Subgroups — #19134213

Order 5504.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583304	C₂	1	4	yes	maximal
2	#14583279	C₂	1	2	yes	maximal
3	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₇₂	—	2	4	no	—
5	#13063325	C₂²	1	4	yes	—
6	#13063259	—	2	8	no	—
7	C₄×C₈×C₄₃	C₂²	1	2	yes	—
8	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₈₆	—	2	4	no	—
10	C₂×C₈×C₄₃	D₄	1	2	yes	—
11	C₂×C₈×C₄₃	D₄	1	4	yes	—
12	C₄²×C₄₃	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₄₃	—	2	8	no	—
14	Dic₁₇₂	—	4	8	no	—
15	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
17	C₂×Dic₄₃	—	4	4	no	—
18	Dic₈₆	—	4	8	no	—
19	C₈×C₄₃	D₈	1	4	yes	—
20	C₈×C₄₃	Q₁₆	1	8	yes	complemented
21	C₂²×C₄₃	#127	1	1	yes	characteristic
22	C₄×C₄₃	C₂×D₈	1	2	yes	—
23	C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
24	Dic₄₃	—	8	4	no	—
25	#1713	—	43	1	no	maximal, Sylow
26	C₂×C₄₃	#493	1	1	yes	characteristic
27	C₂×C₄₃	#494	1	2	yes	—
28	#500	—	43	4	no	—
29	#494	—	43	2	no	—
30	C₈²	D₄₃	1	1	yes	characteristic
31	C₄₃	#1713	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₁₆	—	86	4	no	—
33	C₄⋊Q₈	—	43	4	no	—
34	#107	—	86	8	no	—
35	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
36	C₄×C₈	C₂×D₄₃	1	2	yes	—
37	C₂×Q₈	—	86	4	no	—
38	Q₁₆	—	172	8	no	—
39	C₂×C₈	D₁₇₂	1	2	yes	—
40	C₂×C₈	D₁₇₂	1	4	yes	—
41	C₄⋊C₄	—	86	8	no	—
42	C₄²	C₂²×D₄₃	1	1	yes	characteristic
43	Q₈	—	172	8	no	—
44	C₂×C₄	—	172	4	no	—
45	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
46	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
47	C₈	D₃₄₄	1	4	yes	—
48	C₈	Dic₁₇₂	1	8	yes	complemented
49	C₂²	#13063322	1	1	yes	characteristic
50	C₄	—	344	4	no	—
51	C₄	C₂×D₃₄₄	1	2	yes	—
52	C₄	C₂×Dic₁₇₂	1	4	yes	—
53	C₂	#14583276	1	1	yes	characteristic
54	C₂	#14583279	1	2	yes	—

	subgroup	G/H
center	C₂²	#13063322
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₈²×C₄₃	C₂
socle	C₂²×C₄₃	#127
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	#1713
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₄₃	Q₁₆	semidirect
31. C₄₃	#1713	semidirect
48. C₈	Dic₁₇₂	semidirect