Subgroups — #14582723

Order 2752.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063265	C₂	1	1	yes	maximal, characteristic
2	#13063257	C₂	1	1	yes	maximal, characteristic
3	#108×C₄₃	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₄₃	—	2	1	no	—
5	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₄₃	—	2	1	no	—
7	C₄₃⋊C₁₆	C₄	1	2	yes	complemented
8	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
9	C₂×Dic₄₃	—	4	1	no	—
10	C₈×C₄₃	—	4	1	no	—
11	C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₃	Q₈	1	1	yes	characteristic
13	C₂²×C₄₃	SD₁₆	1	1	yes	characteristic
14	C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₄₃	SD₁₆	1	1	yes	characteristic
16	Dic₄₃	—	8	1	no	—
17	C₂×C₄₃	—	2	1	no	—
18	C₂×C₄₃	#106	1	1	yes	characteristic
19	#365	—	43	1	no	maximal, Sylow
20	C₄₃	#365	1	1	yes	characteristic, complemented, Sylow
21	M₃₂	—	43	1	no	—
22	#108	D₄₃	1	1	yes	characteristic
23	#106	—	43	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
26	C₄⋊C₄	—	86	1	no	—
27	C₁₆	—	43	2	no	—
28	C₂×C₄	—	172	1	no	—
29	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	Dic₈₆	1	1	yes	characteristic
32	C₈	C₄×D₄₃	1	1	yes	characteristic
33	C₂²	#10621884	1	1	yes	characteristic
34	C₄	—	344	1	no	—
35	C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
36	C₄	#10621883	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#13063256	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₄₃⋊C₁₆	C₄	semidirect
20. C₄₃	#365	semidirect

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