Subgroups — #19132734

Order 5504.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063264	C₂	1	1	yes	maximal, characteristic
2	#14582733	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₄₃	C₄	1	1	yes	characteristic
5	#13063264	—	2	1	no	—
6	#13063264	—	2	1	no	—
7	C₂×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
8	C₄₃⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₄₃	—	2	1	no	—
11	C₂×C₄×D₄₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄₃⋊C₈	C₈	1	1	yes	characteristic
14	C₈×D₄₃	—	2	1	no	—
15	C₈×D₄₃	—	2	1	no	—
16	C₁₆×C₄₃	D₄	1	1	yes	characteristic
17	C₁₆×C₄₃	D₄	1	1	yes	characteristic
18	C₄₃⋊C₁₆	—	2	1	no	—
19	C₂²×D₄₃	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₄₃	C₁₆	1	1	yes	characteristic
22	C₄×D₄₃	—	2	1	no	—
23	C₄×D₄₃	—	2	1	no	—
24	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₄₃	M₁₆	1	1	yes	characteristic
26	C₄₃⋊C₈	—	2	1	no	—
27	C₂²×C₄₃	C₂×C₁₆	1	1	yes	characteristic
28	C₂×D₄₃	—	2	1	no	—
29	C₂×D₄₃	—	4	1	no	—
30	C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₄₃	M₃₂	1	1	yes	characteristic
32	Dic₄₃	—	2	1	no	—
33	#1400	—	43	1	no	maximal, Sylow
34	C₂×C₄₃	—	2	1	no	—
35	C₂×C₄₃	C₂²⋊C₁₆	1	1	yes	characteristic
36	D₄₃	—	4	1	no	—
37	C₂×M₃₂	—	43	1	no	—
38	M₆₄	—	43	1	no	—
39	M₆₄	D₄₃	1	1	yes	characteristic, complemented
40	C₄₃	#1400	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	—	43	1	no	—
42	M₃₂	—	86	1	no	—
43	M₃₂	—	86	1	no	—
44	C₂×C₁₆	—	43	1	no	—
45	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
46	C₃₂	—	2	1	no	—
47	C₃₂	—	86	1	no	—
48	C₂²×C₄	—	43	1	no	—
49	C₂×C₈	—	43	1	no	—
50	C₂×C₈	—	86	1	no	—
51	C₂×C₈	—	86	1	no	—
52	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
53	C₁₆	—	86	1	no	—
54	C₁₆	D₁₇₂	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
56	C₂³	—	43	1	no	—
57	C₂×C₄	—	43	1	no	—
58	C₂×C₄	—	86	1	no	—
59	C₂×C₄	—	86	1	no	—
60	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
61	C₈	—	86	1	no	—
62	C₈	#10621872	1	1	yes	characteristic
63	C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
64	C₂²	—	86	1	no	—
65	C₂²	—	172	1	no	—
66	C₂²	C₁₆×D₄₃	1	1	yes	characteristic
67	C₄	—	86	1	no	—
68	C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
69	C₄	#13063264	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	172	1	no	—
72	C₂	(C₂×D₄₃)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₈	(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₄₃×M₆₄	C₂
socle	C₂×C₄₃	C₂²⋊C₁₆
hypercenter	M₆₄	D₄₃
hypocenter	C₄₃	#1400
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #14582733	C₂	semidirect
3. C₄₃×M₆₄	C₂	semidirect
39. M₆₄	D₄₃	semidirect
40. C₄₃	#1400	semidirect