Subgroups — #19132878

Order 5504.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582952	C₂	1	2	yes	maximal
2	#14582620	C₂	1	2	yes	maximal, complemented
3	C₈×C₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊(C₄₃⋊C₈)	C₄	1	4	yes	—
6	C₂²⋊(C₄₃⋊C₈)	C₄	1	4	yes	—
7	C₄×C₄₃⋊C₈	C₂²	1	4	yes	—
8	C₂²×C₈×C₄₃	C₄	1	2	yes	—
9	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₄₃	C₄	1	2	yes	—
11	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₄₃	C₈	1	8	yes	complemented
16	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₄²×C₄₃	C₂×C₄	1	2	yes	—
19	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
22	C₂³×C₄₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₄₃	—	2	4	no	—
24	C₂×C₄×C₄₃	C₄²	1	2	yes	—
25	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₄₃	C₂×C₈	1	4	yes	—
27	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
28	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₄₃	C₂×C₈	1	4	yes	—
30	C₈×C₄₃	C₂×C₈	1	4	yes	—
31	C₄₃⋊C₈	—	2	8	no	—
32	C₂²×C₄₃	—	2	2	no	—
33	C₂²×C₄₃	C₄×C₈	1	2	yes	—
34	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
35	C₄×C₄₃	—	2	2	no	—
36	C₄×C₄₃	C₄×C₈	1	2	yes	—
37	C₄×C₄₃	C₂²×C₈	1	2	yes	—
38	C₄×C₄₃	#131	1	4	yes	—
39	#1450	—	43	1	no	maximal, Sylow
40	C₂×C₄₃	—	2	2	no	—
41	C₂×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
42	C₂×C₄₃	#405	1	2	yes	—
43	#431	—	43	2	no	—
44	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
45	#322	—	43	2	no	—
46	C₈²	—	43	2	no	—
47	C₄₃	#1450	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₈	Dic₄₃	1	2	yes	—
49	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
50	C₄⋊C₈	—	43	4	no	—
51	C₂²⋊C₈	—	43	4	no	—
52	C₄×C₈	—	43	4	no	—
53	C₄×C₈	Dic₄₃	1	2	yes	—
54	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
55	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
56	C₂²×C₄	C₄×D₄₃	1	2	yes	—
57	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
58	C₂×C₈	—	43	8	no	—
59	C₂×C₈	C₄₃⋊C₈	1	8	yes	complemented
60	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
61	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
62	C₄²	C₄×D₄₃	1	2	yes	—
63	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
64	C₄²	C₂²×D₄₃	1	1	yes	characteristic
65	C₂³	C₄×Dic₄₃	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	C₂×C₄₃⋊C₈	1	4	yes	—
68	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
69	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
70	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
71	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
72	C₈	—	86	8	no	—
73	C₈	C₂×C₄₃⋊C₈	1	4	yes	—
74	C₈	C₂×C₄₃⋊C₈	1	4	yes	—
75	C₂²	—	2	2	no	—
76	C₂²	C₄×C₄₃⋊C₈	1	2	yes	—
77	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	C₄×C₄₃⋊C₈	1	2	yes	—
80	C₄	C₂²×C₄₃⋊C₈	1	2	yes	—
81	C₄	#13063331	1	4	yes	—
82	C₂	—	2	2	no	—
83	C₂	C₂×C₄×C₄₃⋊C₈	1	1	yes	characteristic
84	C₂	#14582854	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄²
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#1450
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #14582620	C₂	semidirect
3. C₈×C₄₃⋊C₈	C₂	semidirect
15. C₂×C₈×C₄₃	C₈	semidirect
47. C₄₃	#1450	semidirect
59. C₂×C₈	C₄₃⋊C₈	semidirect