Subgroups — #19132771

Order 5504.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583253	C₂	1	1	yes	maximal, characteristic
2	#14582694	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#355	C₂	1	1	yes	maximal, characteristic
4	#13063317	C₄	1	1	yes	characteristic, complemented
5	#13063249	—	2	1	no	—
6	#13063246	—	2	1	no	—
7	#13063240	—	2	1	no	—
8	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic, complemented
9	#124×C₄₃	C₂²	1	1	yes	characteristic
10	#101×C₄₃	—	2	1	no	—
11	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
12	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
13	M₁₆×C₄₃	—	4	1	no	—
14	C₂²⋊C₄×C₄₃	—	4	1	no	—
15	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²⋊Dic₄₃	—	4	1	no	—
17	C₄⋊Dic₄₃	—	2	1	no	—
18	Dic₄₃⋊C₄	—	4	1	no	—
19	C₂×C₄₃⋊C₈	—	2	1	no	—
20	C₂³×C₄₃	—	2	1	no	—
21	Q₈×C₄₃	—	4	1	no	—
22	D₄×C₄₃	—	4	1	no	—
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	—	2	1	no	—
25	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₄₃	—	4	1	no	—
27	C₂×Dic₄₃	—	8	1	no	—
28	C₈×C₄₃	—	8	1	no	—
29	C₄₃⋊C₈	—	4	1	no	—
30	C₂²×C₄₃	—	4	1	no	—
31	C₂²×C₄₃	—	8	1	no	—
32	C₂²×C₄₃	#99	1	1	yes	characteristic
33	C₄×C₄₃	—	2	1	no	—
34	C₄×C₄₃	—	4	1	no	—
35	C₄×C₄₃	—	4	1	no	—
36	Dic₄₃	—	8	1	no	—
37	Dic₄₃	—	16	1	no	—
38	#1414	—	43	1	no	maximal, Sylow
39	C₂×C₄₃	—	2	1	no	—
40	C₂×C₄₃	—	8	1	no	—
41	C₂×C₄₃	#354	1	1	yes	characteristic
42	#488	—	43	1	no	—
43	#355	D₄₃	1	1	yes	characteristic
44	#354	—	43	1	no	—
45	C₄₃	#1414	1	1	yes	characteristic, complemented, Sylow
46	#125	—	43	1	no	—
47	#124	C₂×D₄₃	1	1	yes	characteristic
48	#103	—	86	1	no	—
49	#102	—	86	1	no	—
50	#101	—	2	1	no	—
51	#99	—	86	1	no	—
52	C₄×C₈	—	43	1	no	—
53	C₂×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
54	C₂×D₄	D₁₇₂	1	1	yes	characteristic
55	M₁₆	—	4	1	no	—
56	C₂×C₈	—	86	1	no	—
57	C₄⋊C₄	—	86	1	no	—
58	C₄⋊C₄	—	172	1	no	—
59	C₂²⋊C₄	—	4	1	no	—
60	C₂²⋊C₄	—	172	1	no	—
61	C₄²	C₄×D₄₃	1	1	yes	characteristic
62	C₂³	—	2	1	no	—
63	Q₈	—	4	1	no	—
64	D₄	—	4	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	344	1	no	—
68	C₂×C₄	—	172	1	no	—
69	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
70	C₈	—	8	1	no	—
71	C₈	—	172	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	8	1	no	—
74	C₂²	#13063239	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	344	1	no	—
79	C₄	—	688	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	#14582693	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582693
commutator	C₄²×C₄₃	C₂×C₄
Frattini	#124	C₂×D₄₃
Fitting	C₄₃×#355	C₂
socle	C₂×C₄₃	#354
hypercenter	#355	D₄₃
hypocenter	C₄₃	#1414
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
4. #13063317	C₄	semidirect
8. C₄×C₄₃⋊C₈	C₄	semidirect
45. C₄₃	#1414	semidirect