Subgroups — #19132590

Order 5504.

100 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	C₄₃⋊#338	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#349	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₇₂	C₄	1	1	yes	characteristic
5	C₂×#10621877	—	2	1	no	—
6	#13063304	—	2	1	no	—
7	#13063257	C₄	1	1	yes	characteristic
8	#13063250	—	2	1	no	—
9	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	M₃₂×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	C₂²⋊Dic₄₃	—	4	1	no	—
17	C₄⋊Dic₄₃	—	2	1	no	—
18	Dic₄₃⋊C₄	—	4	1	no	—
19	#10621877	—	4	1	no	—
20	#10621877	—	4	1	no	—
21	C₂×C₄₃⋊C₈	—	2	2	no	—
22	Dic₁₇₂	—	4	1	no	—
23	C₁₆×C₄₃	—	4	1	no	—
24	C₂³×C₄₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₄₃	—	2	1	no	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
29	C₂×Dic₄₃	—	4	1	no	—
30	C₂×Dic₄₃	—	4	1	no	—
31	Dic₈₆	—	4	1	no	—
32	Dic₈₆	—	4	1	no	—
33	C₈×C₄₃	—	2	1	no	—
34	C₈×C₄₃	—	2	1	no	—
35	C₄₃⋊C₈	—	4	2	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	#99	1	1	yes	characteristic
41	C₄×C₄₃	#104	1	1	yes	characteristic
42	Dic₄₃	—	8	1	no	—
43	Dic₄₃	—	8	1	no	—
44	#1342	—	43	1	no	maximal, Sylow
45	C₂×C₄₃	—	2	1	no	—
46	C₂×C₄₃	—	4	1	no	—
47	C₂×C₄₃	#327	1	1	yes	characteristic
48	#470	—	43	1	no	—
49	#349	D₄₃	1	1	yes	characteristic
50	#338	—	43	1	no	—
51	C₄₃	#1342	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	—	43	1	no	—
53	C₂×M₁₆	—	86	1	no	—
54	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
55	C₂²⋊Q₈	—	86	1	no	—
56	M₃₂	—	2	1	no	—
57	#106	—	43	1	no	—
58	#103	—	86	1	no	—
59	C₂×Q₈	—	86	1	no	—
60	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
61	Q₁₆	—	172	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	172	1	no	—
64	M₁₆	—	172	1	no	—
65	C₂×C₈	—	86	2	no	—
66	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
68	C₄⋊C₄	—	86	1	no	—
69	C₄⋊C₄	—	172	1	no	—
70	C₂²⋊C₄	—	172	1	no	—
71	C₁₆	—	4	1	no	—
72	C₂³	#10621873	1	1	yes	characteristic
73	Q₈	—	172	1	no	—
74	Q₈	—	172	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	172	1	no	—
78	C₂×C₄	—	172	1	no	—
79	C₂×C₄	D₃₄₄	1	1	yes	characteristic
80	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	172	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#13063247	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	344	1	no	—
89	C₄	—	344	1	no	—
90	C₄	#13063239	1	1	yes	characteristic
91	C₄	#13063251	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#14582634	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582634
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₄₃
Fitting	C₄₃×#349	C₂
socle	C₂×C₄₃	#327
hypercenter	#349	D₄₃
hypocenter	C₄₃	#1342
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
51. C₄₃	#1342	semidirect