Subgroups — #19136882

Order 5504.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583304	C₂	1	1	yes	maximal, characteristic
2	#14582726	C₂	1	2	yes	maximal
3	#14582724	C₂	1	2	yes	maximal
4	#14582675	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#499	C₂	1	1	yes	maximal, characteristic
6	#13063325	—	2	1	no	—
7	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
8	#13063259	—	2	1	no	—
9	#13063259	C₂²	1	2	yes	—
10	#125×C₄₃	—	2	1	no	—
11	#107×C₄₃	C₂²	1	1	yes	characteristic
12	#107×C₄₃	C₂²	1	1	yes	characteristic
13	#106×C₄₃	—	2	1	no	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₈₆	—	4	1	no	—
16	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₄₃	—	2	1	no	—
19	C₄⋊C₄×C₄₃	—	2	1	no	—
20	C₄⋊C₄×C₄₃	—	4	1	no	—
21	C₄⋊C₄×C₄₃	—	4	1	no	—
22	C₄²×C₄₃	D₄	1	1	yes	characteristic
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	—	4	1	no	—
25	C₄₃⋊C₁₆	Q₈	1	4	yes	complemented
26	C₂×C₄×C₄₃	—	4	1	no	—
27	C₂×C₄×C₄₃	—	4	1	no	—
28	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₄₃	—	4	2	no	—
32	Dic₈₆	—	8	2	no	—
33	C₈×C₄₃	Q₁₆	1	2	yes	—
34	C₈×C₄₃	C₂×Q₈	1	2	yes	—
35	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₄₃	—	2	1	no	—
37	C₄×C₄₃	—	2	1	no	—
38	C₄×C₄₃	—	8	1	no	—
39	C₄×C₄₃	—	8	1	no	—
40	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
41	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
42	Dic₄₃	—	8	2	no	—
43	#2255	—	43	1	no	maximal, Sylow
44	C₂×C₄₃	#500	1	1	yes	characteristic
45	C₂×C₄₃	#509	1	1	yes	characteristic
46	C₂×C₄₃	#510	1	1	yes	characteristic
47	#500	—	43	1	no	—
48	#499	D₄₃	1	1	yes	characteristic
49	#367	—	43	2	no	—
50	#366	—	43	2	no	—
51	#346	—	43	1	no	—
52	C₄₃	#2255	1	1	yes	characteristic, complemented, Sylow
53	C₄⋊Q₈	—	86	1	no	—
54	#125	—	2	1	no	—
55	C₂×C₁₆	—	43	2	no	—
56	#107	—	43	2	no	—
57	#107	—	86	1	no	—
58	#107	C₂×D₄₃	1	1	yes	characteristic
59	#107	C₂×D₄₃	1	1	yes	characteristic
60	#106	—	2	1	no	—
61	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
62	C₂×Q₈	—	172	1	no	—
63	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
65	C₄⋊C₄	—	2	1	no	—
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄⋊C₄	—	4	1	no	—
69	C₄⋊C₄	—	86	2	no	—
70	C₄⋊C₄	—	172	1	no	—
71	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
72	C₁₆	—	43	4	no	—
73	Q₈	—	344	2	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	172	2	no	—
77	C₂×C₄	#10621882	1	1	yes	characteristic
78	C₂×C₄	#10621882	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
80	C₈	#10621885	1	2	yes	—
81	C₈	Q₈×D₄₃	1	2	yes	—
82	C₂²	C₂×#10621882	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	8	1	no	—
87	C₄	—	344	2	no	—
88	C₄	#13063323	1	1	yes	characteristic
89	C₄	C₂×#10621885	1	1	yes	characteristic
90	C₂	#14583302	1	1	yes	characteristic
91	C₂	#14583334	1	1	yes	characteristic
92	C₂	#14583339	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#499	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#499	D₄₃
hypocenter	C₄₃	#2255
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
25. C₄₃⋊C₁₆	Q₈	semidirect
52. C₄₃	#2255	semidirect