Subgroups — #24984278

Order 11008.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132671	C₂	1	2	yes	maximal
2	C₄×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582720	—	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	#13063265	—	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	—
13	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
15	C₄²×C₄₃	Q₁₆	1	1	yes	characteristic
16	C₁₆×C₄₃	—	2	1	no	—
17	C₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic
18	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
19	C₄₃⋊C₁₆	—	8	2	no	—
20	C₂×C₄×C₄₃	—	2	1	no	—
21	C₂×C₄×C₄₃	#107	1	1	yes	characteristic
22	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
23	C₈×C₄₃	#108	1	1	yes	characteristic
24	C₈×C₄₃	D₁₆	1	1	yes	characteristic
25	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
26	#7462	—	43	1	no	maximal, Sylow
27	C₂²×C₄₃	#368	1	1	yes	characteristic
28	C₄×C₄₃	—	2	2	no	—
29	C₄×C₄₃	#335	1	1	yes	characteristic
30	C₄×C₄₃	#366	1	1	yes	characteristic
31	C₄×C₃₂	D₄₃	1	1	yes	characteristic
32	#1373	—	43	2	no	—
33	C₂×C₄₃	—	2	1	no	—
34	C₂×C₄₃	#1371	1	1	yes	characteristic
35	C₂×C₃₂	Dic₄₃	1	1	yes	characteristic
36	C₂×C₃₂	Dic₄₃	1	1	yes	characteristic
37	#364	—	86	2	no	—
38	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
39	C₄₃	#7462	1	1	yes	characteristic, complemented, Sylow
40	M₃₂	—	172	2	no	—
41	C₂×C₁₆	Dic₈₆	1	1	yes	characteristic
42	C₂×C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
43	C₄×C₈	D₁₇₂	1	1	yes	characteristic
44	C₃₂	—	2	1	no	—
45	C₃₂	C₄₃⋊C₈	1	2	yes	—
46	C₂×C₈	D₃₄₄	1	1	yes	characteristic
47	C₂×C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
48	C₄²	Dic₁₇₂	1	1	yes	characteristic
49	C₁₆	—	2	1	no	—
50	C₁₆	—	344	2	no	—
51	C₁₆	C₂×C₄₃⋊C₈	1	1	yes	characteristic
52	C₁₆	#10621877	1	1	yes	characteristic
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	#13063259	1	1	yes	characteristic
55	C₈	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
56	C₈	#13063261	1	1	yes	characteristic
57	C₈	D₆₈₈	1	1	yes	characteristic
58	C₈	Dic₃₄₄	1	1	yes	characteristic
59	C₂²	#14582729	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	#14582652	1	1	yes	characteristic
62	C₄	#14582725	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#19132667	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₆₈₈
commutator	C₁₆×C₄₃	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₄₃
Fitting	C₄×C₃₂×C₄₃	C₂
socle	C₂×C₄₃	#1371
prime radical	C₂²×C₄₃	#368
cosocle	C₄×C₁₆×C₄₃	C₂²
hypercenter	C₄×C₃₂	D₄₃
hypocenter	C₄₃	#7462
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
39. C₄₃	#7462	semidirect

Maximal subgroups

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

subgroup	index
#19132671	2
C₄×C₃₂×C₄₃	2
#7462	43