Subgroups — #19132644

Order 5504.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#14582652	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#494	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
6	C₂×Q₁₆×C₄₃	—	2	1	no	—
7	C₂×Q₁₆×C₄₃	C₄	1	2	yes	—
8	C₄⋊Q₈×C₄₃	—	2	1	no	—
9	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₄₃	—	2	2	no	—
11	Q₁₆×C₄₃	—	4	2	no	—
12	Q₁₆×C₄₃	—	4	1	no	—
13	Q₁₆×C₄₃	—	4	1	no	—
14	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₄⋊C₄×C₄₃	—	4	1	no	—
17	C₄⋊C₄×C₄₃	—	4	1	no	—
18	C₄²×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄₃⋊C₈	—	4	1	no	—
20	C₄₃⋊C₁₆	—	4	1	no	—
21	Q₈×C₄₃	—	4	2	no	—
22	Q₈×C₄₃	—	4	2	no	—
23	C₂×C₄×C₄₃	—	4	2	no	—
24	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
26	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
27	C₈×C₄₃	—	2	1	no	—
28	C₈×C₄₃	D₈	1	1	yes	characteristic
29	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
30	C₄₃⋊C₈	—	8	1	no	—
31	C₂²×C₄₃	#102	1	1	yes	characteristic
32	C₄×C₄₃	—	2	1	no	—
33	C₄×C₄₃	—	8	2	no	—
34	C₄×C₄₃	#100	1	1	yes	characteristic
35	C₄×C₄₃	#102	1	1	yes	characteristic
36	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
37	C₄×C₄₃	Q₃₂	1	1	yes	characteristic
38	#1362	—	43	1	no	maximal, Sylow
39	C₂×C₄₃	#331	1	1	yes	characteristic
40	C₂×C₄₃	#358	1	1	yes	characteristic
41	C₂×C₄₃	#362	1	1	yes	characteristic
42	#494	D₄₃	1	1	yes	characteristic
43	C₄⋊C₁₆	—	43	1	no	—
44	#335	—	43	1	no	—
45	C₄₃	#1362	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	2	1	no	—
47	C₂×Q₁₆	Dic₄₃	1	2	yes	—
48	C₄⋊Q₈	—	2	1	no	—
49	C₂×C₁₆	—	86	1	no	—
50	C₄⋊C₈	—	86	1	no	—
51	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
52	C₂×Q₈	—	2	2	no	—
53	Q₁₆	—	4	2	no	—
54	Q₁₆	—	4	1	no	—
55	Q₁₆	—	4	1	no	—
56	C₂×C₈	—	172	1	no	—
57	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
59	C₄⋊C₄	—	4	1	no	—
60	C₄⋊C₄	—	4	1	no	—
61	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
62	C₁₆	—	172	1	no	—
63	Q₈	—	4	2	no	—
64	Q₈	—	4	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	#10621882	1	1	yes	characteristic
67	C₂×C₄	#10621883	1	1	yes	characteristic
68	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	344	1	no	—
71	C₈	#10621882	1	1	yes	characteristic
72	C₈	#10621883	1	1	yes	characteristic
73	C₂²	#13063246	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	8	2	no	—
76	C₄	#13063242	1	1	yes	characteristic
77	C₄	#13063246	1	1	yes	characteristic
78	C₄	#13063268	1	1	yes	characteristic
79	C₄	#13063271	1	1	yes	characteristic
80	C₂	#14582643	1	1	yes	characteristic
81	C₂	#14582703	1	1	yes	characteristic
82	C₂	#14582715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063246
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#494	C₂
socle	C₂²×C₄₃	#102
hypercenter	#494	D₄₃
hypocenter	C₄₃	#1362
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
45. C₄₃	#1362	semidirect