Subgroups — #19136390

Order 5504.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063261	C₂	1	2	yes	maximal
2	#14582729	C₂	1	4	yes	maximal, complemented
3	C₂×M₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	—	2	2	no	—
5	#13063261	—	2	2	no	—
6	#13063261	C₂²	1	4	yes	—
7	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	M₃₂×C₄₃	C₄	1	4	yes	—
9	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
10	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
11	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₄₃	Q₈	1	2	yes	—
14	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
15	#10621877	—	2	4	no	—
16	#10621877	—	4	2	no	—
17	C₂×C₄₃⋊C₈	—	4	2	no	—
18	C₁₆×C₄₃	C₂×C₄	1	4	yes	—
19	C₂³×C₄₃	Q₁₆	1	1	yes	characteristic
20	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₄₃	D₈	1	2	yes	—
22	C₂×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
24	C₈×C₄₃	C₄⋊C₄	1	2	yes	—
25	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
27	C₄₃⋊C₈	—	4	4	no	—
28	C₂²×C₄₃	—	4	1	no	—
29	C₂²×C₄₃	#107	1	2	yes	—
30	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
31	C₄×C₄₃	#107	1	2	yes	—
32	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
34	#2161	—	43	1	no	maximal, Sylow
35	C₂×C₄₃	—	2	2	no	—
36	C₂×C₄₃	—	2	1	no	—
37	C₂×C₄₃	C₂×#107	1	1	yes	characteristic
38	C₂×M₃₂	D₄₃	1	1	yes	characteristic
39	C₂×#108	—	43	2	no	—
40	#368	—	43	4	no	—
41	C₄₃	#2161	1	1	yes	characteristic, complemented, Sylow
42	C₂×M₁₆	—	86	2	no	—
43	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
44	M₃₂	Dic₄₃	1	4	yes	—
45	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
46	#108	—	43	4	no	—
47	#108	—	86	2	no	—
48	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
49	M₁₆	—	86	4	no	—
50	M₁₆	—	172	2	no	—
51	C₂×C₈	—	172	2	no	—
52	C₂×C₈	Dic₈₆	1	2	yes	—
53	C₂×C₈	D₁₇₂	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
55	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
56	C₁₆	C₂×Dic₄₃	1	4	yes	—
57	C₂³	Dic₁₇₂	1	1	yes	characteristic
58	C₂×C₄	D₃₄₄	1	2	yes	—
59	C₂×C₄	Dic₁₇₂	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
61	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
62	C₈	—	172	4	no	—
63	C₈	C₄⋊Dic₄₃	1	2	yes	—
64	C₈	C₂×Dic₈₆	1	1	yes	characteristic
65	C₈	C₂²×Dic₄₃	1	1	yes	characteristic
66	C₂²	—	4	1	no	—
67	C₂²	#13063259	1	2	yes	—
68	C₂²	C₂×Dic₁₇₂	1	1	yes	characteristic
69	C₄	#13063259	1	2	yes	—
70	C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
71	C₄	C₂×D₃₄₄	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	C₂×#13063259	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₃₄₄
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×M₃₂×C₄₃	C₂
socle	C₂×C₄₃	C₂×#107
hypercenter	C₂×M₃₂	D₄₃
hypocenter	C₄₃	#2161
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
2. #14582729	C₂	semidirect
41. C₄₃	#2161	semidirect