Subgroups — #19136112

Order 5504.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582948	C₂	1	3	yes	maximal, complemented
2	#14582862	C₂	1	3	yes	maximal
3	C₄₃×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
5	C₂×#10621877	C₂²	1	3	yes	—
6	#13063261	—	2	6	no	—
7	(C₂×D₄₃)⋊C₈	—	2	6	no	—
8	C₂×M₁₆×C₄₃	C₂²	1	3	yes	—
9	C₂³×D₄₃	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
11	C₂²×Dic₄₃	Q₈	1	1	yes	characteristic
12	C₂×C₄×D₄₃	—	2	3	no	—
13	C₂×C₄×D₄₃	—	2	3	no	—
14	M₁₆×C₄₃	—	2	6	no	—
15	C₂×C₈×C₄₃	D₄	1	6	yes	—
16	#10621877	—	2	6	no	—
17	C₂×C₄₃⋊C₈	—	2	3	no	—
18	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
19	C₂²×D₄₃	—	2	3	no	—
20	C₂²×D₄₃	—	4	2	no	—
21	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
22	C₂×C₄×C₄₃	#41	1	3	yes	—
23	C₂×Dic₄₃	—	2	3	no	—
24	C₄×D₄₃	—	4	3	no	—
25	C₄×D₄₃	—	4	1	no	—
26	C₈×C₄₃	—	2	6	no	—
27	C₄₃⋊C₈	—	4	3	no	—
28	C₂²×C₄₃	—	4	1	no	—
29	C₂²×C₄₃	C₂²⋊Q₈	1	3	yes	—
30	C₂×D₄₃	—	2	6	no	—
31	C₂×D₄₃	—	4	3	no	—
32	C₂×D₄₃	—	4	1	no	—
33	C₄×C₄₃	#123	1	3	yes	—
34	C₄×C₄₃	#127	1	1	yes	characteristic
35	Dic₄₃	—	4	1	no	—
36	#2091	—	43	1	no	maximal, Sylow
37	C₂×C₄₃	—	2	3	no	—
38	C₂×C₄₃	#399	1	1	yes	characteristic
39	D₄₃	—	4	2	no	—
40	#430	—	43	3	no	—
41	#407	—	43	3	no	—
42	#338	D₄₃	1	1	yes	characteristic, complemented
43	C₄₃	#2091	1	1	yes	characteristic, complemented, Sylow
44	C₂³×C₄	—	43	1	no	—
45	C₂×M₁₆	—	43	3	no	—
46	C₂×M₁₆	C₂×D₄₃	1	3	yes	—
47	#108	—	86	6	no	—
48	C₂²⋊C₈	—	86	6	no	—
49	C₂⁴	—	43	1	no	—
50	C₂²×C₄	—	43	1	no	—
51	C₂²×C₄	—	86	3	no	—
52	C₂²×C₄	—	86	3	no	—
53	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
54	M₁₆	—	2	6	no	—
55	M₁₆	—	86	6	no	—
56	C₂×C₈	—	86	3	no	—
57	C₂×C₈	D₁₇₂	1	6	yes	—
58	C₂³	—	86	3	no	—
59	C₂³	—	172	2	no	—
60	C₂³	Q₈×D₄₃	1	1	yes	characteristic
61	C₂×C₄	—	86	3	no	—
62	C₂×C₄	—	172	3	no	—
63	C₂×C₄	—	172	1	no	—
64	C₂×C₄	C₂×D₁₇₂	1	3	yes	—
65	C₂×C₄	#10621900	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	172	3	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	86	6	no	—
70	C₂²	—	172	3	no	—
71	C₂²	—	172	1	no	—
72	C₂²	#13063305	1	3	yes	—
73	C₄	—	172	1	no	—
74	C₄	#13063309	1	3	yes	—
75	C₄	#13063322	1	1	yes	characteristic
76	C₂	—	2	3	no	—
77	C₂	—	172	2	no	—
78	C₂	#14582836	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13063322
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#338	C₂
socle	C₂×C₄₃	#399
hypercenter	#338	D₄₃
hypocenter	C₄₃	#2091
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #14582948	C₂	semidirect
3. C₄₃×#338	C₂	semidirect
42. #338	D₄₃	semidirect
43. C₄₃	#2091	semidirect