Subgroups — #24984273

Order 11008.

86 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	#19132667	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1371	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	#14582652	—	2	1	no	—
7	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×#335	—	2	1	no	—
9	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
10	C₄₃⋊C₃₂	—	2	1	no	—
11	C₄₃⋊C₃₂	C₈	1	2	yes	complemented
12	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₄₃	Q₈	1	1	yes	characteristic
14	C₄⋊C₈×C₄₃	—	4	1	no	—
15	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	—	8	1	no	—
17	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	Q₁₆	1	1	yes	characteristic
19	C₄²×C₄₃	D₈	1	1	yes	characteristic
20	C₂×C₄₃⋊C₈	—	8	1	no	—
21	C₁₆×C₄₃	—	2	1	no	—
22	C₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
25	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
26	C₂×C₄×C₄₃	Q₃₂	1	1	yes	characteristic
27	C₈×C₄₃	—	2	1	no	—
28	C₈×C₄₃	—	16	1	no	—
29	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
30	C₈×C₄₃	#108	1	1	yes	characteristic
31	C₄₃⋊C₈	—	16	1	no	—
32	#7460	—	43	1	no	maximal, Sylow
33	C₂²×C₄₃	#366	1	1	yes	characteristic
34	C₄×C₄₃	—	2	1	no	—
35	C₄×C₄₃	#335	1	1	yes	characteristic
36	C₄×C₄₃	#368	1	1	yes	characteristic
37	C₄×C₄₃	D₃₂	1	1	yes	characteristic
38	C₄×C₄₃	Q₆₄	1	1	yes	characteristic
39	C₄×C₃₂	—	43	1	no	—
40	#1371	—	43	1	no	—
41	#1371	D₄₃	1	1	yes	characteristic
42	C₂×C₄₃	#1371	1	1	yes	characteristic
43	C₂×C₄₃	#1423	1	1	yes	characteristic
44	C₂×C₄₃	#1425	1	1	yes	characteristic
45	C₂×C₃₂	—	43	1	no	—
46	C₂×C₃₂	—	43	1	no	—
47	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
48	#335	—	2	1	no	—
49	#335	—	86	1	no	—
50	C₄₃	#7460	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₁₆	Dic₈₆	1	1	yes	characteristic
52	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
53	C₄⋊C₈	—	4	1	no	—
54	C₄⋊C₈	—	172	1	no	—
55	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
56	C₃₂	—	43	2	no	—
57	C₃₂	—	86	1	no	—
58	C₂×C₈	—	8	1	no	—
59	C₂×C₈	—	344	1	no	—
60	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
61	C₂×C₈	#10621885	1	1	yes	characteristic
62	C₄²	#10621882	1	1	yes	characteristic
63	C₁₆	—	2	1	no	—
64	C₁₆	C₈×D₄₃	1	1	yes	characteristic
65	C₁₆	#10621872	1	1	yes	characteristic
66	C₂×C₄	#13063258	1	1	yes	characteristic
67	C₂×C₄	#13063266	1	1	yes	characteristic
68	C₂×C₄	#13063271	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	16	1	no	—
71	C₈	—	688	1	no	—
72	C₈	Dic₄₃⋊C₈	1	1	yes	characteristic
73	C₈	#13063260	1	1	yes	characteristic
74	C₂²	#14582724	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	#14582651	1	1	yes	characteristic
77	C₄	#14582728	1	1	yes	characteristic
78	C₄	#14582734	1	1	yes	characteristic
79	C₄	#14582739	1	1	yes	characteristic
80	C₂	#19132666	1	1	yes	characteristic
81	C₂	#19132794	1	1	yes	characteristic
82	C₂	#19132798	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063266
commutator	C₁₆×C₄₃	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄₃×#1371	C₂
socle, prime radical	C₂²×C₄₃	#366
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	#1371	D₄₃
hypocenter	C₄₃	#7460
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

Complements

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

N	H ≅ G/N	type
11. C₄₃⋊C₃₂	C₈	semidirect
50. C₄₃	#7460	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
#19132667	2
C₄₃×#1371	2
#7460	43