Subgroups — #19136482

Order 5504.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583331	C₂	1	1	yes	maximal, characteristic
2	#14583017	C₂	1	2	yes	maximal, complemented
3	#14582729	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582707	C₂	1	2	yes	maximal, complemented
5	C₄₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063347	C₂²	1	2	yes	—
7	#13063331	—	2	2	no	—
8	Dic₃₄₄	C₄	1	1	yes	characteristic, complemented
9	#13063270	C₄	1	2	yes	complemented
10	D₆₈₈	C₄	1	1	yes	characteristic, complemented
11	#13063261	C₂²	1	2	yes	—
12	#13063253	—	2	2	no	—
13	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	#10621898	—	2	2	no	—
17	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄²×C₄₃	D₄	1	1	yes	characteristic
20	#10621877	—	2	2	no	—
21	Dic₁₇₂	C₂×C₄	1	2	yes	—
22	D₃₄₄	C₂×C₄	1	2	yes	—
23	#10621873	—	2	2	no	—
24	#10621872	—	4	2	no	—
25	C₈×D₄₃	—	4	2	no	—
26	C₁₆×C₄₃	—	2	1	no	—
27	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₄₃	—	4	2	no	—
32	D₁₇₂	—	2	2	no	—
33	C₄×D₄₃	—	4	2	no	—
34	Dic₈₆	—	2	2	no	—
35	C₈×C₄₃	D₈	1	2	yes	—
36	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₄₃	#41	1	1	yes	characteristic
38	C₄₃⋊C₈	—	4	2	no	—
39	C₂²×C₄₃	#135	1	1	yes	characteristic
40	C₂×D₄₃	—	4	2	no	—
41	C₄×C₄₃	—	4	1	no	—
42	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
43	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
44	Dic₄₃	—	4	2	no	—
45	#2179	—	43	1	no	maximal, Sylow
46	C₂×C₄₃	—	2	1	no	—
47	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
48	D₄₃	—	8	2	no	—
49	#508	—	43	1	no	—
50	#443	—	43	2	no	—
51	#368	—	43	1	no	—
52	#359	—	43	2	no	—
53	#346	D₄₃	1	1	yes	characteristic, complemented
54	C₄₃	#2179	1	1	yes	characteristic, complemented, Sylow
55	#135	—	43	2	no	—
56	#131	—	86	2	no	—
57	Q₃₂	—	43	1	no	—
58	SD₃₂	—	43	2	no	—
59	D₁₆	—	43	1	no	—
60	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
61	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
62	#108	—	43	2	no	—
63	#104	—	86	2	no	—
64	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
65	#41	—	86	2	no	—
66	Q₁₆	—	43	2	no	—
67	SD₁₆	—	86	2	no	—
68	D₈	—	43	2	no	—
69	M₁₆	—	86	2	no	—
70	M₁₆	—	172	2	no	—
71	C₂×C₈	—	172	2	no	—
72	C₂×C₈	D₁₇₂	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
74	C₄²	D₁₇₂	1	1	yes	characteristic
75	C₁₆	—	2	1	no	—
76	C₁₆	C₄×D₄₃	1	1	yes	characteristic
77	C₁₆	C₄×D₄₃	1	1	yes	characteristic
78	Q₈	—	86	2	no	—
79	D₄	—	86	2	no	—
80	D₄	—	172	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	172	2	no	—
83	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
84	C₈	—	172	2	no	—
85	C₈	D₃₄₄	1	2	yes	—
86	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
87	C₈	#10621898	1	1	yes	characteristic
88	C₂²	—	172	2	no	—
89	C₂²	#13063347	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	172	2	no	—
92	C₄	C₄×D₁₇₂	1	1	yes	characteristic
93	C₄	C₂×D₃₄₄	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	344	2	no	—
96	C₂	C₄×D₃₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₃₄₄
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#346	C₂
socle	C₂×C₄₃	C₄×D₈
hypercenter	#346	D₄₃
hypocenter	C₄₃	#2179
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #14583017	C₂	semidirect
3. #14582729	C₂	semidirect
4. #14582707	C₂	semidirect
5. C₄₃×#346	C₂	semidirect
8. Dic₃₄₄	C₄	semidirect
9. #13063270	C₄	semidirect
10. D₆₈₈	C₄	semidirect
53. #346	D₄₃	semidirect
54. C₄₃	#2179	semidirect