Subgroups — #22589920

Order 9088.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986048	C₂	1	1	yes	maximal, characteristic
2	#17985769	C₂	1	2	yes	maximal
3	#17985764	C₂	1	2	yes	maximal
4	C₇₁⋊#338	C₂	1	1	yes	maximal, characteristic
5	#424×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11765849	C₂²	1	2	yes	—
7	C₂×#11765849	C₂²	1	2	yes	—
8	#14556064	—	2	2	no	—
9	C₂×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	#117×C₇₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₇₁	—	2	2	no	—
13	#11765849	—	2	2	no	—
14	#11765849	—	2	2	no	—
15	#11765849	—	2	2	no	—
16	#11765849	—	2	2	no	—
17	C₂×C₇₁⋊C₈	—	2	2	no	—
18	C₂×C₇₁⋊C₈	—	2	2	no	—
19	C₂²×C₄×C₇₁	C₂³	1	1	yes	characteristic
20	M₁₆×C₇₁	—	2	2	no	—
21	C₂×C₈×C₇₁	—	2	1	no	—
22	C₂×C₈×C₇₁	—	2	2	no	—
23	C₂×C₈×C₇₁	D₄	1	2	yes	—
24	C₄⋊C₄×C₇₁	—	2	1	no	—
25	C₂²⋊C₄×C₇₁	Q₈	1	2	yes	—
26	C₄²×C₇₁	—	2	1	no	—
27	C₂³×C₇₁	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₇₁	—	2	2	no	—
29	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₇₁	#41	1	2	yes	—
31	C₂×C₄×C₇₁	#41	1	1	yes	characteristic
32	C₂×C₄×C₇₁	#41	1	2	yes	—
33	C₈×C₇₁	—	2	2	no	—
34	C₈×C₇₁	—	4	1	no	—
35	C₇₁⋊C₈	—	4	2	no	—
36	C₇₁⋊C₈	—	4	2	no	—
37	C₂²×C₇₁	—	4	1	no	—
38	C₂²×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
39	C₂²×C₇₁	#125	1	2	yes	—
40	C₄×C₇₁	—	4	2	no	—
41	C₄×C₇₁	#123	1	1	yes	characteristic
42	C₄×C₇₁	#124	1	1	yes	characteristic
43	C₄×C₇₁	#126	1	2	yes	—
44	C₂×C₇₁	—	2	1	no	—
45	C₂×C₇₁	—	2	2	no	—
46	C₂×C₇₁	#400	1	1	yes	characteristic
47	#2103	—	71	1	no	maximal, Sylow
48	C₇₁	#2103	1	1	yes	characteristic, complemented, Sylow
49	#430	—	71	1	no	—
50	#424	D₇₁	1	1	yes	characteristic
51	#344	—	71	2	no	—
52	#341	—	71	2	no	—
53	#338	—	71	1	no	—
54	C₂×M₁₆	—	71	2	no	—
55	C₂×M₁₆	—	71	2	no	—
56	C₂×M₁₆	C₂×D₇₁	1	1	yes	characteristic
57	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
58	#117	C₂×D₇₁	1	1	yes	characteristic
59	#108	—	142	2	no	—
60	C₄⋊C₈	—	2	2	no	—
61	C₂²×C₄	C₂²×D₇₁	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	142	2	no	—
64	M₁₆	—	142	2	no	—
65	M₁₆	—	142	2	no	—
66	M₁₆	—	142	2	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	142	2	no	—
70	C₂×C₈	—	142	2	no	—
71	C₂×C₈	C₂²⋊D₇₁	1	2	yes	—
72	C₄⋊C₄	—	2	1	no	—
73	C₂²⋊C₄	Dic₁₄₂	1	2	yes	—
74	C₄²	—	2	1	no	—
75	C₂³	C₂×Dic₁₄₂	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
78	C₂×C₄	#11765864	1	2	yes	—
79	C₂×C₄	#11765865	1	1	yes	characteristic
80	C₂×C₄	#11765866	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	284	2	no	—
84	C₈	—	284	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#14556107	1	1	yes	characteristic
87	C₂²	#14556119	1	2	yes	—
88	C₄	—	4	2	no	—
89	C₄	#14556109	1	1	yes	characteristic
90	C₄	#14556117	1	1	yes	characteristic
91	C₄	#14556123	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#17985938	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556117
commutator	C₂²×C₄×C₇₁	C₂³
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	#424×C₇₁	C₂
socle	C₂×C₇₁	#400
hypercenter	#424	D₇₁
hypocenter	C₇₁	#2103
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
48. C₇₁	#2103	semidirect