Subgroups — #19132506

Order 5504.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582956	C₂	1	2	yes	maximal
2	C₄₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
4	C₂²⋊(C₄₃⋊C₈)	C₄	1	4	yes	—
5	#13063236	—	2	2	no	—
6	C₂×M₁₆×C₄₃	C₄	1	2	yes	—
7	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₄₃	—	2	2	no	—
9	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
11	M₁₆×C₄₃	—	4	2	no	—
12	C₂×C₈×C₄₃	—	2	2	no	—
13	C₄²×C₄₃	D₄	1	1	yes	characteristic
14	C₄²×C₄₃	D₄	1	2	yes	—
15	C₄²×C₄₃	Q₈	1	1	yes	characteristic
16	C₂×C₄₃⋊C₈	—	2	4	no	—
17	C₂³×C₄₃	C₄²	1	1	yes	characteristic
18	C₂×C₄×C₄₃	—	2	1	no	—
19	C₂×C₄×C₄₃	—	2	1	no	—
20	C₂×C₄×C₄₃	—	4	2	no	—
21	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
25	C₈×C₄₃	—	4	2	no	—
26	C₄₃⋊C₈	—	4	4	no	—
27	C₂²×C₄₃	—	2	1	no	—
28	C₂²×C₄₃	—	2	2	no	—
29	C₂²×C₄₃	#95	1	1	yes	characteristic
30	C₄×C₄₃	—	2	1	no	—
31	C₄×C₄₃	—	2	2	no	—
32	C₄×C₄₃	—	2	2	no	—
33	C₄×C₄₃	#100	1	1	yes	characteristic
34	C₄×C₄₃	#101	1	1	yes	characteristic
35	#1307	—	43	1	no	maximal, Sylow
36	C₂×C₄₃	—	4	1	no	—
37	C₂×C₄₃	#343	1	1	yes	characteristic
38	C₂×C₄₃	#344	1	2	yes	—
39	#432	—	43	2	no	—
40	#423	D₄₃	1	1	yes	characteristic
41	C₄₃	#1307	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	Dic₄₃	1	2	yes	—
43	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
44	C₄⋊C₈	—	2	2	no	—
45	C₄⋊C₈	—	86	2	no	—
46	C₂²⋊C₈	—	43	4	no	—
47	#97	—	86	2	no	—
48	C₂²×C₄	C₄×D₄₃	1	2	yes	—
49	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
50	M₁₆	—	4	2	no	—
51	C₂×C₈	—	2	2	no	—
52	C₂×C₈	—	86	4	no	—
53	C₄²	Dic₈₆	1	1	yes	characteristic
54	C₄²	D₁₇₂	1	1	yes	characteristic
55	C₄²	C₂²⋊D₄₃	1	2	yes	—
56	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	4	2	no	—
60	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
62	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
63	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
64	C₈	—	4	2	no	—
65	C₈	—	172	4	no	—
66	C₂²	—	2	1	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₄₃⋊#95	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	2	2	no	—
71	C₄	—	2	2	no	—
72	C₄	#13063242	1	1	yes	characteristic
73	C₄	#13063244	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	#14582668	1	1	yes	characteristic
76	C₂	#14582671	1	2	yes	—

	subgroup	G/H
center	C₂²	C₄₃⋊#95
commutator	C₂³×C₄₃	C₄²
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂²×C₄₃	#95
hypercenter	#423	D₄₃
hypocenter	C₄₃	#1307
LCS	G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
41. C₄₃	#1307	semidirect