Subgroups — #24984496

Order 11008.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#19132795	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1423	C₂	1	1	yes	maximal, characteristic
4	#14582725	—	2	1	no	—
5	C₄₃⋊C₆₄	C₄	1	2	yes	complemented
6	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
7	C₄₃×#366	—	2	1	no	—
8	#13063259	—	4	1	no	—
9	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
10	#107×C₄₃	—	4	1	no	—
11	C₃₂×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₄₃	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
14	C₄⋊C₄×C₄₃	—	8	1	no	—
15	C₄⋊Dic₄₃	—	8	1	no	—
16	C₁₆×C₄₃	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₄₃	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₄₃	—	16	1	no	—
19	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
20	C₂×Dic₄₃	—	16	1	no	—
21	C₈×C₄₃	#107	1	1	yes	characteristic
22	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
23	#7545	—	43	1	no	maximal, Sylow
24	C₂²×C₄₃	D₃₂	1	1	yes	characteristic
25	C₄×C₄₃	—	32	1	no	—
26	C₄×C₄₃	#366	1	1	yes	characteristic
27	C₄×C₄₃	Q₆₄	1	1	yes	characteristic
28	Dic₄₃	—	32	1	no	—
29	C₂×C₆₄	—	43	1	no	—
30	#1423	—	43	1	no	—
31	#1423	D₄₃	1	1	yes	characteristic
32	C₂×C₄₃	#1423	1	1	yes	characteristic
33	C₂×C₄₃	D₆₄	1	1	yes	characteristic
34	C₂×C₄₃	Q₁₂₈	1	1	yes	characteristic
35	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
36	#366	—	2	1	no	—
37	#366	—	86	1	no	—
38	C₆₄	—	43	2	no	—
39	C₄₃	#7545	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
41	#107	—	4	1	no	—
42	#107	—	172	1	no	—
43	C₃₂	Dic₈₆	1	1	yes	characteristic
44	C₃₂	C₄×D₄₃	1	1	yes	characteristic
45	C₂×C₈	#10621882	1	1	yes	characteristic
46	C₄⋊C₄	—	8	1	no	—
47	C₄⋊C₄	—	344	1	no	—
48	C₁₆	Dic₄₃⋊C₄	1	1	yes	characteristic
49	C₁₆	#10621885	1	1	yes	characteristic
50	C₂×C₄	—	16	1	no	—
51	C₂×C₄	—	688	1	no	—
52	C₂×C₄	#13063266	1	1	yes	characteristic
53	C₈	#13063258	1	1	yes	characteristic
54	C₈	#13063271	1	1	yes	characteristic
55	C₂²	#14582734	1	1	yes	characteristic
56	C₄	—	32	1	no	—
57	C₄	—	1376	1	no	—
58	C₄	#14582724	1	1	yes	characteristic
59	C₄	#14582739	1	1	yes	characteristic
60	C₂	#19132794	1	1	yes	characteristic
61	C₂	#19132807	1	1	yes	characteristic
62	C₂	#19132812	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14582734
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₄₃×#1423	C₂
socle, prime radical	C₂²×C₄₃	D₃₂
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	#1423	D₄₃
hypocenter	C₄₃	#7545
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
5. C₄₃⋊C₆₄	C₄	semidirect
39. C₄₃	#7545	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃⋊C₆₄	2
#19132795	2
C₄₃×#1423	2
#7545	43