Subgroups — #22586261

Order 9088.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17985775	C₂	1	1	yes	maximal, characteristic
2	#17985775	C₂	1	1	yes	maximal, characteristic
3	#322×C₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇₁⋊C₁₆	C₄	1	2	yes	—
5	C₂×C₇₁⋊C₁₆	C₄	1	2	yes	—
6	C₄×C₈×C₇₁	C₄	1	2	yes	—
7	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
8	C₇₁⋊C₁₆	—	2	2	no	—
9	C₇₁⋊C₁₆	C₈	1	4	yes	complemented
10	C₂×C₈×C₇₁	—	2	2	no	—
11	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
13	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₇₁	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₇₁	M₁₆	1	2	yes	—
16	C₈×C₇₁	—	4	2	no	—
17	C₈×C₇₁	C₂×C₈	1	2	yes	—
18	C₈×C₇₁	M₁₆	1	2	yes	—
19	C₂²×C₇₁	#97	1	1	yes	characteristic
20	C₄×C₇₁	—	2	2	no	—
21	C₄×C₇₁	C₄×C₈	1	1	yes	characteristic
22	C₄×C₇₁	#97	1	1	yes	characteristic
23	C₂×C₇₁	#322	1	1	yes	characteristic
24	C₂×C₇₁	#347	1	2	yes	—
25	#1313	—	71	1	no	maximal, Sylow
26	C₇₁	#1313	1	1	yes	characteristic, complemented, Sylow
27	#346	—	71	1	no	—
28	#346	—	71	1	no	—
29	#322	D₇₁	1	1	yes	characteristic
30	C₂×C₁₆	—	71	2	no	—
31	C₂×C₁₆	—	71	2	no	—
32	C₄×C₈	Dic₇₁	1	2	yes	—
33	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
34	C₂×C₈	—	2	2	no	—
35	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
36	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
37	C₄²	C₂×Dic₇₁	1	1	yes	characteristic
38	C₁₆	—	71	4	no	—
39	C₁₆	—	142	2	no	—
40	C₂×C₄	C₄×Dic₇₁	1	1	yes	characteristic
41	C₂×C₄	#11765849	1	2	yes	—
42	C₈	—	4	2	no	—
43	C₈	C₈×D₇₁	1	2	yes	—
44	C₈	#11765848	1	2	yes	—
45	C₂²	#14556039	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₈×Dic₇₁	1	1	yes	characteristic
48	C₄	#14556038	1	1	yes	characteristic
49	C₂	#17985721	1	1	yes	characteristic
50	C₂	#17985777	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₇₁
commutator	C₄×C₇₁	C₄×C₈
Frattini	C₄×C₈	C₂×D₇₁
Fitting	#322×C₇₁	C₂
socle	C₂²×C₇₁	#97
hypercenter	#322	D₇₁
hypocenter	C₇₁	#1313
LCS	G ▷ C₄×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ #322

Complements

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

N	H ≅ G/N	type
9. C₇₁⋊C₁₆	C₈	semidirect
26. C₇₁	#1313	semidirect