Subgroups — #14582726

Order 2752.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#13063259	C₂	1	1	yes	maximal, characteristic
3	#107×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
5	C₄⋊C₄×C₄₃	—	2	1	no	—
6	C₄⋊Dic₄₃	—	2	1	no	—
7	C₄₃⋊C₁₆	C₄	1	2	yes	complemented
8	C₂×C₄×C₄₃	—	4	1	no	—
9	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
10	C₂×Dic₄₃	—	4	1	no	—
11	C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₄₃	Q₈	1	1	yes	characteristic
13	C₂²×C₄₃	D₈	1	1	yes	characteristic
14	C₄×C₄₃	—	8	1	no	—
15	C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₄₃	Q₁₆	1	1	yes	characteristic
17	Dic₄₃	—	8	1	no	—
18	C₂×C₄₃	#107	1	1	yes	characteristic
19	C₂×C₄₃	SD₃₂	1	1	yes	characteristic
20	C₂×C₄₃	SD₃₂	1	1	yes	characteristic
21	#367	—	43	1	no	maximal, Sylow
22	C₄₃	#367	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	43	1	no	—
24	#107	—	43	1	no	—
25	#107	D₄₃	1	1	yes	characteristic
26	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	86	1	no	—
29	C₁₆	—	43	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	172	1	no	—
32	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
33	C₈	Dic₈₆	1	1	yes	characteristic
34	C₈	C₄×D₄₃	1	1	yes	characteristic
35	C₂²	#10621882	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	344	1	no	—
38	C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
39	C₄	#10621885	1	1	yes	characteristic
40	C₂	#13063258	1	1	yes	characteristic
41	C₂	#13063268	1	1	yes	characteristic
42	C₂	#13063269	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₄₃⋊C₁₆	C₄	semidirect
22. C₄₃	#367	semidirect

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