Subgroups — #24984264

Order 11008.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132793	C₂	1	1	yes	maximal, characteristic
2	#19132511	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1422	C₂	1	1	yes	maximal, characteristic
4	#14582733	—	2	1	no	—
5	C₄×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
6	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
7	C₄₃×M₆₄	—	2	1	no	—
8	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
10	C₂×C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
11	C₄×C₄₃⋊C₈	—	2	1	no	—
12	C₄₃⋊C₃₂	—	4	1	no	—
13	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	Q₈	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₄₃	—	4	1	no	—
17	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₄²×C₄₃	M₁₆	1	1	yes	characteristic
20	C₂×C₄₃⋊C₈	—	2	2	no	—
21	C₁₆×C₄₃	—	2	1	no	—
22	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
23	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
24	C₄₃⋊C₁₆	—	2	1	no	—
25	C₄₃⋊C₁₆	C₁₆	1	2	yes	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
28	C₈×C₄₃	#106	1	1	yes	characteristic
29	C₈×C₄₃	#108	1	1	yes	characteristic
30	C₈×C₄₃	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₄₃	M₃₂	1	1	yes	characteristic
32	C₄₃⋊C₈	—	4	2	no	—
33	#7456	—	43	1	no	maximal, Sylow
34	C₂²×C₄₃	#364	1	1	yes	characteristic
35	C₄×C₄₃	—	2	2	no	—
36	C₄×C₄₃	#334	1	1	yes	characteristic
37	C₄×C₄₃	C₄⋊C₁₆	1	1	yes	characteristic
38	#1422	—	43	1	no	—
39	#1422	D₄₃	1	1	yes	characteristic
40	#1311	—	43	1	no	—
41	C₂×C₄₃	—	2	1	no	—
42	C₂×C₄₃	#1367	1	1	yes	characteristic
43	M₆₄	—	2	1	no	—
44	M₆₄	—	86	1	no	—
45	C₄×C₁₆	—	43	1	no	—
46	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
47	C₈²	—	43	1	no	—
48	C₄₃	#7456	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₁₆	—	43	1	no	—
50	C₂×C₁₆	—	43	1	no	—
51	C₂×C₁₆	Dic₈₆	1	1	yes	characteristic
52	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
53	C₄×C₈	—	86	1	no	—
54	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
55	C₃₂	—	4	1	no	—
56	C₃₂	—	172	1	no	—
57	C₂×C₈	—	86	2	no	—
58	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
59	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
60	C₄²	#10621872	1	1	yes	characteristic
61	C₁₆	—	2	1	no	—
62	C₁₆	—	43	2	no	—
63	C₁₆	—	86	1	no	—
64	C₁₆	#10621883	1	1	yes	characteristic
65	C₁₆	#10621884	1	1	yes	characteristic
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	Dic₄₃⋊C₈	1	1	yes	characteristic
68	C₈	—	172	2	no	—
69	C₈	#13063256	1	1	yes	characteristic
70	C₈	#13063260	1	1	yes	characteristic
71	C₈	C₁₆×D₄₃	1	1	yes	characteristic
72	C₈	#13063264	1	1	yes	characteristic
73	C₂²	#14582719	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	#14582649	1	1	yes	characteristic
76	C₄	Dic₄₃⋊C₁₆	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	#19132658	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#13063256
commutator	C₈×C₄₃	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄₃×#1422	C₂
socle	C₂×C₄₃	#1367
prime radical	C₂²×C₄₃	#364
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	#1422	D₄₃
hypocenter	C₄₃	#7456
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
48. C₄₃	#7456	semidirect

Maximal subgroups

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

subgroup	index
#19132793	2
#19132511	2
C₄₃×#1422	2
#7456	43