Subgroups — #24984259

Order 11008.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136874	C₂	1	1	yes	maximal, characteristic
2	#19132671	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1422	C₂	1	1	yes	maximal, characteristic
4	#14583301	—	2	1	no	—
5	#14582727	C₄	1	2	yes	—
6	#14582725	—	2	1	no	—
7	#14582720	—	2	1	no	—
8	C₄₃×M₆₄	—	2	1	no	—
9	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	#13063317	—	4	1	no	—
11	#13063265	—	4	1	no	—
12	#13063259	—	2	2	no	—
13	#13063257	—	4	1	no	—
14	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
16	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
17	C₃₂×C₄₃	—	4	1	no	—
18	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
20	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
21	C₄⋊Dic₄₃	—	4	2	no	—
22	Dic₄₃⋊C₄	—	8	2	no	—
23	C₁₆×C₄₃	—	2	1	no	—
24	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
25	C₁₆×C₄₃	Q₁₆	1	1	yes	characteristic
26	C₄₃⋊C₁₆	—	8	1	no	—
27	C₂×C₄×C₄₃	—	2	1	no	—
28	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
29	C₂×Dic₄₃	—	8	2	no	—
30	C₈×C₄₃	#101	1	1	yes	characteristic
31	C₈×C₄₃	#103	1	1	yes	characteristic
32	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
33	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
34	#7454	—	43	1	no	maximal, Sylow
35	C₂²×C₄₃	#361	1	1	yes	characteristic
36	C₄×C₄₃	—	4	1	no	—
37	C₄×C₄₃	#332	1	1	yes	characteristic
38	C₄×C₄₃	#358	1	1	yes	characteristic
39	Dic₄₃	—	16	2	no	—
40	#2253	—	43	1	no	—
41	#1422	D₄₃	1	1	yes	characteristic
42	#1373	—	43	1	no	—
43	C₂×C₄₃	—	2	1	no	—
44	C₂×C₄₃	#1365	1	1	yes	characteristic
45	#499	—	86	1	no	—
46	M₆₄	—	2	1	no	—
47	#367	—	43	2	no	—
48	#366	—	86	1	no	—
49	#364	—	86	1	no	—
50	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
51	C₄₃	#7454	1	1	yes	characteristic, complemented, Sylow
52	#125	—	172	1	no	—
53	M₃₂	—	172	1	no	—
54	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
55	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
56	#107	—	86	2	no	—
57	#106	—	172	1	no	—
58	C₄×C₈	D₁₇₂	1	1	yes	characteristic
59	C₃₂	—	4	1	no	—
60	C₂×C₈	D₃₄₄	1	1	yes	characteristic
61	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
62	C₄⋊C₄	—	344	2	no	—
63	C₄⋊C₄	—	172	2	no	—
64	C₄²	#10621873	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	344	1	no	—
67	C₁₆	#10621883	1	1	yes	characteristic
68	C₁₆	#10621885	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	344	2	no	—
71	C₂×C₄	#13063247	1	1	yes	characteristic
72	C₈	#13063243	1	1	yes	characteristic
73	C₈	#13063248	1	1	yes	characteristic
74	C₈	#13063270	1	1	yes	characteristic
75	C₈	Dic₃₄₄	1	1	yes	characteristic
76	C₂²	#14582713	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	688	2	no	—
79	C₄	#14582644	1	1	yes	characteristic
80	C₄	#14582704	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#19132652	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19132652
commutator	C₂×C₁₆×C₄₃	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄₃×#1422	C₂
socle	C₂×C₄₃	#1365
prime radical	C₂²×C₄₃	#361
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	#1422	D₄₃
hypocenter	C₄₃	#7454
LCS	G ▷ C₂×C₁₆×C₄₃ ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
51. C₄₃	#7454	semidirect

Maximal subgroups

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

subgroup	index
#19136874	2
#19132671	2
C₄₃×#1422	2
#7454	43