Subgroups — #24984276

Order 11008.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132667	C₂	1	2	yes	maximal
2	C₄×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582652	—	2	2	no	—
4	C₂×C₃₂×C₄₃	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₄₃	C₄	1	1	yes	characteristic
6	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
7	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
8	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₄₃	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
11	C₃₂×C₄₃	—	2	1	no	—
12	C₃₂×C₄₃	C₈	1	2	yes	complemented
13	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₃	Q₁₆	1	1	yes	characteristic
15	C₄²×C₄₃	D₈	1	1	yes	characteristic
16	C₂×C₄₃⋊C₈	—	8	2	no	—
17	C₁₆×C₄₃	—	2	1	no	—
18	C₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
21	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
22	C₂×C₄×C₄₃	Q₃₂	1	1	yes	characteristic
23	C₈×C₄₃	—	2	1	no	—
24	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
25	C₈×C₄₃	#108	1	1	yes	characteristic
26	C₄₃⋊C₈	—	16	2	no	—
27	#7461	—	43	1	no	maximal, Sylow
28	C₂²×C₄₃	#366	1	1	yes	characteristic
29	C₄×C₄₃	—	2	1	no	—
30	C₄×C₄₃	#335	1	1	yes	characteristic
31	C₄×C₄₃	#368	1	1	yes	characteristic
32	C₄×C₄₃	SD₆₄	1	2	yes	—
33	C₄×C₃₂	D₄₃	1	1	yes	characteristic
34	#1371	—	43	2	no	—
35	C₂×C₄₃	#1371	1	1	yes	characteristic
36	C₂×C₄₃	#1424	1	1	yes	characteristic
37	C₂×C₄₃	#1425	1	1	yes	characteristic
38	C₂×C₃₂	Dic₄₃	1	1	yes	characteristic
39	C₂×C₃₂	Dic₄₃	1	1	yes	characteristic
40	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
41	#335	—	86	2	no	—
42	C₄₃	#7461	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₁₆	Dic₈₆	1	1	yes	characteristic
44	C₂×C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
45	C₄⋊C₈	—	172	2	no	—
46	C₄×C₈	D₁₇₂	1	1	yes	characteristic
47	C₃₂	—	2	1	no	—
48	C₃₂	C₄₃⋊C₈	1	2	yes	complemented
49	C₂×C₈	—	344	2	no	—
50	C₂×C₈	Dic₁₇₂	1	1	yes	characteristic
51	C₂×C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
52	C₄²	D₃₄₄	1	1	yes	characteristic
53	C₁₆	—	2	1	no	—
54	C₁₆	C₂×C₄₃⋊C₈	1	1	yes	characteristic
55	C₁₆	#10621877	1	1	yes	characteristic
56	C₂×C₄	#13063259	1	1	yes	characteristic
57	C₂×C₄	D₆₈₈	1	1	yes	characteristic
58	C₂×C₄	Dic₃₄₄	1	1	yes	characteristic
59	C₈	—	2	1	no	—
60	C₈	—	688	2	no	—
61	C₈	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
62	C₈	#13063261	1	1	yes	characteristic
63	C₂²	#14582725	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	#14582652	1	1	yes	characteristic
66	C₄	#14582729	1	1	yes	characteristic
67	C₄	#14582738	1	2	yes	—
68	C₂	#19132667	1	1	yes	characteristic
69	C₂	#19132797	1	1	yes	characteristic
70	C₂	#19132799	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₆₈₈
commutator	C₁₆×C₄₃	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄×C₃₂×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	#366
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	C₄×C₃₂	D₄₃
hypocenter	C₄₃	#7461
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
12. C₃₂×C₄₃	C₈	semidirect
42. C₄₃	#7461	semidirect
48. 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
#19132667	2
C₄×C₃₂×C₄₃	2
#7461	43