Subgroups — #22586434

Order 9088.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556064	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#11765849	—	2	2	no	—
4	#14556064	—	2	2	no	—
5	#14556064	C₄	1	4	yes	—
6	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₇₁	—	2	2	no	—
8	C₂×C₁₆×C₇₁	C₄	1	2	yes	—
9	#11765849	—	2	4	no	—
10	#11765849	—	4	2	no	—
11	C₂×C₇₁⋊C₈	—	4	2	no	—
12	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₇₁	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₇₁	D₄	1	2	yes	—
16	C₂×C₈×C₇₁	Q₈	1	1	yes	characteristic
17	C₁₆×C₇₁	—	2	2	no	—
18	C₂³×C₇₁	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₇₁	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₇₁	SD₁₆	1	2	yes	—
23	C₈×C₇₁	C₄²	1	1	yes	characteristic
24	C₈×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₇₁	C₄⋊C₄	1	2	yes	—
26	C₇₁⋊C₈	—	4	4	no	—
27	C₂²×C₇₁	—	2	2	no	—
28	C₂²×C₇₁	#103	1	2	yes	—
29	C₂²×C₇₁	#107	1	1	yes	characteristic
30	C₄×C₇₁	#95	1	1	yes	characteristic
31	C₄×C₇₁	#102	1	2	yes	—
32	C₄×C₇₁	#106	1	1	yes	characteristic
33	C₂×C₇₁	—	2	2	no	—
34	C₂×C₇₁	#340	1	1	yes	characteristic
35	C₂×C₇₁	#368	1	2	yes	—
36	#1381	—	71	1	no	maximal, Sylow
37	C₇₁	#1381	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₁₆	D₇₁	1	1	yes	characteristic
39	C₂×#108	—	71	2	no	—
40	C₂×M₁₆	—	142	2	no	—
41	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
42	C₂×C₁₆	—	2	2	no	—
43	C₂×C₁₆	Dic₇₁	1	2	yes	—
44	#108	—	71	4	no	—
45	#108	—	142	2	no	—
46	C₂²×C₄	D₂₈₄	1	1	yes	characteristic
47	M₁₆	—	284	2	no	—
48	M₁₆	—	142	4	no	—
49	C₂×C₈	—	284	2	no	—
50	C₂×C₈	Dic₁₄₂	1	1	yes	characteristic
51	C₂×C₈	C₄×D₇₁	1	2	yes	—
52	C₂×C₈	C₂×Dic₇₁	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₇₁	1	2	yes	—
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₂₈₄	1	1	yes	characteristic
56	C₂×C₄	(C₂×D₇₁)⋊C₄	1	2	yes	—
57	C₂×C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
58	C₂×C₄	D₅₆₈	1	1	yes	characteristic
59	C₂×C₄	#11765854	1	2	yes	—
60	C₈	—	284	4	no	—
61	C₈	C₄×Dic₇₁	1	1	yes	characteristic
62	C₈	C₂²⋊Dic₇₁	1	1	yes	characteristic
63	C₈	Dic₇₁⋊C₄	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	#14556053	1	2	yes	—
66	C₂²	#14556062	1	1	yes	characteristic
67	C₄	C₇₁⋊#95	1	1	yes	characteristic
68	C₄	#14556050	1	2	yes	—
69	C₄	#14556060	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	#17985762	1	1	yes	characteristic
72	C₂	#17985829	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₅₆₈
commutator	C₈×C₇₁	C₄²
Frattini	C₂²×C₈	C₂×D₇₁
Fitting	C₂²×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	#107
hypercenter	C₂²×C₁₆	D₇₁
hypocenter	C₇₁	#1381
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
37. C₇₁	#1381	semidirect