Subgroups — #24983930

Order 11008.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132729	C₂	1	2	yes	maximal
2	C₄₃×#1311	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃⋊C₃₂	C₄	1	4	yes	—
4	C₄×C₁₆×C₄₃	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
6	C₈²×C₄₃	C₄	1	1	yes	characteristic
7	C₄₃⋊C₃₂	—	2	4	no	—
8	C₂×C₁₆×C₄₃	C₈	1	2	yes	—
9	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
10	C₄×C₈×C₄₃	C₈	1	2	yes	—
11	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₄₃	—	2	2	no	—
13	C₂×C₈×C₄₃	C₄²	1	1	yes	characteristic
14	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₄₃	C₂×C₈	1	1	yes	characteristic
16	C₁₆×C₄₃	C₁₆	1	4	yes	—
17	C₁₆×C₄₃	M₁₆	1	4	yes	—
18	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
19	C₂×C₄×C₄₃	M₃₂	1	2	yes	—
20	C₈×C₄₃	—	4	2	no	—
21	C₈×C₄₃	#97	1	2	yes	—
22	C₈×C₄₃	C₂×C₁₆	1	2	yes	—
23	#7332	—	43	1	no	maximal, Sylow
24	C₂²×C₄₃	#346	1	1	yes	characteristic
25	C₄×C₄₃	—	2	2	no	—
26	C₄×C₄₃	#322	1	1	yes	characteristic
27	C₄×C₄₃	C₄×C₁₆	1	1	yes	characteristic
28	#1397	—	43	2	no	—
29	#1311	D₄₃	1	1	yes	characteristic
30	C₂×C₄₃	#1312	1	1	yes	characteristic
31	C₂×C₄₃	#1398	1	2	yes	—
32	C₂×C₃₂	—	43	4	no	—
33	C₄×C₁₆	Dic₄₃	1	1	yes	characteristic
34	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
35	C₈²	Dic₄₃	1	1	yes	characteristic
36	C₄₃	#7332	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	C₄₃⋊C₈	1	2	yes	—
38	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
39	C₄×C₈	C₄₃⋊C₈	1	2	yes	—
40	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
41	C₃₂	—	86	4	no	—
42	C₂×C₈	—	2	2	no	—
43	C₂×C₈	C₂×C₄₃⋊C₈	1	1	yes	characteristic
44	C₂×C₈	C₄×Dic₄₃	1	1	yes	characteristic
45	C₄²	C₂×C₄₃⋊C₈	1	1	yes	characteristic
46	C₁₆	C₄₃⋊C₁₆	1	4	yes	—
47	C₁₆	#10621872	1	4	yes	—
48	C₂×C₄	C₄×C₄₃⋊C₈	1	1	yes	characteristic
49	C₂×C₄	#13063265	1	2	yes	—
50	C₈	—	4	2	no	—
51	C₈	#13063235	1	2	yes	—
52	C₈	C₂×C₄₃⋊C₁₆	1	2	yes	—
53	C₂²	#14582675	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#14582620	1	1	yes	characteristic
56	C₄	C₄×C₄₃⋊C₁₆	1	1	yes	characteristic
57	C₂	#19132513	1	1	yes	characteristic
58	C₂	#19132731	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₄×Dic₄₃
commutator	C₄×C₄₃	C₄×C₁₆
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄₃×#1311	C₂
socle, prime radical	C₂²×C₄₃	#346
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	#1311	D₄₃
hypocenter	C₄₃	#7332
LCS	G ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ #1311

Complements

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

N	H ≅ G/N	type
36. C₄₃	#7332	semidirect

Maximal subgroups

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

subgroup	index
#19132729	2
C₄₃×#1311	2
#7332	43