	#14556087	1	12	yes	—
59	C₂²	#14556122	1	16	yes	—
60	C₂²	C₂³×Dic₇₁	1	1	yes	characteristic
61	C₂²	C₂×#11765865	1	6	yes	—
62	C₄	—	2	12	no	—
63	C₄	—	284	8	no	—
64	C₂	#17985867	1	8	yes	direct product factor
65	C₂	C₂×#14556087	1	3	yes	—
66	C₂	C₂×#14556122	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₇₁
commutator	C₂²×C₇₁	C₂³×C₄
Frattini	C₂³	C₂³×D₇₁
Fitting	C₂²×C₄²×C₇₁	C₂
socle	C₂⁴×C₇₁	C₂³
hypercenter	C₂²×C₄²	D₇₁
hypocenter	C₇₁	C₂×#383
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. #17985867	C₂	direct (N × H)
7. C₂×C₄²×C₇₁	C₄	semidirect
15. C₄²×C₇₁	C₂×C₄	semidirect
30. C₂×C₇₁	#383	semidirect
34. C₇₁	C₂×#383	semidirect
40. C₂×C₄²	Dic₇₁	semidirect
49. C₄²	C₂×Dic₇₁	semidirect
64. C₂	#17985867	direct (N × H)

Subgroups — C2×#17985867 #22590730

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17985867 #22590730