Subgroups — #24984501

Order 11008.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132799	C₂	1	2	yes	maximal
2	C₂×C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	#14582729	—	2	2	no	—
4	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
5	C₄₃×C₆₄	C₄	1	2	yes	—
6	#13063261	—	4	2	no	—
7	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
8	C₃₂×C₄₃	C₂×C₄	1	1	yes	characteristic
9	C₃₂×C₄₃	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
11	#10621877	—	8	2	no	—
12	C₁₆×C₄₃	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₄₃	Q₁₆	1	1	yes	characteristic
14	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
15	C₈×C₄₃	#107	1	1	yes	characteristic
16	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
17	C₄₃⋊C₈	—	16	2	no	—
18	#7547	—	43	1	no	maximal, Sylow
19	C₂²×C₄₃	Q₆₄	1	1	yes	characteristic
20	C₄×C₄₃	#366	1	1	yes	characteristic
21	C₄×C₄₃	D₃₂	1	1	yes	characteristic
22	C₂×C₆₄	D₄₃	1	1	yes	characteristic
23	#1425	—	43	2	no	—
24	C₂×C₄₃	—	2	1	no	—
25	C₂×C₄₃	#1423	1	1	yes	characteristic
26	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
27	#368	—	86	2	no	—
28	C₆₄	Dic₄₃	1	2	yes	—
29	C₄₃	#7547	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
31	#108	—	172	2	no	—
32	C₃₂	Dic₈₆	1	1	yes	characteristic
33	C₃₂	C₂×Dic₄₃	1	1	yes	characteristic
34	M₁₆	—	344	2	no	—
35	C₂×C₈	D₃₄₄	1	1	yes	characteristic
36	C₁₆	Dic₁₇₂	1	1	yes	characteristic
37	C₁₆	C₄⋊Dic₄₃	1	1	yes	characteristic
38	C₂×C₄	D₆₈₈	1	1	yes	characteristic
39	C₈	—	688	2	no	—
40	C₈	#13063259	1	1	yes	characteristic
41	C₈	Dic₃₄₄	1	1	yes	characteristic
42	C₂²	Dic₆₈₈	1	1	yes	characteristic
43	C₄	#14582725	1	1	yes	characteristic
44	C₄	D₁₃₇₆	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#19132795	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃₇₆
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₂×C₄₃×C₆₄	C₂
socle	C₂×C₄₃	#1423
prime radical	C₂²×C₄₃	Q₆₄
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	C₂×C₆₄	D₄₃
hypocenter	C₄₃	#7547
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
29. C₄₃	#7547	semidirect

Maximal subgroups

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

subgroup	index
#19132799	2
C₂×C₄₃×C₆₄	2
#7547	43