Subgroups — #19134706

Order 5504.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063242	C₂	1	2	yes	maximal
2	#14582669	C₂	1	4	yes	maximal, complemented
3	C₄₃×#518	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	C₂²	1	4	yes	—
5	#13063242	—	2	4	no	—
6	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₄×D₄×C₄₃	—	2	4	no	—
8	#117×C₄₃	C₂²	1	2	yes	—
9	C₂×C₂²⋊C₄×C₄₃	C₄	1	4	yes	—
10	C₂⁴×C₄₃	C₂×C₄	1	2	yes	—
11	C₂×D₄×C₄₃	—	2	4	no	—
12	C₂×D₄×C₄₃	D₄	1	4	yes	—
13	C₂²×C₄×C₄₃	—	2	4	no	—
14	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
15	C₄⋊C₄×C₄₃	—	2	2	no	—
16	C₂²⋊C₄×C₄₃	—	2	4	no	—
17	C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
18	C₄²×C₄₃	—	2	2	no	—
19	#10621877	—	2	4	no	—
20	#10621877	—	2	4	no	—
21	C₂×C₄₃⋊C₈	—	2	4	no	—
22	C₂³×C₄₃	—	2	4	no	—
23	C₂³×C₄₃	—	8	2	no	—
24	C₂³×C₄₃	C₂²⋊C₄	1	4	yes	—
25	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	D₄×C₄₃	—	2	8	no	—
27	C₂×C₄×C₄₃	—	2	4	no	—
28	C₂×C₄×C₄₃	—	8	4	no	—
29	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
30	C₂×C₄×C₄₃	#41	1	4	yes	—
31	C₄₃⋊C₈	—	4	4	no	—
32	C₂²×C₄₃	—	2	4	no	—
33	C₂²×C₄₃	—	4	1	no	—
34	C₂²×C₄₃	—	4	4	no	—
35	C₂²×C₄₃	—	8	4	no	—
36	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₄₃	#117	1	2	yes	—
38	C₄×C₄₃	—	4	4	no	—
39	C₄×C₄₃	#123	1	4	yes	—
40	#1829	—	43	1	no	maximal, Sylow
41	C₂×C₄₃	—	2	1	no	—
42	C₂×C₄₃	—	2	2	no	—
43	C₂×C₄₃	—	4	4	no	—
44	C₂×C₄₃	#381	1	1	yes	characteristic
45	#518	D₄₃	1	1	yes	characteristic
46	C₂×#100	—	43	2	no	—
47	#344	—	43	4	no	—
48	C₄₃	#1829	1	1	yes	characteristic, complemented, Sylow
49	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
50	C₂×M₁₆	—	43	4	no	—
51	C₄×D₄	—	2	4	no	—
52	#117	C₂×D₄₃	1	2	yes	—
53	C₂×C₂²⋊C₄	Dic₄₃	1	4	yes	—
54	#100	—	86	4	no	—
55	C₂⁴	C₂×Dic₄₃	1	2	yes	—
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	C₂²⋊D₄₃	1	4	yes	—
58	C₂²×C₄	—	2	4	no	—
59	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
60	M₁₆	—	86	4	no	—
61	M₁₆	—	86	4	no	—
62	C₂×C₈	—	86	4	no	—
63	C₄⋊C₄	—	2	2	no	—
64	C₂²⋊C₄	—	2	4	no	—
65	C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
66	C₄²	—	2	2	no	—
67	C₂³	—	2	4	no	—
68	C₂³	—	8	2	no	—
69	C₂³	C₂²⋊Dic₄₃	1	4	yes	—
70	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
71	D₄	—	2	8	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	8	4	no	—
74	C₂×C₄	#10621898	1	4	yes	—
75	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
76	C₈	—	172	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	4	4	no	—
80	C₂²	—	8	4	no	—
81	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
82	C₂²	#13063284	1	2	yes	—
83	C₄	—	4	4	no	—
84	C₄	#13063308	1	4	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	2	2	no	—
87	C₂	—	4	4	no	—
88	C₂	#14582762	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582762
commutator	C₂³×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#518	C₂
socle	C₂×C₄₃	#381
hypercenter	#518	D₄₃
hypocenter	C₄₃	#1829
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #518

Complements

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

N	H ≅ G/N	type
2. #14582669	C₂	semidirect
48. C₄₃	#1829	semidirect