Subgroups — #24984475

Order 11008.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#19132795	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×D₃₂	C₂	1	1	yes	maximal, characteristic
4	#14582725	—	2	1	no	—
5	C₄₃⋊C₆₄	—	2	1	no	—
6	C₂×D₁₆×C₄₃	—	2	1	no	—
7	C₄₃×D₃₂	—	2	1	no	—
8	C₄₃×D₃₂	C₄	1	2	yes	complemented
9	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
10	#13063259	—	4	1	no	—
11	C₂×D₈×C₄₃	—	4	1	no	—
12	D₁₆×C₄₃	—	2	2	no	—
13	D₁₆×C₄₃	—	4	1	no	—
14	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
15	C₃₂×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₄₃	D₄	1	1	yes	characteristic
17	C₂×D₄×C₄₃	—	8	1	no	—
18	D₈×C₄₃	—	4	2	no	—
19	D₈×C₄₃	—	8	1	no	—
20	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
21	C₄⋊Dic₄₃	—	8	1	no	—
22	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
24	C₂³×C₄₃	—	16	1	no	—
25	D₄×C₄₃	—	8	2	no	—
26	D₄×C₄₃	—	16	1	no	—
27	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
28	C₂×Dic₄₃	—	16	1	no	—
29	C₈×C₄₃	#102	1	1	yes	characteristic
30	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
31	#7537	—	43	1	no	maximal, Sylow
32	C₂²×C₄₃	—	16	2	no	—
33	C₂²×C₄₃	—	32	1	no	—
34	C₂²×C₄₃	—	32	1	no	—
35	C₂²×C₄₃	D₃₂	1	1	yes	characteristic
36	C₄×C₄₃	#357	1	1	yes	characteristic
37	C₄×C₄₃	SD₆₄	1	1	yes	characteristic
38	Dic₄₃	—	32	1	no	—
39	C₂×D₃₂	D₄₃	1	1	yes	characteristic
40	C₂×C₆₄	—	43	1	no	—
41	#1423	—	43	1	no	—
42	C₂×C₄₃	—	32	2	no	—
43	C₂×C₄₃	#1415	1	1	yes	characteristic
44	C₂×C₄₃	D₆₄	1	1	yes	characteristic
45	C₂×C₄₃	SD₁₂₈	1	1	yes	characteristic
46	C₂×D₁₆	—	2	1	no	—
47	D₃₂	—	2	1	no	—
48	D₃₂	Dic₄₃	1	2	yes	complemented
49	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
50	#366	—	86	1	no	—
51	C₆₄	—	86	1	no	—
52	C₄₃	#7537	1	1	yes	characteristic, complemented, Sylow
53	C₂×D₈	—	4	1	no	—
54	D₁₆	—	2	2	no	—
55	D₁₆	—	4	1	no	—
56	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
57	#107	—	172	1	no	—
58	C₃₂	C₂×Dic₄₃	1	1	yes	characteristic
59	C₃₂	C₂²⋊D₄₃	1	1	yes	characteristic
60	C₂×D₄	—	8	1	no	—
61	D₈	—	4	2	no	—
62	D₈	—	8	1	no	—
63	C₂×C₈	#10621882	1	1	yes	characteristic
64	C₄⋊C₄	—	344	1	no	—
65	C₁₆	#10621883	1	1	yes	characteristic
66	C₁₆	C₂²⋊Dic₄₃	1	1	yes	characteristic
67	C₂³	—	16	1	no	—
68	D₄	—	8	2	no	—
69	D₄	—	16	1	no	—
70	C₂×C₄	—	688	1	no	—
71	C₂×C₄	#13063266	1	1	yes	characteristic
72	C₈	#13063246	1	1	yes	characteristic
73	C₈	#13063269	1	1	yes	characteristic
74	C₂²	—	16	2	no	—
75	C₂²	—	32	1	no	—
76	C₂²	—	32	1	no	—
77	C₂²	#14582734	1	1	yes	characteristic
78	C₄	—	1376	1	no	—
79	C₄	#14582700	1	1	yes	characteristic
80	C₄	#14582737	1	1	yes	characteristic
81	C₂	—	32	2	no	—
82	C₂	#19132773	1	1	yes	characteristic
83	C₂	#19132807	1	1	yes	characteristic
84	C₂	#19132810	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14582734
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting, prime radical	C₂×C₄₃×D₃₂	C₂
socle	C₂²×C₄₃	D₃₂
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	C₂×D₃₂	D₄₃
hypocenter	C₄₃	#7537
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×D₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃⋊C₆₄	C₂	semidirect
2. #19132795	C₂	semidirect
8. C₄₃×D₃₂	C₄	semidirect
48. D₃₂	Dic₄₃	semidirect
52. C₄₃	#7537	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃⋊C₆₄	2
#19132795	2
C₂×C₄₃×D₃₂	2
#7537	43