Subgroups — #22590582

Order 9088.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986401	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986376	C₂	1	1	yes	maximal, characteristic
3	#17985801	C₂	1	4	yes	maximal, complemented
4	#346×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₅₆₈	—	2	1	no	—
6	C₂×D₅₆₈	C₂²	1	2	yes	—
7	#14556125	—	2	1	no	—
8	#14556120	—	2	1	no	—
9	#14556062	C₂²	1	2	yes	—
10	#14556060	—	2	1	no	—
11	C₂×C₁₆×C₇₁	C₂²	1	2	yes	—
12	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
13	C₂×D₂₈₄	—	2	2	no	—
14	C₂×D₂₈₄	—	4	2	no	—
15	D₅₆₈	—	2	4	no	—
16	D₅₆₈	—	4	2	no	—
17	C₄⋊Dic₇₁	—	2	2	no	—
18	Dic₇₁⋊C₄	—	4	2	no	—
19	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
21	C₄²×C₇₁	D₄	1	1	yes	characteristic
22	C₁₆×C₇₁	—	2	2	no	—
23	C₂²×D₇₁	—	4	2	no	—
24	C₂×C₄×C₇₁	D₈	1	2	yes	—
25	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₇₁	—	4	2	no	—
27	D₂₈₄	—	4	2	no	—
28	D₂₈₄	—	4	2	no	—
29	D₂₈₄	—	8	4	no	—
30	C₈×C₇₁	SD₁₆	1	2	yes	—
31	C₈×C₇₁	#41	1	2	yes	—
32	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
33	C₂×D₇₁	—	8	2	no	—
34	C₂×D₇₁	—	8	4	no	—
35	C₄×C₇₁	—	2	2	no	—
36	C₄×C₇₁	#124	1	1	yes	characteristic
37	C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
38	Dic₇₁	—	8	2	no	—
39	C₂×C₇₁	#486	1	1	yes	characteristic
40	C₂×C₇₁	#509	1	2	yes	—
41	D₇₁	—	16	2	no	—
42	#2244	—	71	1	no	maximal, Sylow
43	C₇₁	#2244	1	1	yes	characteristic, complemented, Sylow
44	#499	—	71	1	no	—
45	#493	—	71	1	no	—
46	#357	—	71	4	no	—
47	#346	D₇₁	1	1	yes	characteristic, complemented
48	C₂×D₈	—	71	2	no	—
49	C₂×D₈	—	142	1	no	—
50	#127	—	142	1	no	—
51	#125	—	142	1	no	—
52	C₂×C₁₆	C₂×D₇₁	1	2	yes	—
53	#107	—	71	2	no	—
54	#106	—	142	1	no	—
55	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
56	C₂×D₄	—	284	2	no	—
57	C₂×D₄	—	142	2	no	—
58	D₈	—	284	2	no	—
59	D₈	—	142	4	no	—
60	C₂×C₈	D₂₈₄	1	1	yes	characteristic
61	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
62	C₄⋊C₄	—	284	2	no	—
63	C₄⋊C₄	—	142	2	no	—
64	C₄²	D₂₈₄	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	284	2	no	—
67	D₄	—	284	2	no	—
68	D₄	—	284	2	no	—
69	D₄	—	568	4	no	—
70	C₂×C₄	—	284	2	no	—
71	C₂×C₄	D₅₆₈	1	2	yes	—
72	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
73	C₈	#11765854	1	2	yes	—
74	C₈	#11765865	1	2	yes	—
75	C₂²	—	568	2	no	—
76	C₂²	—	568	4	no	—
77	C₂²	C₂×D₅₆₈	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	568	2	no	—
80	C₄	#14556116	1	1	yes	characteristic
81	C₄	C₂×#11765854	1	1	yes	characteristic
82	C₂	—	1136	2	no	—
83	C₂	#17986346	1	1	yes	characteristic
84	C₂	#17986437	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₅₆₈
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#346×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	#346	D₇₁
hypocenter	C₇₁	#2244
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
1. #17986401	C₂	semidirect
3. #17985801	C₂	semidirect
4. #346×C₇₁	C₂	semidirect
43. C₇₁	#2244	semidirect
47. #346	D₇₁	semidirect