Subgroups — #19134209

Order 5504.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583276	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583275	C₂	1	4	yes	maximal, complemented
3	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₄₄	—	2	2	no	—
6	C₂×#10621882	—	2	8	no	—
7	#13063322	C₂²	1	2	yes	—
8	C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
9	C₂×D₈×C₄₃	—	2	2	no	—
10	#127×C₄₃	C₂²	1	2	yes	—
11	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×D₄×C₄₃	—	2	2	no	—
13	C₂×D₄×C₄₃	—	2	4	no	—
14	C₂×D₁₇₂	—	2	4	no	—
15	C₂×D₁₇₂	—	2	2	no	—
16	D₈×C₄₃	—	4	4	no	—
17	C₂×C₈×C₄₃	D₄	1	2	yes	—
18	C₄²×C₄₃	C₂³	1	1	yes	characteristic
19	#10621882	—	4	16	no	—
20	C₂×C₄₃⋊C₈	D₄	1	4	yes	—
21	D₃₄₄	—	4	4	no	—
22	C₂³×C₄₃	—	4	2	no	—
23	C₂²×D₄₃	—	4	2	no	—
24	D₄×C₄₃	—	4	8	no	—
25	D₄×C₄₃	—	4	4	no	—
26	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
28	D₁₇₂	—	4	4	no	—
29	D₁₇₂	—	4	8	no	—
30	C₈×C₄₃	D₈	1	4	yes	complemented
31	C₄₃⋊C₈	D₈	1	8	yes	complemented
32	C₂²×C₄₃	—	8	4	no	—
33	C₂²×C₄₃	—	8	2	no	—
34	C₂²×C₄₃	#127	1	1	yes	characteristic
35	C₂×D₄₃	—	8	4	no	—
36	C₂×D₄₃	—	8	2	no	—
37	C₄×C₄₃	C₂×D₈	1	4	yes	—
38	C₄×C₄₃	C₂×D₈	1	2	yes	—
39	#1712	—	43	1	no	maximal, Sylow
40	C₂×C₄₃	—	16	2	no	—
41	C₂×C₄₃	#493	1	2	yes	—
42	C₂×C₄₃	#493	1	1	yes	characteristic
43	D₄₃	—	16	2	no	—
44	#493	—	43	4	no	—
45	#493	—	43	1	no	—
46	#493	D₄₃	1	1	yes	characteristic, complemented
47	C₈²	—	43	1	no	—
48	C₄₃	#1712	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₈	—	2	2	no	—
50	C₂×D₈	—	86	8	no	—
51	C₂×D₈	—	86	2	no	—
52	#127	—	43	2	no	—
53	#127	C₂×D₄₃	1	2	yes	—
54	C₄×C₈	—	43	2	no	—
55	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	—	2	2	no	—
58	C₂×D₄	—	86	4	no	—
59	C₂×D₄	—	86	2	no	—
60	D₈	—	4	4	no	—
61	D₈	—	172	16	no	—
62	D₈	—	172	4	no	—
63	C₂×C₈	—	43	4	no	—
64	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
65	C₄²	C₂²×D₄₃	1	1	yes	characteristic
66	C₂³	—	4	2	no	—
67	C₂³	—	172	2	no	—
68	D₄	—	4	8	no	—
69	D₄	—	4	4	no	—
70	D₄	—	172	8	no	—
71	D₄	—	172	4	no	—
72	C₂×C₄	D₄×D₄₃	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
74	C₈	—	43	8	no	—
75	C₈	#10621882	1	4	yes	complemented
76	C₂²	—	8	4	no	—
77	C₂²	—	8	2	no	—
78	C₂²	—	344	4	no	—
79	C₂²	—	344	2	no	—
80	C₂²	#13063321	1	1	yes	characteristic
81	C₄	D₈×D₄₃	1	4	yes	—
82	C₄	C₂×#10621882	1	2	yes	—
83	C₂	—	16	2	no	—
84	C₂	—	688	2	no	—
85	C₂	#14583274	1	2	yes	—
86	C₂	#14583275	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#493	C₂
socle	C₂²×C₄₃	#127
hypercenter	#493	D₄₃
hypocenter	C₄₃	#1712
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

Complements

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

N	H ≅ G/N	type
1. #14583276	C₂	semidirect
2. #14583275	C₂	semidirect
3. C₈×C₄₃⋊C₈	C₂	semidirect
4. C₄₃×#493	C₂	semidirect
30. C₈×C₄₃	D₈	semidirect
31. C₄₃⋊C₈	D₈	semidirect
46. #493	D₄₃	semidirect
48. C₄₃	#1712	semidirect
75. C₈	#10621882	semidirect