Subgroups — #19134211

Order 5504.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583302	C₂	1	4	yes	maximal
2	#14583279	C₂	1	1	yes	maximal, characteristic
3	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#494	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₇₂	—	2	2	no	—
6	#13063325	C₂²	1	2	yes	—
7	#13063258	—	2	8	no	—
8	C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₄₃	—	2	2	no	—
10	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
11	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₄₃	—	2	2	no	—
13	C₂×Dic₈₆	—	2	2	no	—
14	Q₁₆×C₄₃	—	4	4	no	—
15	C₂×C₈×C₄₃	D₄	1	2	yes	—
16	C₄⋊C₄×C₄₃	—	2	4	no	—
17	C₄²×C₄₃	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₄₃	—	2	4	no	—
19	C₂×C₄₃⋊C₈	D₄	1	4	yes	—
20	Dic₁₇₂	—	4	4	no	—
21	Q₈×C₄₃	—	4	4	no	—
22	C₂×C₄×C₄₃	—	4	2	no	—
23	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
24	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₄₃	—	4	2	no	—
26	Dic₈₆	—	4	4	no	—
27	C₈×C₄₃	D₈	1	4	yes	—
28	C₄₃⋊C₈	Q₁₆	1	8	yes	complemented
29	C₂²×C₄₃	#127	1	1	yes	characteristic
30	C₄×C₄₃	—	8	2	no	—
31	C₄×C₄₃	C₂×D₈	1	2	yes	—
32	C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
33	Dic₄₃	—	8	2	no	—
34	#1713	—	43	1	no	maximal, Sylow
35	C₂×C₄₃	#493	1	1	yes	characteristic
36	C₂×C₄₃	#494	1	2	yes	—
37	#500	—	43	4	no	—
38	#494	—	43	1	no	—
39	#494	D₄₃	1	1	yes	characteristic
40	C₈²	—	43	1	no	—
41	C₄₃	#1713	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₁₆	—	2	2	no	—
43	C₂×Q₁₆	—	86	2	no	—
44	C₄⋊Q₈	—	43	2	no	—
45	C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
46	#107	—	86	8	no	—
47	C₄×C₈	—	43	2	no	—
48	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
49	C₂×Q₈	—	2	2	no	—
50	C₂×Q₈	—	86	2	no	—
51	Q₁₆	—	4	4	no	—
52	Q₁₆	—	172	4	no	—
53	C₂×C₈	—	43	4	no	—
54	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
55	C₄⋊C₄	—	2	4	no	—
56	C₄⋊C₄	—	86	4	no	—
57	C₄²	C₂²×D₄₃	1	1	yes	characteristic
58	Q₈	—	4	4	no	—
59	Q₈	—	172	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	172	2	no	—
62	C₂×C₄	D₄×D₄₃	1	2	yes	—
63	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
64	C₈	—	43	8	no	—
65	C₈	#10621882	1	4	yes	—
66	C₂²	#13063321	1	1	yes	characteristic
67	C₄	—	8	2	no	—
68	C₄	—	344	2	no	—
69	C₄	C₂×#10621882	1	2	yes	—
70	C₄	Q₁₆×D₄₃	1	4	yes	—
71	C₂	#14583275	1	1	yes	characteristic
72	C₂	#14583277	1	2	yes	—

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#494	C₂
socle	C₂²×C₄₃	#127
hypercenter	#494	D₄₃
hypocenter	C₄₃	#1713
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
28. C₄₃⋊C₈	Q₁₆	semidirect
41. C₄₃	#1713	semidirect