Subgroups — #19134736

Order 5504.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582923	C₂	1	2	yes	maximal
2	#14582664	C₂	1	4	yes	maximal
3	C₂×#97×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	C₂²	1	4	yes	—
5	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
6	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
7	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
8	#97×C₄₃	C₄	1	4	yes	—
9	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
10	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
11	C₂×C₈×C₄₃	—	2	4	no	—
12	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
13	C₄²×C₄₃	C₂×C₄	1	2	yes	—
14	C₄²×C₄₃	D₄	1	2	yes	—
15	#10621877	—	2	8	no	—
16	C₂×C₄₃⋊C₈	—	2	4	no	—
17	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
18	C₂×C₄×C₄₃	—	4	2	no	—
19	C₂×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
20	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₃	#41	1	4	yes	—
23	C₈×C₄₃	—	2	4	no	—
24	C₄₃⋊C₈	—	4	4	no	—
25	C₂²×C₄₃	—	2	2	no	—
26	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₃	#125	1	2	yes	—
28	C₄×C₄₃	—	2	4	no	—
29	C₄×C₄₃	#117	1	2	yes	—
30	C₄×C₄₃	#124	1	2	yes	—
31	#1838	—	43	1	no	maximal, Sylow
32	C₂×C₄₃	—	2	2	no	—
33	C₂×C₄₃	#382	1	1	yes	characteristic
34	C₂×C₄₃	#430	1	2	yes	—
35	#423	—	43	2	no	—
36	C₂×#97	D₄₃	1	1	yes	characteristic
37	#341	—	43	4	no	—
38	C₄₃	#1838	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₁₆	—	43	4	no	—
40	C₂²×C₈	C₂×D₄₃	1	2	yes	—
41	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
42	C₄⋊C₈	—	86	4	no	—
43	#97	Dic₄₃	1	4	yes	—
44	C₂²×C₄	Dic₈₆	1	2	yes	—
45	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
46	M₁₆	—	86	8	no	—
47	C₂×C₈	—	2	4	no	—
48	C₂×C₈	—	86	4	no	—
49	C₂×C₈	C₂×Dic₄₃	1	4	yes	—
50	C₄²	D₁₇₂	1	2	yes	—
51	C₄²	C₂×Dic₄₃	1	2	yes	—
52	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
53	C₂×C₄	—	4	2	no	—
54	C₂×C₄	C₄⋊Dic₄₃	1	4	yes	—
55	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
56	C₂×C₄	#10621898	1	4	yes	—
57	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
58	C₈	—	2	4	no	—
59	C₈	—	172	4	no	—
60	C₂²	—	2	2	no	—
61	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
62	C₂²	#13063317	1	2	yes	—
63	C₄	—	2	4	no	—
64	C₄	#13063284	1	2	yes	—
65	C₄	#13063313	1	2	yes	—
66	C₂	—	2	2	no	—
67	C₂	#14582765	1	1	yes	characteristic
68	C₂	#14582948	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#97×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	C₂×#97	D₄₃
hypocenter	C₄₃	#1838
LCS	G ▷ C₂×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
38. C₄₃	#1838	semidirect