Subgroups — #19136453

Order 5504.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₄₄	C₂	1	1	yes	maximal, characteristic
2	#14582993	C₂	1	2	yes	maximal
3	#14582702	C₂	1	2	yes	maximal
4	C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#366	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₂²	1	2	yes	—
7	#13063290	—	2	2	no	—
8	Dic₃₄₄	C₄	1	4	yes	complemented
9	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	#13063248	—	2	2	no	—
11	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	#107×C₄₃	C₂²	1	2	yes	—
14	C₂×Dic₈₆	—	2	2	no	—
15	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₄₃	—	2	2	no	—
17	Dic₄₃⋊C₄	—	4	2	no	—
18	C₄×Dic₄₃	—	4	2	no	—
19	C₄×Dic₄₃	D₄	1	1	yes	characteristic
20	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
21	Dic₁₇₂	—	2	2	no	—
22	Dic₁₇₂	C₂×C₄	1	4	yes	—
23	C₁₆×C₄₃	C₂×C₄	1	2	yes	—
24	C₄₃⋊C₁₆	—	2	1	no	—
25	C₂×C₄×C₄₃	—	4	2	no	—
26	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₄₃	—	4	2	no	—
28	C₂×Dic₄₃	D₈	1	1	yes	characteristic
29	C₂×Dic₄₃	D₈	1	1	yes	characteristic
30	Dic₈₆	—	2	4	no	—
31	Dic₈₆	—	4	2	no	—
32	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₄₃	#41	1	1	yes	characteristic
34	C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₄₃	—	8	2	no	—
37	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
38	C₄×C₄₃	#135	1	1	yes	characteristic
39	Dic₄₃	—	2	1	no	—
40	Dic₄₃	—	4	4	no	—
41	Dic₄₃	Q₃₂	1	2	yes	complemented
42	C₄×Q₃₂	—	43	1	no	maximal, Sylow
43	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
44	C₂×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
45	C₂×C₄₃	#508	1	1	yes	characteristic
46	C₂×Q₃₂	—	43	1	no	—
47	C₄×Q₁₆	—	43	2	no	—
48	#366	D₄₃	1	1	yes	characteristic
49	#358	—	43	2	no	—
50	C₄×C₁₆	—	43	1	no	—
51	C₄₃	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	—	43	2	no	—
53	C₄×Q₈	—	86	2	no	—
54	Q₃₂	—	43	4	no	—
55	C₂×C₁₆	—	43	1	no	—
56	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
57	#107	C₂×D₄₃	1	2	yes	—
58	#103	—	86	2	no	—
59	C₄×C₈	—	43	1	no	—
60	C₂×Q₈	—	86	2	no	—
61	Q₁₆	—	43	4	no	—
62	Q₁₆	—	86	2	no	—
63	C₂×C₈	—	43	1	no	—
64	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	172	2	no	—
67	C₄²	—	43	1	no	—
68	C₄²	—	172	2	no	—
69	C₁₆	—	86	1	no	—
70	C₁₆	C₄×D₄₃	1	2	yes	—
71	Q₈	—	86	4	no	—
72	Q₈	—	172	2	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	43	1	no	—
75	C₂×C₄	—	43	1	no	—
76	C₂×C₄	—	172	2	no	—
77	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
78	C₈	—	86	1	no	—
79	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
80	C₈	#10621902	1	1	yes	characteristic
81	C₂²	D₈×D₄₃	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	43	2	no	—
84	C₄	—	86	1	no	—
85	C₄	—	172	4	no	—
86	C₄	#13063287	1	1	yes	characteristic
87	C₄	#13063348	1	1	yes	characteristic
88	C₂	#14582981	1	1	yes	characteristic
89	C₂	Q₃₂×D₄₃	1	1	yes	characteristic
90	C₂	#14583328	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#366	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#366	D₄₃
hypocenter	C₄₃	C₄×Q₃₂
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
8. Dic₃₄₄	C₄	semidirect
41. Dic₄₃	Q₃₂	semidirect
51. C₄₃	C₄×Q₃₂	semidirect