Subgroups — #19140560

Order 5504.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃⋊#401	C₂	1	2	yes	maximal
2	#14582840	C₂	1	6	yes	maximal
3	#14582805	C₂	1	3	yes	maximal
4	#14582797	C₂	1	3	yes	maximal
5	C₄₃×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
8	C₂×Dic₄₃⋊C₄	C₂²	1	6	yes	—
9	C₄₃⋊#95	C₂²	1	6	yes	—
10	C₄₃⋊#95	C₂²	1	6	yes	—
11	C₄₃⋊#95	C₂²	1	6	yes	—
12	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
13	#95×C₄₃	C₂²	1	3	yes	—
14	#95×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
16	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	C₂³	1	2	yes	—
19	C₂²×Dic₄₃	C₂³	1	6	yes	—
20	C₂×Dic₈₆	—	2	6	no	—
21	C₄²×C₄₃	—	2	6	no	—
22	C₄⋊Dic₄₃	—	2	6	no	—
23	Dic₄₃⋊C₄	—	4	6	no	—
24	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₄₃	—	2	3	no	—
26	C₂×C₄×C₄₃	—	2	3	no	—
27	C₂×C₄×C₄₃	—	2	3	no	—
28	C₂×C₄×C₄₃	—	2	6	no	—
29	C₂×C₄×C₄₃	—	2	3	no	—
30	C₂×C₄×C₄₃	#41	1	6	yes	—
31	C₂×Dic₄₃	—	2	6	no	—
32	C₂×Dic₄₃	—	2	6	no	—
33	C₂×Dic₄₃	—	2	6	no	—
34	C₂×Dic₄₃	—	2	6	no	—
35	Dic₈₆	—	4	4	no	—
36	C₂²×C₄₃	C₂×#41	1	3	yes	—
37	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
38	C₂²×C₄₃	2₋¹⁺⁴	1	3	yes	—
39	C₄×C₄₃	—	4	3	no	—
40	C₄×C₄₃	—	4	3	no	—
41	C₄×C₄₃	#126	1	4	yes	—
42	Dic₄₃	—	4	2	no	—
43	Dic₄₃	—	4	6	no	—
44	#2645	—	43	1	no	maximal, Sylow
45	C₂×C₄₃	C₂×#126	1	1	yes	characteristic
46	C₂×C₄₃	#541	1	3	yes	—
47	C₂×C₄₃	#542	1	3	yes	—
48	#401	—	43	2	no	—
49	#400	—	43	6	no	—
50	#391	—	43	3	no	—
51	#389	—	43	3	no	—
52	#376	D₄₃	1	1	yes	characteristic
53	C₄₃	#2645	1	1	yes	characteristic, complemented, Sylow
54	C₂²×Q₈	—	43	1	no	—
55	C₂×C₄⋊C₄	—	43	3	no	—
56	C₂×C₄⋊C₄	—	43	6	no	—
57	C₂×C₄²	C₂×D₄₃	1	3	yes	—
58	#95	—	43	6	no	—
59	#95	—	43	6	no	—
60	#95	—	43	6	no	—
61	#95	C₂×D₄₃	1	3	yes	—
62	#95	C₂×D₄₃	1	1	yes	characteristic
63	C₂×Q₈	—	86	6	no	—
64	C₂²×C₄	—	43	2	no	—
65	C₂²×C₄	—	43	6	no	—
66	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
67	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
68	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
69	C₄⋊C₄	—	86	6	no	—
70	C₄⋊C₄	—	172	6	no	—
71	C₄²	—	2	6	no	—
72	C₂³	C₂³×D₄₃	1	1	yes	characteristic
73	Q₈	—	172	4	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	3	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	6	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	86	6	no	—
80	C₂×C₄	—	86	6	no	—
81	C₂×C₄	—	86	6	no	—
82	C₂×C₄	—	86	6	no	—
83	C₂×C₄	#10621898	1	6	yes	—
84	C₂²	C₂×#10621898	1	3	yes	—
85	C₂²	#13063371	1	1	yes	characteristic
86	C₂²	#13063372	1	3	yes	—
87	C₄	—	4	3	no	—
88	C₄	—	4	3	no	—
89	C₄	—	172	2	no	—
90	C₄	—	172	6	no	—
91	C₄	#13063319	1	4	yes	—
92	C₂	C₂×#13063319	1	1	yes	characteristic
93	C₂	#14583511	1	3	yes	—
94	C₂	#14583520	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#376	C₂
hypercenter	#376	D₄₃
hypocenter	C₄₃	#2645
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
53. C₄₃	#2645	semidirect