Subgroups — #19133884

Order 5504.

262 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583289	C₂	1	3	yes	maximal, complemented
2	#14582639	C₂	1	3	yes	maximal, complemented
3	C₄₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10621884	—	2	3	no	—
5	C₂×#10621882	—	2	3	no	—
6	#13063322	C₂²	1	1	yes	characteristic, complemented
7	#13063236	C₂²	1	3	yes	complemented
8	#124×C₄₃	—	2	3	no	—
9	#124×C₄₃	C₂²	1	3	yes	—
10	#120×C₄₃	—	2	3	no	—
11	C₂⁴×C₄₃	—	2	1	no	—
12	C₂×Q₈×C₄₃	D₄	1	3	yes	—
13	C₂×D₄×C₄₃	—	2	3	no	—
14	C₂×D₄×C₄₃	D₄	1	3	yes	—
15	C₂×D₁₇₂	—	2	3	no	—
16	C₂²⋊C₄×C₄₃	—	2	3	no	—
17	C₂²⋊C₄×C₄₃	—	2	6	no	—
18	C₄²×C₄₃	—	2	1	no	—
19	C₄²×C₄₃	C₂³	1	1	yes	characteristic
20	#10621884	—	4	6	no	—
21	#10621882	—	4	6	no	—
22	C₂×C₄₃⋊C₈	—	2	3	no	—
23	C₂³×C₄₃	—	2	3	no	—
24	C₂³×C₄₃	—	8	3	no	—
25	C₂²×D₄₃	—	4	1	no	—
26	Q₈×C₄₃	—	4	3	no	—
27	D₄×C₄₃	—	4	3	no	—
28	D₄×C₄₃	—	8	3	no	—
29	C₂×C₄×C₄₃	—	2	3	no	—
30	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
31	D₁₇₂	—	4	3	no	—
32	D₁₇₂	—	4	3	no	—
33	C₄₃⋊C₈	—	2	6	no	—
34	C₂²×C₄₃	—	4	3	no	—
35	C₂²×C₄₃	—	4	6	no	—
36	C₂²×C₄₃	—	8	4	no	—
37	C₂²×C₄₃	#120	1	1	yes	characteristic
38	C₂×D₄₃	—	8	3	no	—
39	C₄×C₄₃	—	2	3	no	—
40	C₄×C₄₃	—	4	3	no	—
41	#1655	—	43	1	no	maximal, Sylow
42	C₂×C₄₃	—	8	3	no	—
43	C₂×C₄₃	#453	1	3	yes	—
44	D₄₃	—	16	1	no	—
45	H(3,𝔽₄)	D₄₃	1	1	yes	characteristic, complemented
46	#496	—	43	3	no	—
47	#329	—	43	3	no	—
48	C₄₃	#1655	1	1	yes	characteristic, complemented, Sylow
49	C₂×SD₁₆	—	86	3	no	—
50	C₂×D₈	—	86	3	no	—
51	#127	—	43	1	no	—
52	#124	—	2	3	no	—
53	#124	C₂×D₄₃	1	3	yes	—
54	#120	—	2	3	no	—
55	#97	—	43	3	no	—
56	C₂⁴	—	2	1	no	—
57	C₂×Q₈	C₂²⋊D₄₃	1	3	yes	—
58	C₂×D₄	—	2	3	no	—
59	C₂×D₄	—	86	3	no	—
60	C₂×D₄	C₂²⋊D₄₃	1	3	yes	—
61	SD₁₆	—	172	6	no	—
62	D₈	—	172	6	no	—
63	C₂×C₈	—	86	3	no	—
64	C₂²⋊C₄	—	2	3	no	—
65	C₂²⋊C₄	—	2	6	no	—
66	C₄²	—	2	1	no	—
67	C₄²	C₂²×D₄₃	1	1	yes	characteristic
68	C₂³	—	2	3	no	—
69	C₂³	—	8	3	no	—
70	C₂³	—	172	1	no	—
71	Q₈	—	4	3	no	—
72	D₄	—	4	3	no	—
73	D₄	—	8	3	no	—
74	D₄	—	172	3	no	—
75	D₄	—	172	3	no	—
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
78	C₈	—	86	6	no	—
79	C₂²	—	4	3	no	—
80	C₂²	—	4	6	no	—
81	C₂²	—	8	4	no	—
82	C₂²	—	344	3	no	—
83	C₂²	#13063294	1	1	yes	characteristic
84	C₄	—	2	3	no	—
85	C₄	—	4	3	no	—
86	C₂	—	8	3	no	—
87	C₂	—	688	1	no	—
88	C₂	#14583067	1	3	yes	—

	subgroup	G/H
center	C₂²	#13063294
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×H(3,𝔽₄)	C₂
socle	C₂²×C₄₃	#120
hypercenter	H(3,𝔽₄)	D₄₃
hypocenter	C₄₃	#1655
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #14583289	C₂	semidirect
2. #14582639	C₂	semidirect
3. C₄₃×H(3,𝔽₄)	C₂	semidirect
6. #13063322	C₂²	semidirect
7. #13063236	C₂²	semidirect
45. H(3,𝔽₄)	D₄₃	semidirect
48. C₄₃	#1655	semidirect