Subgroups — #19134501

Order 5504.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063261	C₂	1	2	yes	maximal
2	C₄×#10621877	C₂	1	2	yes	maximal
3	#14582664	C₂	1	2	yes	maximal
4	C₂×#97×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#10621877	C₂²	1	4	yes	—
6	#13063261	C₄	1	8	yes	complemented
7	#13063236	—	2	2	no	—
8	C₄×C₄₃⋊C₈	—	2	2	no	—
9	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	#97×C₄₃	C₄	1	4	yes	—
13	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
14	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₄₃	—	2	2	no	—
16	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
19	C₄²×C₄₃	C₂×C₄	1	2	yes	—
20	C₄²×C₄₃	D₄	1	2	yes	—
21	#10621877	—	2	4	no	—
22	#10621877	C₂×C₄	1	8	yes	—
23	C₂×C₄₃⋊C₈	—	2	4	no	—
24	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₄₃	—	4	2	no	—
26	C₂×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
27	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
28	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	#41	1	2	yes	—
31	C₈×C₄₃	—	2	2	no	—
32	C₈×C₄₃	C₄²	1	4	yes	—
33	C₄₃⋊C₈	—	2	8	no	—
34	C₂²×C₄₃	—	2	2	no	—
35	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₄₃	C₄×Q₈	1	2	yes	—
37	C₄×C₄₃	—	2	4	no	—
38	C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₄₃	#117	1	1	yes	characteristic
40	C₄×C₄₃	C₄×D₄	1	2	yes	—
41	#1778	—	43	1	no	maximal, Sylow
42	C₂×C₄₃	—	2	2	no	—
43	C₂×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄₃	#430	1	2	yes	—
45	C₂×#108	—	43	2	no	—
46	C₄×M₁₆	—	43	2	no	—
47	C₂×#97	D₄₃	1	1	yes	characteristic
48	#341	—	43	2	no	—
49	C₄₃	#1778	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	43	4	no	—
51	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
52	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
53	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
54	#108	—	43	8	no	—
55	#97	—	86	2	no	—
56	#97	Dic₄₃	1	4	yes	—
57	C₄×C₈	—	86	2	no	—
58	C₂²×C₄	Dic₈₆	1	2	yes	—
59	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
60	M₁₆	—	43	8	no	—
61	M₁₆	—	86	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	86	4	no	—
64	C₂×C₈	C₄×D₄₃	1	4	yes	—
65	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
66	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
67	C₄²	D₁₇₂	1	2	yes	—
68	C₄²	C₂×Dic₄₃	1	2	yes	—
69	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	C₄⋊Dic₄₃	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
73	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
74	C₂×C₄	#10621898	1	2	yes	—
75	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
76	C₈	—	2	2	no	—
77	C₈	—	86	8	no	—
78	C₈	C₄×Dic₄₃	1	4	yes	—
79	C₂²	—	2	2	no	—
80	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
81	C₂²	C₄×Dic₈₆	1	2	yes	—
82	C₄	—	2	4	no	—
83	C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
84	C₄	#13063284	1	1	yes	characteristic
85	C₄	C₄×D₁₇₂	1	2	yes	—
86	C₂	—	2	2	no	—
87	C₂	C₄×C₄⋊Dic₄₃	1	1	yes	characteristic
88	C₂	#14582948	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₄×C₄₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#97×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	C₂×#97	D₄₃
hypocenter	C₄₃	#1778
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
6. #13063261	C₄	semidirect
49. C₄₃	#1778	semidirect