Subgroups — #25017648

Order 11008.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136901	C₂	1	2	yes	maximal, complemented
2	Dic₁₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#19132810	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583328	—	2	2	no	—
7	Dic₆₈₈	C₂²	1	2	yes	—
8	#14582737	—	2	2	no	—
9	C₃₂×D₄₃	C₂²	1	1	yes	characteristic
10	C₄₃⋊C₆₄	C₂²	1	1	yes	characteristic
11	C₄₃×D₃₂	C₂²	1	2	yes	—
12	C₄₃×C₆₄	C₂²	1	1	yes	characteristic
13	#13063344	—	4	2	no	—
14	Dic₃₄₄	—	2	2	no	—
15	#13063269	—	4	2	no	—
16	C₁₆×D₄₃	D₄	1	1	yes	characteristic
17	C₄₃⋊C₃₂	D₄	1	1	yes	characteristic
18	D₁₆×C₄₃	—	2	2	no	—
19	C₃₂×C₄₃	C₂³	1	1	yes	characteristic
20	#10621900	—	8	2	no	—
21	D₈×C₄₃	—	4	2	no	—
22	#10621883	—	8	2	no	—
23	Dic₁₇₂	—	4	2	no	—
24	C₈×D₄₃	D₈	1	1	yes	characteristic
25	C₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
26	C₄₃⋊C₁₆	D₈	1	1	yes	characteristic
27	D₄×C₄₃	—	8	2	no	—
28	C₂²⋊D₄₃	—	16	2	no	—
29	C₂×Dic₄₃	—	16	2	no	—
30	C₄×D₄₃	D₁₆	1	1	yes	characteristic
31	Dic₈₆	—	8	2	no	—
32	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
33	C₄₃⋊C₈	D₁₆	1	1	yes	characteristic
34	#13741	—	43	1	no	maximal, Sylow
35	C₂²×C₄₃	—	16	2	no	—
36	C₂×D₄₃	D₃₂	1	1	yes	characteristic
37	C₄×C₄₃	C₂×D₁₆	1	1	yes	characteristic
38	Dic₄₃	—	16	2	no	—
39	Dic₄₃	D₃₂	1	1	yes	characteristic
40	#2262	—	43	2	no	—
41	Q₁₂₈	—	43	1	no	—
42	SD₁₂₈	—	43	2	no	—
43	D₆₄	D₄₃	1	1	yes	characteristic, complemented
44	C₂×C₆₄	—	43	1	no	—
45	C₂×C₄₃	—	32	2	no	—
46	C₂×C₄₃	C₂×D₃₂	1	1	yes	characteristic
47	D₄₃	—	2	1	no	—
48	#508	—	86	2	no	—
49	Q₆₄	—	43	2	no	—
50	SD₆₄	—	86	2	no	—
51	D₃₂	C₂×D₄₃	1	2	yes	—
52	C₂×C₃₂	—	43	1	no	—
53	C₆₄	—	43	1	no	—
54	C₆₄	C₂×D₄₃	1	1	yes	characteristic
55	C₄₃	#13741	1	1	yes	characteristic, complemented, Sylow
56	#135	—	172	2	no	—
57	Q₃₂	—	86	2	no	—
58	SD₃₂	—	172	2	no	—
59	D₁₆	—	2	2	no	—
60	C₂×C₁₆	—	43	1	no	—
61	C₃₂	—	43	1	no	—
62	C₃₂	C₂²×D₄₃	1	1	yes	characteristic
63	#41	—	344	2	no	—
64	Q₁₆	—	172	2	no	—
65	SD₁₆	—	344	2	no	—
66	D₈	—	4	2	no	—
67	C₂×C₈	—	43	1	no	—
68	C₁₆	—	43	1	no	—
69	C₁₆	D₄×D₄₃	1	1	yes	characteristic
70	Q₈	—	344	2	no	—
71	D₄	—	8	2	no	—
72	D₄	—	688	2	no	—
73	C₂×C₄	—	43	1	no	—
74	C₂×C₄	—	688	2	no	—
75	C₈	—	43	1	no	—
76	C₈	D₈×D₄₃	1	1	yes	characteristic
77	C₂²	—	16	2	no	—
78	C₂²	—	43	1	no	—
79	C₄	—	43	1	no	—
80	C₄	—	688	2	no	—
81	C₄	D₁₆×D₄₃	1	1	yes	characteristic
82	C₂	—	32	2	no	—
83	C₂	—	86	1	no	—
84	C₂	D₃₂×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₄₃
commutator, cosocle	C₃₂×C₄₃	C₂³
Frattini	C₃₂	C₂²×D₄₃
Fitting	C₄₃×D₆₄	C₂
socle	C₂×C₄₃	C₂×D₃₂
hypercenter	D₆₄	D₄₃
hypocenter	C₄₃	#13741
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₆₄

Complements

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

N	H ≅ G/N	type
1. #19136901	C₂	semidirect
2. Dic₁₃₇₆	C₂	semidirect
3. #19132810	C₂	semidirect
4. C₆₄×D₄₃	C₂	semidirect
5. C₄₃×D₆₄	C₂	semidirect
43. D₆₄	D₄₃	semidirect
55. C₄₃	#13741	semidirect

Maximal subgroups

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

subgroup	index
#19136901	2
Dic₁₃₇₆	2
#19132810	2
C₆₄×D₄₃	2
C₄₃×D₆₄	2
#13741	43