Subgroups — #19136361

Order 5504.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063265	C₂	1	2	yes	maximal
2	#14582720	C₂	1	4	yes	maximal, complemented
3	C₄₃×#405	C₂	1	1	yes	maximal, characteristic
4	#13063265	—	2	2	no	—
5	#13063265	C₂²	1	4	yes	—
6	C₂×C₄₃⋊C₁₆	—	2	2	no	—
7	C₂×M₁₆×C₄₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	#117×C₄₃	C₄	1	1	yes	characteristic
10	#97×C₄₃	C₄	1	2	yes	—
11	C₄×C₈×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
13	M₁₆×C₄₃	C₈	1	4	yes	—
14	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₄₃	D₄	1	2	yes	—
17	C₂×C₈×C₄₃	Q₈	1	2	yes	—
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₄₃	—	2	1	no	—
20	C₂²⋊C₄×C₄₃	—	2	1	no	—
21	C₄²×C₄₃	C₂×C₄	1	2	yes	—
22	C₄₃⋊C₁₆	—	2	4	no	—
23	C₂³×C₄₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₄₃	—	2	2	no	—
25	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₄₃	C₄⋊C₄	1	2	yes	—
30	C₈×C₄₃	C₂×C₈	1	4	yes	—
31	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₄₃	—	4	1	no	—
34	C₂²×C₄₃	C₄⋊C₈	1	2	yes	—
35	C₂²×C₄₃	C₂×M₁₆	1	1	yes	characteristic
36	C₄×C₄₃	—	4	2	no	—
37	C₄×C₄₃	C₄⋊C₈	1	2	yes	—
38	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
40	#2153	—	43	1	no	maximal, Sylow
41	C₂×C₄₃	—	2	1	no	—
42	C₂×C₄₃	—	2	2	no	—
43	C₂×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
44	C₂×M₃₂	—	43	2	no	—
45	#405	D₄₃	1	1	yes	characteristic
46	#364	—	43	4	no	—
47	C₄₃	#2153	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₁₆	Dic₄₃	1	1	yes	characteristic
49	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
50	#117	Dic₄₃	1	1	yes	characteristic
51	M₃₂	—	43	4	no	—
52	M₃₂	—	86	2	no	—
53	C₂×C₁₆	—	86	2	no	—
54	#97	Dic₄₃	1	2	yes	—
55	C₄×C₈	C₂×D₄₃	1	2	yes	—
56	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
57	M₁₆	C₄₃⋊C₈	1	4	yes	—
58	C₂×C₈	Dic₈₆	1	2	yes	—
59	C₂×C₈	D₁₇₂	1	2	yes	—
60	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
61	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
62	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×Dic₄₃	1	2	yes	—
66	C₁₆	—	86	4	no	—
67	C₂³	#10621877	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
70	C₂×C₄	#10621877	1	1	yes	characteristic
71	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
72	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
73	C₈	C₂×C₄₃⋊C₈	1	4	yes	—
74	C₈	C₄⋊Dic₄₃	1	2	yes	—
75	C₈	C₂×Dic₈₆	1	1	yes	characteristic
76	C₈	C₂×D₁₇₂	1	1	yes	characteristic
77	C₂²	—	4	1	no	—
78	C₂²	C₄⋊(C₄₃⋊C₈)	1	2	yes	—
79	C₂²	C₂×#10621877	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	C₄⋊(C₄₃⋊C₈)	1	2	yes	—
82	C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
83	C₄	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₁₇₂
commutator	C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#405	C₂
socle	C₂×C₄₃	C₂×C₄⋊C₈
hypercenter	#405	D₄₃
hypocenter	C₄₃	#2153
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #14582720	C₂	semidirect
47. C₄₃	#2153	semidirect