Subgroups — #24983212

Order 11008.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄₃⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₄₃⋊C₁₆	C₄	1	2	yes	—
6	C₄×C₁₆×C₄₃	C₄	1	2	yes	—
7	C₈²×C₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₄₃⋊C₁₆	C₈	1	4	yes	—
9	C₂×C₄₃⋊C₁₆	C₈	1	4	yes	—
10	C₂×C₁₆×C₄₃	C₈	1	4	yes	—
11	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
15	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
16	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
17	C₄²×C₄₃	C₄²	1	1	yes	characteristic
18	C₁₆×C₄₃	—	2	4	no	—
19	C₄₃⋊C₁₆	—	2	4	no	—
20	C₄₃⋊C₁₆	C₁₆	1	8	yes	complemented
21	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
23	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
24	C₈×C₄₃	C₂×C₁₆	1	4	yes	—
25	C₈×C₄₃	M₃₂	1	4	yes	—
26	C₈×C₄₃	M₃₂	1	4	yes	—
27	#7052	—	43	1	no	maximal, Sylow
28	C₂²×C₄₃	C₈²	1	1	yes	characteristic
29	C₄×C₄₃	C₄×C₁₆	1	2	yes	—
30	C₄×C₄₃	#346	1	2	yes	—
31	C₄×C₄₃	#346	1	2	yes	—
32	C₈×C₁₆	—	43	1	no	—
33	C₈×C₁₆	—	43	1	no	—
34	C₈×C₁₆	D₄₃	1	1	yes	characteristic
35	C₂×C₄₃	C₈×C₁₆	1	1	yes	characteristic
36	C₂×C₄₃	#1311	1	1	yes	characteristic
37	C₂×C₄₃	#1311	1	1	yes	characteristic
38	C₄×C₁₆	—	43	2	no	—
39	C₄×C₁₆	—	43	2	no	—
40	C₄×C₁₆	Dic₄₃	1	2	yes	—
41	C₈²	C₂×D₄₃	1	1	yes	characteristic
42	C₄₃	#7052	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₁₆	—	43	4	no	—
44	C₂×C₁₆	—	43	4	no	—
45	C₂×C₁₆	C₄₃⋊C₈	1	4	yes	—
46	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
47	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
48	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
49	C₂×C₈	C₈×D₄₃	1	2	yes	—
50	C₂×C₈	C₈×D₄₃	1	2	yes	—
51	C₂×C₈	C₂×C₄₃⋊C₈	1	2	yes	—
52	C₄²	C₄×Dic₄₃	1	1	yes	characteristic
53	C₁₆	—	2	4	no	—
54	C₁₆	—	43	8	no	—
55	C₁₆	—	86	4	no	—
56	C₂×C₄	C₈×Dic₄₃	1	1	yes	characteristic
57	C₂×C₄	C₈×Dic₄₃	1	1	yes	characteristic
58	C₂×C₄	C₄×C₄₃⋊C₈	1	1	yes	characteristic
59	C₈	C₁₆×D₄₃	1	4	yes	—
60	C₈	#13063264	1	4	yes	—
61	C₈	#13063265	1	4	yes	—
62	C₂²	C₈×C₄₃⋊C₈	1	1	yes	characteristic
63	C₄	C₁₆×Dic₄₃	1	2	yes	—
64	C₄	#14582674	1	2	yes	—
65	C₄	#14582675	1	2	yes	—
66	C₂	C₁₆×C₄₃⋊C₈	1	1	yes	characteristic
67	C₂	#19132511	1	1	yes	characteristic
68	C₂	#19132512	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈²	C₂×D₄₃
commutator	C₂×C₄₃	C₈×C₁₆
Fitting	C₈×C₁₆×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₈²
cosocle	C₈²×C₄₃	C₂²
hypercenter	C₈×C₁₆	D₄₃
hypocenter	C₄₃	#7052
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
20. C₄₃⋊C₁₆	C₁₆	semidirect
42. C₄₃	#7052	semidirect

Maximal subgroups

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

subgroup	index
C₈×C₄₃⋊C₁₆	2
C₈×C₁₆×C₄₃	2
#7052	43