Subgroups — #24983334

Order 11008.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132659	C₂	1	1	yes	maximal, characteristic
2	#19132512	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1367	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₃⋊C₁₆)	—	2	1	no	—
5	C₄×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
7	C₄₃×C₄⋊C₁₆	—	2	1	no	—
8	C₈²×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄₃⋊C₁₆	—	2	1	no	—
10	C₂×C₄₃⋊C₁₆	—	4	1	no	—
11	C₂×C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
12	C₂×C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
13	C₂×C₁₆×C₄₃	—	4	1	no	—
14	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₄×C₈×C₄₃	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₄₃	—	2	1	no	—
18	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₂×C₈×C₄₃	M₁₆	1	1	yes	characteristic
20	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
21	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
22	C₄²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
23	C₁₆×C₄₃	—	8	1	no	—
24	C₄₃⋊C₁₆	—	2	2	no	—
25	C₄₃⋊C₁₆	—	2	1	no	—
26	C₄₃⋊C₁₆	—	8	1	no	—
27	C₄₃⋊C₁₆	C₁₆	1	2	yes	complemented
28	C₂×C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
29	C₂×C₄×C₄₃	#106	1	1	yes	characteristic
30	C₂×C₄×C₄₃	#108	1	1	yes	characteristic
31	C₈×C₄₃	—	2	1	no	—
32	C₈×C₄₃	—	2	1	no	—
33	C₈×C₄₃	—	2	1	no	—
34	C₈×C₄₃	—	4	1	no	—
35	C₈×C₄₃	C₂×C₁₆	1	1	yes	characteristic
36	C₈×C₄₃	M₃₂	1	1	yes	characteristic
37	#7099	—	43	1	no	maximal, Sylow
38	C₂²×C₄₃	#334	1	1	yes	characteristic
39	C₄×C₄₃	—	2	1	no	—
40	C₄×C₄₃	C₄⋊C₁₆	1	1	yes	characteristic
41	C₄×C₄₃	#364	1	1	yes	characteristic
42	C₄×C₄₃	#365	1	1	yes	characteristic
43	C₄×C₄₃	#365	1	1	yes	characteristic
44	#1367	—	43	1	no	—
45	#1367	D₄₃	1	1	yes	characteristic
46	#1311	—	43	1	no	—
47	C₂×C₄₃	#1367	1	1	yes	characteristic
48	C₂×C₄₃	#1368	1	1	yes	characteristic
49	C₂×C₄₃	#1369	1	1	yes	characteristic
50	C₄⋊C₁₆	—	2	1	no	—
51	C₄⋊C₁₆	—	86	1	no	—
52	C₄×C₁₆	—	43	1	no	—
53	C₄×C₁₆	—	43	1	no	—
54	C₈²	C₂×D₄₃	1	1	yes	characteristic
55	C₄₃	#7099	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₁₆	—	4	1	no	—
57	C₂×C₁₆	—	43	1	no	—
58	C₂×C₁₆	—	43	1	no	—
59	C₂×C₁₆	—	86	1	no	—
60	C₂×C₁₆	—	172	1	no	—
61	C₄×C₈	Dic₈₆	1	1	yes	characteristic
62	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
63	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
66	C₂×C₈	#10621872	1	1	yes	characteristic
67	C₂×C₈	#10621883	1	1	yes	characteristic
68	C₂×C₈	#10621884	1	1	yes	characteristic
69	C₄²	Dic₄₃⋊C₄	1	1	yes	characteristic
70	C₁₆	—	8	1	no	—
71	C₁₆	—	43	2	no	—
72	C₁₆	—	86	2	no	—
73	C₁₆	—	86	1	no	—
74	C₁₆	—	344	1	no	—
75	C₂×C₄	Dic₄₃⋊C₈	1	1	yes	characteristic
76	C₂×C₄	#13063256	1	1	yes	characteristic
77	C₂×C₄	#13063260	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	2	1	no	—
80	C₈	—	2	1	no	—
81	C₈	—	4	1	no	—
82	C₈	C₁₆×D₄₃	1	1	yes	characteristic
83	C₈	#13063264	1	1	yes	characteristic
84	C₂²	#14582649	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	Dic₄₃⋊C₁₆	1	1	yes	characteristic
87	C₄	#14582719	1	1	yes	characteristic
88	C₄	#14582721	1	1	yes	characteristic
89	C₄	#14582723	1	1	yes	characteristic
90	C₂	#19132658	1	1	yes	characteristic
91	C₂	#19132660	1	1	yes	characteristic
92	C₂	#19132662	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063256
commutator	C₈×C₄₃	C₂×C₁₆
Frattini	C₈²	C₂×D₄₃
Fitting	C₄₃×#1367	C₂
socle, prime radical	C₂²×C₄₃	#334
cosocle	C₈²×C₄₃	C₂²
hypercenter	#1367	D₄₃
hypocenter	C₄₃	#7099
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈² ◁ #1367

Complements

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

N	H ≅ G/N	type
27. C₄₃⋊C₁₆	C₁₆	semidirect
55. C₄₃	#7099	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19132659	2
#19132512	2
C₄₃×#1367	2
#7099	43