Subgroups — #24984407

Order 11008.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582732	C₂	1	1	yes	maximal, characteristic
2	#19132806	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×D₄₃	C₄	1	1	yes	characteristic
5	#14582732	—	2	1	no	—
6	#14582732	—	2	1	no	—
7	C₂×C₄₃⋊C₃₂	C₄	1	1	yes	characteristic
8	C₄₃⋊C₆₄	—	2	1	no	—
9	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
10	C₄₃×C₆₄	—	2	1	no	—
11	C₂×C₈×D₄₃	C₈	1	1	yes	characteristic
12	C₂×C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
13	C₁₆×D₄₃	—	2	1	no	—
14	C₁₆×D₄₃	—	2	1	no	—
15	C₄₃⋊C₃₂	—	2	1	no	—
16	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₄₃	D₄	1	1	yes	characteristic
18	C₃₂×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄×D₄₃	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
21	C₂×C₄₃⋊C₈	C₁₆	1	1	yes	characteristic
22	C₈×D₄₃	—	2	1	no	—
23	C₈×D₄₃	—	2	1	no	—
24	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
26	C₄₃⋊C₁₆	—	2	1	no	—
27	C₂²×D₄₃	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
29	C₂×Dic₄₃	C₃₂	1	1	yes	characteristic
30	C₄×D₄₃	—	2	1	no	—
31	C₄×D₄₃	—	2	1	no	—
32	C₈×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₈×C₄₃	M₃₂	1	1	yes	characteristic
34	C₄₃⋊C₈	—	2	1	no	—
35	#7513	—	43	1	no	maximal, Sylow
36	C₂²×C₄₃	C₂×C₃₂	1	1	yes	characteristic
37	C₂×D₄₃	—	2	1	no	—
38	C₂×D₄₃	—	4	1	no	—
39	C₄×C₄₃	C₂²⋊C₁₆	1	1	yes	characteristic
40	C₄×C₄₃	M₆₄	1	1	yes	characteristic
41	Dic₄₃	—	2	1	no	—
42	C₂×M₆₄	—	43	1	no	—
43	M₁₂₈	—	43	1	no	—
44	M₁₂₈	D₄₃	1	1	yes	characteristic, complemented
45	C₂×C₄₃	—	2	1	no	—
46	C₂×C₄₃	C₂²⋊C₃₂	1	1	yes	characteristic
47	D₄₃	—	4	1	no	—
48	C₂²×C₁₆	—	43	1	no	—
49	M₆₄	—	86	1	no	—
50	M₆₄	—	86	1	no	—
51	C₂×C₃₂	—	43	1	no	—
52	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
53	C₆₄	—	2	1	no	—
54	C₆₄	—	86	1	no	—
55	C₄₃	#7513	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₈	—	43	1	no	—
57	C₂×C₁₆	—	43	1	no	—
58	C₂×C₁₆	—	86	1	no	—
59	C₂×C₁₆	—	86	1	no	—
60	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
61	C₃₂	—	86	1	no	—
62	C₃₂	D₁₇₂	1	1	yes	characteristic
63	C₃₂	C₂²⋊D₄₃	1	1	yes	characteristic
64	C₂²×C₄	—	43	1	no	—
65	C₂×C₈	—	43	1	no	—
66	C₂×C₈	—	86	1	no	—
67	C₂×C₈	—	86	1	no	—
68	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
69	C₁₆	—	86	1	no	—
70	C₁₆	#10621872	1	1	yes	characteristic
71	C₁₆	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
72	C₂³	—	43	1	no	—
73	C₂×C₄	—	43	1	no	—
74	C₂×C₄	—	86	1	no	—
75	C₂×C₄	—	86	1	no	—
76	C₂×C₄	C₁₆×D₄₃	1	1	yes	characteristic
77	C₈	—	86	1	no	—
78	C₈	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
79	C₈	#13063264	1	1	yes	characteristic
80	C₂²	—	86	1	no	—
81	C₂²	—	172	1	no	—
82	C₂²	C₃₂×D₄₃	1	1	yes	characteristic
83	C₄	—	86	1	no	—
84	C₄	(C₂×D₄₃)⋊C₁₆	1	1	yes	characteristic
85	C₄	#14582732	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	172	1	no	—
88	C₂	(C₂×D₄₃)⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄₃	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₄₃×M₁₂₈	C₂
socle	C₂×C₄₃	C₂²⋊C₃₂
prime radical	C₂²×D₄₃	C₃₂
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	M₁₂₈	D₄₃
hypocenter	C₄₃	#7513
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #19132806	C₂	semidirect
3. C₄₃×M₁₂₈	C₂	semidirect
44. M₁₂₈	D₄₃	semidirect
55. C₄₃	#7513	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582732	2
#19132806	2
C₄₃×M₁₂₈	2
#7513	43