Subgroups — #24984277

Order 11008.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#19132671	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1373	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₃₂	C₄	1	1	yes	characteristic
5	C₂×C₄₃⋊C₃₂	C₄	1	1	yes	characteristic
6	#14582720	—	2	1	no	—
7	C₄₃×#364	—	2	1	no	—
8	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
9	#13063265	—	4	1	no	—
10	C₄₃⋊C₃₂	—	2	1	no	—
11	C₄₃⋊C₃₂	C₈	1	2	yes	—
12	M₃₂×C₄₃	—	4	1	no	—
13	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	Q₈	1	1	yes	characteristic
15	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
18	C₄²×C₄₃	Q₁₆	1	1	yes	characteristic
19	C₁₆×C₄₃	—	2	1	no	—
20	C₁₆×C₄₃	—	8	1	no	—
21	C₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic
22	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
23	C₄₃⋊C₁₆	—	8	1	no	—
24	C₂×C₄×C₄₃	—	2	1	no	—
25	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
26	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
27	C₈×C₄₃	#108	1	1	yes	characteristic
28	C₈×C₄₃	D₁₆	1	1	yes	characteristic
29	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
30	#7462	—	43	1	no	maximal, Sylow
31	C₂²×C₄₃	#368	1	1	yes	characteristic
32	C₄×C₄₃	—	2	2	no	—
33	C₄×C₄₃	#335	1	1	yes	characteristic
34	C₄×C₄₃	#366	1	1	yes	characteristic
35	C₄×C₃₂	—	43	1	no	—
36	#1373	—	43	1	no	—
37	#1373	D₄₃	1	1	yes	characteristic
38	C₂×C₄₃	—	2	1	no	—
39	C₂×C₄₃	#1371	1	1	yes	characteristic
40	C₂×C₃₂	—	43	1	no	—
41	C₂×C₃₂	—	43	1	no	—
42	#364	—	2	1	no	—
43	#364	—	86	1	no	—
44	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
45	C₄₃	#7462	1	1	yes	characteristic, complemented, Sylow
46	M₃₂	—	4	1	no	—
47	M₃₂	—	172	1	no	—
48	C₂×C₁₆	Dic₈₆	1	1	yes	characteristic
49	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
50	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
51	C₃₂	—	43	2	no	—
52	C₃₂	—	86	1	no	—
53	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
54	C₂×C₈	#10621882	1	1	yes	characteristic
55	C₄²	#10621885	1	1	yes	characteristic
56	C₁₆	—	2	1	no	—
57	C₁₆	—	8	1	no	—
58	C₁₆	—	344	1	no	—
59	C₁₆	C₈×D₄₃	1	1	yes	characteristic
60	C₁₆	#10621872	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#13063258	1	1	yes	characteristic
63	C₈	Dic₄₃⋊C₈	1	1	yes	characteristic
64	C₈	#13063260	1	1	yes	characteristic
65	C₈	#13063266	1	1	yes	characteristic
66	C₈	#13063271	1	1	yes	characteristic
67	C₂²	#14582728	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	#14582651	1	1	yes	characteristic
70	C₄	#14582724	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#19132666	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#13063266
commutator	C₁₆×C₄₃	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄₃×#1373	C₂
socle	C₂×C₄₃	#1371
prime radical	C₂²×C₄₃	#368
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	#1373	D₄₃
hypocenter	C₄₃	#7462
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

Complements

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

N	H ≅ G/N	type
45. C₄₃	#7462	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄₃⋊C₃₂	2
#19132671	2
C₄₃×#1373	2
#7462	43