Subgroups — #19134194

Order 5504.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583297	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583251	C₂	1	2	yes	maximal, complemented
3	#14583245	C₂	1	2	yes	maximal
4	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#492	C₂	1	1	yes	maximal, characteristic
6	#13063325	C₂²	1	2	yes	—
7	#13063257	—	2	2	no	—
8	#13063248	—	2	4	no	—
9	#13063246	—	2	4	no	—
10	C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
11	C₂×SD₁₆×C₄₃	—	2	2	no	—
12	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	#127×C₄₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₃	—	2	1	no	—
16	C₂×D₄×C₄₃	—	2	1	no	—
17	C₂×D₄×C₄₃	—	2	2	no	—
18	C₂×Dic₈₆	—	2	2	no	—
19	SD₁₆×C₄₃	—	4	4	no	—
20	C₂×C₈×C₄₃	D₄	1	2	yes	—
21	C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₄²×C₄₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	—	2	2	no	—
25	C₂×C₄₃⋊C₈	D₄	1	4	yes	—
26	C₂³×C₄₃	—	4	1	no	—
27	Q₈×C₄₃	—	4	2	no	—
28	D₄×C₄₃	—	4	2	no	—
29	D₄×C₄₃	—	4	4	no	—
30	C₂×C₄×C₄₃	—	4	1	no	—
31	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₄₃	—	4	2	no	—
34	Dic₈₆	—	4	4	no	—
35	C₈×C₄₃	SD₁₆	1	4	yes	—
36	C₄₃⋊C₈	—	2	4	no	—
37	C₂²×C₄₃	—	8	1	no	—
38	C₂²×C₄₃	—	8	2	no	—
39	C₂²×C₄₃	#127	1	1	yes	characteristic
40	C₄×C₄₃	—	8	1	no	—
41	C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
42	C₄×C₄₃	#135	1	4	yes	—
43	Dic₄₃	—	8	2	no	—
44	#1708	—	43	1	no	maximal, Sylow
45	C₂×C₄₃	—	16	1	no	—
46	C₂×C₄₃	#492	1	1	yes	characteristic
47	C₂×C₄₃	#495	1	2	yes	—
48	#498	—	43	1	no	—
49	#492	D₄₃	1	1	yes	characteristic
50	#487	—	43	2	no	—
51	#486	—	43	2	no	—
52	C₈²	—	43	1	no	—
53	C₄₃	#1708	1	1	yes	characteristic, complemented, Sylow
54	C₂×SD₁₆	—	2	2	no	—
55	C₄⋊Q₈	—	43	2	no	—
56	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
57	#127	C₂×D₄₃	1	1	yes	characteristic
58	#106	—	86	2	no	—
59	#103	—	86	4	no	—
60	#102	—	86	4	no	—
61	C₄×C₈	—	43	2	no	—
62	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
63	C₂×Q₈	—	2	1	no	—
64	C₂×Q₈	—	86	2	no	—
65	C₂×D₄	—	2	2	no	—
66	C₂×D₄	—	2	1	no	—
67	SD₁₆	—	4	4	no	—
68	C₂×C₈	—	43	4	no	—
69	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	86	2	no	—
72	C₄⋊C₄	—	86	2	no	—
73	C₄²	C₂²×D₄₃	1	1	yes	characteristic
74	C₂³	—	4	1	no	—
75	Q₈	—	4	2	no	—
76	Q₈	—	172	4	no	—
77	D₄	—	4	2	no	—
78	D₄	—	4	4	no	—
79	C₂×C₄	—	4	1	no	—
80	C₂×C₄	—	172	2	no	—
81	C₂×C₄	D₄×D₄₃	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
83	C₈	—	86	4	no	—
84	C₈	#10621883	1	4	yes	—
85	C₂²	—	8	1	no	—
86	C₂²	—	8	2	no	—
87	C₂²	#13063321	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	344	2	no	—
90	C₄	C₂×#10621883	1	2	yes	—
91	C₄	#13063346	1	4	yes	—
92	C₂	—	16	1	no	—
93	C₂	#14583271	1	1	yes	characteristic
94	C₂	#14583280	1	2	yes	—

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#492	C₂
socle	C₂²×C₄₃	#127
hypercenter	#492	D₄₃
hypocenter	C₄₃	#1708
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

Complements

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

N	H ≅ G/N	type
1. #14583297	C₂	semidirect
2. #14583251	C₂	semidirect
4. C₈×C₄₃⋊C₈	C₂	semidirect
53. C₄₃	#1708	semidirect