Subgroups — #14582769

Order 2752.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₄₃	C₂	1	6	yes	maximal
2	C₂×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₃	C₂²	1	3	yes	—
4	C₂²×Dic₄₃	C₂²	1	4	yes	—
5	C₄²×C₄₃	C₄	1	4	yes	complemented
6	C₄⋊Dic₄₃	—	2	12	no	—
7	C₂³×C₄₃	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₄₃	C₂×C₄	1	6	yes	—
9	C₂×C₄×C₄₃	D₄	1	6	yes	—
10	C₂×C₄×C₄₃	Q₈	1	6	yes	—
11	C₂×Dic₄₃	—	2	12	no	—
12	C₂²×C₄₃	C₂²×C₄	1	1	yes	characteristic
13	C₂²×C₄₃	C₂×D₄	1	3	yes	—
14	C₂²×C₄₃	C₂×Q₈	1	3	yes	—
15	C₄×C₄₃	C₄⋊C₄	1	12	yes	complemented
16	Dic₄₃	—	4	4	no	—
17	C₂×C₄₃	C₂×C₄⋊C₄	1	3	yes	—
18	C₂×C₄₃	#127	1	1	yes	characteristic
19	C₂×C₄₃	C₄⋊Q₈	1	3	yes	—
20	#384	—	43	1	no	maximal, Sylow
21	C₄₃	#384	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₄⋊C₄	—	43	6	no	—
23	C₂×C₄²	D₄₃	1	1	yes	characteristic
24	C₂²×C₄	—	43	4	no	—
25	C₂²×C₄	C₂×D₄₃	1	3	yes	—
26	C₄⋊C₄	—	86	12	no	—
27	C₄²	Dic₄₃	1	4	yes	complemented
28	C₂³	C₂²×D₄₃	1	1	yes	characteristic
29	C₂×C₄	—	86	12	no	—
30	C₂×C₄	Dic₈₆	1	6	yes	—
31	C₂×C₄	D₁₇₂	1	6	yes	—
32	C₂×C₄	C₂×Dic₄₃	1	6	yes	—
33	C₂²	C₂×Dic₈₆	1	3	yes	—
34	C₂²	C₂×D₁₇₂	1	3	yes	—
35	C₂²	C₂²×Dic₄₃	1	1	yes	characteristic
36	C₄	—	172	4	no	—
37	C₄	C₄⋊Dic₄₃	1	12	yes	complemented
38	C₂	C₂×C₄⋊Dic₄₃	1	3	yes	—
39	C₂	#13063322	1	1	yes	characteristic
40	C₂	#13063325	1	3	yes	—

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

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