Subgroups — #19132631

Order 5504.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583276	C₂	1	1	yes	maximal, characteristic
2	#14582720	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₄₄	—	2	1	no	—
5	C₂×D₃₄₄	—	2	1	no	—
6	#13063322	C₄	1	2	yes	—
7	#13063265	—	2	1	no	—
8	M₃₂×C₄₃	—	2	1	no	—
9	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×D₁₇₂	—	2	2	no	—
11	C₂×D₁₇₂	—	4	2	no	—
12	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
14	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
15	D₃₄₄	—	4	1	no	—
16	D₃₄₄	—	4	1	no	—
17	D₃₄₄	—	4	1	no	—
18	D₃₄₄	—	4	1	no	—
19	C₁₆×C₄₃	—	4	1	no	—
20	C₄₃⋊C₁₆	—	4	1	no	—
21	C₂²×D₄₃	—	4	2	no	—
22	C₂×C₄×C₄₃	—	2	1	no	—
23	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
24	D₁₇₂	—	4	2	no	—
25	D₁₇₂	—	4	2	no	—
26	D₁₇₂	—	8	4	no	—
27	C₈×C₄₃	D₈	1	1	yes	characteristic
28	C₈×C₄₃	D₈	1	1	yes	characteristic
29	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
31	C₂²×C₄₃	#100	1	1	yes	characteristic
32	C₂×D₄₃	—	8	4	no	—
33	C₂×D₄₃	—	8	2	no	—
34	C₄×C₄₃	—	2	2	no	—
35	C₄×C₄₃	#102	1	1	yes	characteristic
36	C₄×C₄₃	#102	1	1	yes	characteristic
37	#1357	—	43	1	no	maximal, Sylow
38	C₂×C₄₃	—	2	1	no	—
39	C₂×C₄₃	#331	1	1	yes	characteristic
40	D₄₃	—	16	2	no	—
41	#493	—	43	1	no	—
42	#364	—	43	1	no	—
43	#364	D₄₃	1	1	yes	characteristic, complemented
44	C₄₃	#1357	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₈	—	86	1	no	—
46	C₂×D₈	—	86	1	no	—
47	#127	—	43	2	no	—
48	M₃₂	—	2	1	no	—
49	M₃₂	—	86	1	no	—
50	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
51	C₂×D₄	—	86	2	no	—
52	C₂×D₄	—	172	2	no	—
53	D₈	—	172	1	no	—
54	D₈	—	172	1	no	—
55	D₈	—	172	1	no	—
56	D₈	—	172	1	no	—
57	C₂×C₈	D₁₇₂	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
59	C₄²	C₄×D₄₃	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	172	1	no	—
62	C₂³	—	172	2	no	—
63	D₄	—	344	4	no	—
64	D₄	—	172	2	no	—
65	D₄	—	172	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
68	C₈	#10621873	1	1	yes	characteristic
69	C₈	D₃₄₄	1	1	yes	characteristic
70	C₈	#10621882	1	1	yes	characteristic
71	C₈	#10621884	1	1	yes	characteristic
72	C₂²	—	344	4	no	—
73	C₂²	—	344	2	no	—
74	C₂²	#13063241	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#13063245	1	1	yes	characteristic
77	C₄	#13063247	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	688	2	no	—
80	C₂	#14582642	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582642
commutator	C₄²×C₄₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#364	C₂
socle	C₂×C₄₃	#331
hypercenter	#364	D₄₃
hypocenter	C₄₃	#1357
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #14582720	C₂	semidirect
3. C₄₃×#364	C₂	semidirect
43. #364	D₄₃	semidirect
44. C₄₃	#1357	semidirect