Subgroups — C₂×#14582732 #19136886

Order 5504.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#14582732	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₄₃	C₄	1	1	yes	characteristic
6	C₂×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
7	C₁₆×D₄₃	C₄	1	2	yes	—
8	C₁₆×D₄₃	C₂²	1	2	yes	—
9	C₄₃⋊C₃₂	C₂²	1	2	yes	complemented
10	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
11	C₃₂×C₄₃	C₂²	1	2	yes	complemented
12	C₂×C₄×D₄₃	C₈	1	1	yes	characteristic
13	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄₃⋊C₈	C₈	1	1	yes	characteristic
15	C₈×D₄₃	C₈	1	2	yes	—
16	C₈×D₄₃	C₂×C₄	1	2	yes	—
17	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
19	C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
20	C₂²×D₄₃	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₄₃	C₁₆	1	1	yes	characteristic
23	C₄×D₄₃	C₁₆	1	2	yes	—
24	C₄×D₄₃	C₂×C₈	1	2	yes	—
25	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
26	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₄₃⋊C₈	C₂×C₈	1	2	yes	—
28	C₂²×C₄₃	C₂×C₁₆	1	1	yes	characteristic
29	C₂×D₄₃	—	2	2	no	—
30	C₂×D₄₃	C₂×C₁₆	1	2	yes	—
31	C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
32	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
33	Dic₄₃	C₂×C₁₆	1	2	yes	—
34	C₂×M₆₄	—	43	1	no	maximal, Sylow
35	C₂×C₄₃	M₆₄	1	2	yes	complemented
36	C₂×C₄₃	C₂²×C₁₆	1	1	yes	characteristic
37	D₄₃	—	2	2	no	—
38	C₂²×C₁₆	—	43	1	no	—
39	M₆₄	—	43	4	no	—
40	C₂×C₃₂	—	43	1	no	—
41	C₂×C₃₂	D₄₃	1	1	yes	characteristic, complemented
42	C₄₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₈	—	43	1	no	—
44	C₂×C₁₆	—	43	1	no	—
45	C₂×C₁₆	—	43	2	no	—
46	C₂×C₁₆	—	43	2	no	—
47	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
48	C₃₂	—	43	2	no	—
49	C₃₂	C₂×D₄₃	1	2	yes	complemented
50	C₂²×C₄	—	43	1	no	—
51	C₂×C₈	—	43	1	no	—
52	C₂×C₈	—	43	2	no	—
53	C₂×C₈	—	43	2	no	—
54	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
55	C₁₆	—	43	2	no	—
56	C₁₆	C₄×D₄₃	1	1	yes	characteristic
57	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
58	C₂³	—	43	1	no	—
59	C₂×C₄	—	43	1	no	—
60	C₂×C₄	—	43	2	no	—
61	C₂×C₄	—	43	2	no	—
62	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
63	C₈	—	43	2	no	—
64	C₈	C₈×D₄₃	1	1	yes	characteristic
65	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
66	C₂²	—	43	2	no	—
67	C₂²	—	86	2	no	—
68	C₂²	C₁₆×D₄₃	1	1	yes	characteristic
69	C₄	—	43	2	no	—
70	C₄	C₁₆×D₄₃	1	1	yes	characteristic
71	C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
72	C₂	—	86	2	no	—
73	C₂	#14582732	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₄₃
commutator	C₂×C₄₃	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₂×C₃₂×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₁₆
hypercenter	C₂×C₃₂	D₄₃
hypocenter	C₄₃	C₂×M₆₄
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #14582732	C₂	direct (N × H)
3. C₂×C₄₃⋊C₃₂	C₂	semidirect
4. C₂×C₃₂×C₄₃	C₂	semidirect
9. C₄₃⋊C₃₂	C₂²	semidirect
11. C₃₂×C₄₃	C₂²	semidirect
35. C₂×C₄₃	M₆₄	semidirect
41. C₂×C₃₂	D₄₃	semidirect
42. C₄₃	C₂×M₆₄	semidirect
49. C₃₂	C₂×D₄₃	semidirect
73. C₂	#14582732	direct (N × H)

Subgroups — C2×#14582732 #19136886

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582732 #19136886