Subgroups — #19134767

Order 5504.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063261	C₂	1	4	yes	maximal
2	#14582923	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	C₂²	1	4	yes	—
5	#13063261	—	2	8	no	—
6	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
7	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
8	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₄₃	C₄	1	2	yes	—
10	C₄×C₈×C₄₃	C₄	1	2	yes	—
11	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
12	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₄₃	D₄	1	4	yes	—
15	C₂×C₈×C₄₃	Q₈	1	4	yes	—
16	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₄₃	D₄	1	2	yes	—
19	#10621877	—	2	8	no	—
20	C₂×C₄₃⋊C₈	—	2	4	no	—
21	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₄₃	—	2	4	no	—
23	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
29	C₈×C₄₃	C₄⋊C₄	1	8	yes	—
30	C₄₃⋊C₈	—	4	4	no	—
31	C₂²×C₄₃	—	2	2	no	—
32	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₄₃	C₄⋊Q₈	1	2	yes	—
34	C₄×C₄₃	—	2	2	no	—
35	C₄×C₄₃	#108	1	4	yes	complemented
36	C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
37	C₄×C₄₃	#127	1	1	yes	characteristic
38	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
39	#1848	—	43	1	no	maximal, Sylow
40	C₂×C₄₃	—	2	2	no	—
41	C₂×C₄₃	#384	1	1	yes	characteristic
42	C₂×C₄₃	C₂×#108	1	2	yes	—
43	C₂×#108	—	43	4	no	—
44	#423	—	43	2	no	—
45	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
46	C₄₃	#1848	1	1	yes	characteristic, complemented, Sylow
47	C₂×M₁₆	—	43	4	no	—
48	C₂²×C₈	C₂×D₄₃	1	2	yes	—
49	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
50	#108	—	86	8	no	—
51	C₄⋊C₈	—	86	4	no	—
52	C₄×C₈	Dic₄₃	1	2	yes	—
53	C₄×C₈	Dic₄₃	1	2	yes	—
54	C₂²×C₄	Dic₈₆	1	2	yes	—
55	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
56	M₁₆	—	86	8	no	—
57	C₂×C₈	—	86	4	no	—
58	C₂×C₈	Dic₈₆	1	4	yes	—
59	C₂×C₈	D₁₇₂	1	4	yes	—
60	C₂×C₈	C₂×Dic₄₃	1	4	yes	—
61	C₄²	D₁₇₂	1	2	yes	—
62	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
63	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
64	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
68	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
69	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
70	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
71	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
72	C₈	—	172	4	no	—
73	C₈	C₄⋊Dic₄₃	1	8	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
76	C₂²	#13063325	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	#13063261	1	4	yes	complemented
79	C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
80	C₄	#13063322	1	1	yes	characteristic
81	C₄	#13063325	1	1	yes	characteristic
82	C₂	—	2	2	no	—
83	C₂	#14582769	1	1	yes	characteristic
84	C₂	C₂×#13063261	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#1848
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
35. C₄×C₄₃	#108	semidirect
46. C₄₃	#1848	semidirect
78. C₄	#13063261	semidirect