Subgroups — #24983214

Order 11008.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132513	C₂	1	1	yes	maximal, characteristic
2	#19132512	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1312	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄₃⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
7	C₄×C₁₆×C₄₃	C₄	1	2	yes	—
8	C₈²×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄₃⋊C₁₆	—	2	2	no	—
10	C₂×C₄₃⋊C₁₆	C₈	1	2	yes	—
11	C₂×C₄₃⋊C₁₆	C₈	1	2	yes	—
12	C₂×C₁₆×C₄₃	—	2	2	no	—
13	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈×C₄₃	M₁₆	1	2	yes	—
19	C₂×C₈×C₄₃	M₁₆	1	2	yes	—
20	C₄²×C₄₃	C₄²	1	1	yes	characteristic
21	C₁₆×C₄₃	—	4	2	no	—
22	C₄₃⋊C₁₆	—	2	2	no	—
23	C₄₃⋊C₁₆	—	4	2	no	—
24	C₄₃⋊C₁₆	C₁₆	1	4	yes	complemented
25	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
26	C₂×C₄×C₄₃	#97	1	1	yes	characteristic
27	C₂×C₄×C₄₃	#97	1	1	yes	characteristic
28	C₈×C₄₃	—	2	2	no	—
29	C₈×C₄₃	—	2	2	no	—
30	C₈×C₄₃	C₂×C₁₆	1	2	yes	—
31	C₈×C₄₃	M₃₂	1	2	yes	—
32	#7053	—	43	1	no	maximal, Sylow
33	C₂²×C₄₃	#322	1	1	yes	characteristic
34	C₄×C₄₃	C₄×C₁₆	1	1	yes	characteristic
35	C₄×C₄₃	#346	1	1	yes	characteristic
36	C₄×C₄₃	#347	1	2	yes	—
37	C₄×C₄₃	#347	1	2	yes	—
38	#1312	—	43	1	no	—
39	#1312	D₄₃	1	1	yes	characteristic
40	#1311	—	43	1	no	—
41	C₂×C₄₃	#1312	1	1	yes	characteristic
42	C₂×C₄₃	#1313	1	1	yes	characteristic
43	C₂×C₄₃	#1313	1	1	yes	characteristic
44	C₄×C₁₆	—	43	1	no	—
45	C₄×C₁₆	—	43	1	no	—
46	C₄×C₁₆	—	43	2	no	—
47	C₄×C₁₆	Dic₄₃	1	2	yes	—
48	C₈²	C₂×D₄₃	1	1	yes	characteristic
49	C₄₃	#7053	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₁₆	—	2	2	no	—
51	C₂×C₁₆	—	43	2	no	—
52	C₂×C₁₆	—	43	2	no	—
53	C₂×C₁₆	—	86	2	no	—
54	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
55	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
56	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
57	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
58	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
59	C₂×C₈	#10621872	1	2	yes	—
60	C₂×C₈	#10621877	1	2	yes	—
61	C₄²	C₄×Dic₄₃	1	1	yes	characteristic
62	C₁₆	—	4	2	no	—
63	C₁₆	—	43	4	no	—
64	C₁₆	—	86	2	no	—
65	C₁₆	—	172	2	no	—
66	C₂×C₄	C₈×Dic₄₃	1	1	yes	characteristic
67	C₂×C₄	#13063235	1	1	yes	characteristic
68	C₂×C₄	#13063236	1	1	yes	characteristic
69	C₈	—	2	2	no	—
70	C₈	—	2	2	no	—
71	C₈	C₁₆×D₄₃	1	2	yes	—
72	C₈	#13063264	1	2	yes	—
73	C₂²	#14582621	1	1	yes	characteristic
74	C₄	C₁₆×Dic₄₃	1	1	yes	characteristic
75	C₄	#14582674	1	1	yes	characteristic
76	C₄	#14582676	1	2	yes	—
77	C₄	#14582677	1	2	yes	—
78	C₂	#19132514	1	1	yes	characteristic
79	C₂	#19132516	1	1	yes	characteristic
80	C₂	#19132517	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₄×Dic₄₃
commutator	C₄×C₄₃	C₄×C₁₆
Frattini	C₈²	C₂×D₄₃
Fitting	C₄₃×#1312	C₂
socle, prime radical	C₂²×C₄₃	#322
cosocle	C₈²×C₄₃	C₂²
hypercenter	#1312	D₄₃
hypocenter	C₄₃	#7053
LCS	G ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ #1312

Complements

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

N	H ≅ G/N	type
24. C₄₃⋊C₁₆	C₁₆	semidirect
49. C₄₃	#7053	semidirect

Maximal subgroups

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

subgroup	index
#19132513	2
#19132512	2
C₄₃×#1312	2
#7053	43