Subgroups — #24983932

Order 11008.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132731	C₂	1	1	yes	maximal, characteristic
2	#19132515	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1398	C₂	1	1	yes	maximal, characteristic
4	#14582733	C₄	1	2	yes	—
5	#14582675	C₄	1	1	yes	characteristic
6	#14582620	C₄	1	1	yes	characteristic
7	C₄₃×M₆₄	C₄	1	2	yes	—
8	C₄₃×#346	C₂²	1	1	yes	characteristic
9	C₂×C₄₃⋊C₁₆	—	2	1	no	—
10	C₄×C₄₃⋊C₈	—	2	1	no	—
11	C₄₃⋊C₃₂	—	2	2	no	—
12	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₃₂×C₄₃	C₈	1	4	yes	complemented
16	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
17	C₂×C₈×C₄₃	M₁₆	1	1	yes	characteristic
18	C₄²×C₄₃	M₁₆	1	1	yes	characteristic
19	C₂×C₄₃⋊C₈	—	4	1	no	—
20	C₁₆×C₄₃	C₂×C₈	1	2	yes	—
21	C₁₆×C₄₃	M₁₆	1	2	yes	—
22	C₄₃⋊C₁₆	—	4	1	no	—
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	#97	1	1	yes	characteristic
25	C₈×C₄₃	—	2	1	no	—
26	C₈×C₄₃	C₄×C₈	1	1	yes	characteristic
27	C₈×C₄₃	#97	1	1	yes	characteristic
28	C₄₃⋊C₈	—	8	1	no	—
29	#7333	—	43	1	no	maximal, Sylow
30	C₂²×C₄₃	#347	1	1	yes	characteristic
31	C₄×C₄₃	—	4	1	no	—
32	C₄×C₄₃	#322	1	1	yes	characteristic
33	C₄×C₄₃	#347	1	1	yes	characteristic
34	#1398	—	43	1	no	—
35	#1398	D₄₃	1	1	yes	characteristic
36	#1313	—	43	1	no	—
37	C₂×C₄₃	—	2	1	no	—
38	C₂×C₄₃	#1313	1	1	yes	characteristic
39	M₆₄	—	43	2	no	—
40	M₆₄	Dic₄₃	1	2	yes	—
41	#346	—	43	1	no	—
42	#346	C₂×D₄₃	1	1	yes	characteristic
43	#322	—	43	1	no	—
44	C₄₃	#7333	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₁₆	—	86	1	no	—
46	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
47	C₂×C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
48	C₄×C₈	—	86	1	no	—
49	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
50	C₃₂	—	86	2	no	—
51	C₃₂	C₄₃⋊C₈	1	4	yes	complemented
52	C₂×C₈	—	172	1	no	—
53	C₂×C₈	#10621872	1	1	yes	characteristic
54	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
55	C₄²	#10621872	1	1	yes	characteristic
56	C₁₆	—	172	1	no	—
57	C₁₆	#10621872	1	2	yes	—
58	C₁₆	C₂×C₄₃⋊C₈	1	2	yes	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	#13063235	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	344	1	no	—
63	C₈	C₄×C₄₃⋊C₈	1	1	yes	characteristic
64	C₈	#13063235	1	1	yes	characteristic
65	C₂²	#14582676	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	#14582620	1	1	yes	characteristic
68	C₄	#14582676	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#19132515	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14582620
commutator	C₈×C₄₃	C₄×C₈
Frattini	#346	C₂×D₄₃
Fitting	C₄₃×#1398	C₂
socle	C₂×C₄₃	#1313
prime radical	C₂²×C₄₃	#347
cosocle	C₄₃×#346	C₂²
hypercenter	#1398	D₄₃
hypocenter	C₄₃	#7333
LCS	G ▷ C₈×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ #346 ◁ #1398

Complements

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

N	H ≅ G/N	type
15. C₃₂×C₄₃	C₈	semidirect
44. C₄₃	#7333	semidirect
51. C₃₂	C₄₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#19132731	2
#19132515	2
C₄₃×#1398	2
#7333	43