Subgroups — #22588481

Order 9088.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986023	C₂	1	2	yes	maximal
2	#17985764	C₂	1	4	yes	maximal
3	C₂×#97×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11765849	C₂²	1	4	yes	—
5	C₄⋊(C₇₁⋊C₈)	—	2	4	no	—
6	C₂²×C₈×C₇₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₇₁	C₂²	1	1	yes	characteristic
8	#97×C₇₁	C₄	1	4	yes	—
9	#11765849	—	2	8	no	—
10	C₂×C₇₁⋊C₈	—	2	4	no	—
11	C₂²×C₄×C₇₁	Q₈	1	2	yes	—
12	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₇₁	—	2	4	no	—
14	C₂×C₈×C₇₁	C₂×C₄	1	4	yes	—
15	C₄²×C₇₁	C₂×C₄	1	2	yes	—
16	C₄²×C₇₁	D₄	1	2	yes	—
17	C₂³×C₇₁	C₂×Q₈	1	1	yes	characteristic
18	C₂×C₄×C₇₁	—	4	2	no	—
19	C₂×C₄×C₇₁	C₄⋊C₄	1	4	yes	—
20	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₇₁	#41	1	4	yes	—
23	C₈×C₇₁	—	2	4	no	—
24	C₇₁⋊C₈	—	4	4	no	—
25	C₂²×C₇₁	—	2	2	no	—
26	C₂²×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₇₁	#125	1	2	yes	—
28	C₄×C₇₁	—	2	4	no	—
29	C₄×C₇₁	#117	1	2	yes	—
30	C₄×C₇₁	#124	1	2	yes	—
31	C₂×C₇₁	—	2	2	no	—
32	C₂×C₇₁	#382	1	1	yes	characteristic
33	C₂×C₇₁	#430	1	2	yes	—
34	#1838	—	71	1	no	maximal, Sylow
35	C₇₁	#1838	1	1	yes	characteristic, complemented, Sylow
36	#423	—	71	2	no	—
37	C₂×#97	D₇₁	1	1	yes	characteristic
38	#341	—	71	4	no	—
39	C₂×M₁₆	—	71	4	no	—
40	C₂²×C₈	C₂×D₇₁	1	2	yes	—
41	C₂×C₄²	C₂×D₇₁	1	1	yes	characteristic
42	C₄⋊C₈	—	142	4	no	—
43	#97	Dic₇₁	1	4	yes	—
44	C₂²×C₄	Dic₁₄₂	1	2	yes	—
45	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
46	M₁₆	—	142	8	no	—
47	C₂×C₈	—	2	4	no	—
48	C₂×C₈	—	142	4	no	—
49	C₂×C₈	C₂×Dic₇₁	1	4	yes	—
50	C₄²	D₂₈₄	1	2	yes	—
51	C₄²	C₂×Dic₇₁	1	2	yes	—
52	C₂³	C₂×Dic₁₄₂	1	1	yes	characteristic
53	C₂×C₄	—	4	2	no	—
54	C₂×C₄	C₄⋊Dic₇₁	1	4	yes	—
55	C₂×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
56	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
57	C₂×C₄	#11765865	1	4	yes	—
58	C₈	—	2	4	no	—
59	C₈	—	284	4	no	—
60	C₂²	—	2	2	no	—
61	C₂²	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
62	C₂²	#14556120	1	2	yes	—
63	C₄	—	2	4	no	—
64	C₄	#14556087	1	2	yes	—
65	C₄	#14556116	1	2	yes	—
66	C₂	—	2	2	no	—
67	C₂	#17985865	1	1	yes	characteristic
68	C₂	#17986048	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₂₈₄
commutator	C₂×C₄×C₇₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	C₂×#97×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₄⋊C₄
hypercenter	C₂×#97	D₇₁
hypocenter	C₇₁	#1838
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
35. C₇₁	#1838	semidirect