Subgroups — #19132582

Order 5504.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583157	C₂	1	1	yes	maximal, characteristic
2	#14582681	C₂	1	1	yes	maximal, characteristic
3	C₄₃×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₇₂	C₄	1	1	yes	characteristic, complemented
5	#13063304	—	2	1	no	—
6	#13063265	—	2	1	no	—
7	#13063257	C₄	1	1	yes	characteristic, complemented
8	#13063250	—	2	1	no	—
9	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	#117×C₄₃	—	2	1	no	—
11	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
12	C₂×Dic₈₆	—	2	1	no	—
13	M₁₆×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	C₂²⋊C₄×C₄₃	—	4	1	no	—
18	C₄²×C₄₃	—	2	2	no	—
19	C₂²⋊Dic₄₃	—	4	1	no	—
20	C₄⋊Dic₄₃	—	2	1	no	—
21	Dic₄₃⋊C₄	—	4	1	no	—
22	Dic₁₇₂	—	4	1	no	—
23	C₄₃⋊C₁₆	—	4	1	no	—
24	C₂³×C₄₃	D₈	1	1	yes	characteristic
25	C₂×C₄×C₄₃	—	2	1	no	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	—	4	2	no	—
28	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
30	C₂×Dic₄₃	—	4	1	no	—
31	C₂×Dic₄₃	—	4	1	no	—
32	Dic₈₆	—	4	1	no	—
33	Dic₈₆	—	4	1	no	—
34	C₈×C₄₃	—	2	1	no	—
35	C₈×C₄₃	—	2	1	no	—
36	C₂²×C₄₃	—	2	1	no	—
37	C₂²×C₄₃	—	4	1	no	—
38	C₂²×C₄₃	#102	1	1	yes	characteristic
39	C₄×C₄₃	—	2	1	no	—
40	C₄×C₄₃	—	8	2	no	—
41	C₄×C₄₃	#99	1	1	yes	characteristic
42	C₄×C₄₃	#104	1	1	yes	characteristic
43	Dic₄₃	—	8	1	no	—
44	Dic₄₃	—	8	1	no	—
45	#1340	—	43	1	no	maximal, Sylow
46	C₂×C₄₃	—	2	1	no	—
47	C₂×C₄₃	—	4	1	no	—
48	C₂×C₄₃	#327	1	1	yes	characteristic
49	#470	—	43	1	no	—
50	#349	—	43	1	no	—
51	H(3,ℤ/4)	D₄₃	1	1	yes	characteristic
52	C₄₃	#1340	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	—	43	1	no	—
54	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
55	C₂²⋊Q₈	—	86	1	no	—
56	#117	—	2	1	no	—
57	M₃₂	—	86	1	no	—
58	#106	—	43	1	no	—
59	#103	—	86	1	no	—
60	C₂×Q₈	—	86	1	no	—
61	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
62	Q₁₆	—	172	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
65	C₂×C₈	D₁₇₂	1	1	yes	characteristic
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	86	1	no	—
68	C₄⋊C₄	—	172	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	172	1	no	—
71	C₄²	—	2	2	no	—
72	C₁₆	—	172	1	no	—
73	C₂³	#10621882	1	1	yes	characteristic
74	Q₈	—	172	1	no	—
75	Q₈	—	172	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	172	1	no	—
80	C₂×C₄	—	172	1	no	—
81	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
82	C₂×C₄	#10621884	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#13063245	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	8	2	no	—
90	C₄	—	344	1	no	—
91	C₄	—	344	1	no	—
92	C₄	#13063239	1	1	yes	characteristic
93	C₄	#13063253	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#14582632	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582632
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₄₃
Fitting	C₄₃×H(3,ℤ/4)	C₂
socle	C₂×C₄₃	#327
hypercenter	H(3,ℤ/4)	D₄₃
hypocenter	C₄₃	#1340
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
4. C₂×Dic₁₇₂	C₄	semidirect
7. #13063257	C₄	semidirect
52. C₄₃	#1340	semidirect