Subgroups — C₂³×#157 #64391

Order 288.

370 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#157	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₃²	C₄	1	1	yes	characteristic, complemented
4	C₂²×C₃⋊D₃	C₄	1	7	yes	complemented
5	C₂²×C₃⋊D₃	C₂²	1	7	yes	—
6	C₂×#157	C₂²	1	28	yes	direct product factor
7	C₂³×D₃	—	6	2	no	—
8	C₂²×C₃²	C₂×C₄	1	7	yes	complemented
9	C₂×C₃⋊D₃	C₂×C₄	1	21	yes	complemented
10	C₂×C₃⋊D₃	C₂³	1	7	yes	—
11	#157	C₂³	1	8	yes	direct product factor
12	C₂³×C₄	—	9	1	no	maximal, Sylow
13	C₂³×C₃	—	2	2	no	—
14	C₂²×D₃	—	6	14	no	—
15	C₂²×D₃	—	6	14	no	—
16	C₂×C₃²	C₂²×C₄	1	7	yes	complemented
17	C₃⋊D₃	C₂²×C₄	1	7	yes	complemented
18	C₃⋊D₃	C₂⁴	1	1	yes	characteristic
19	C₂⁴	—	9	1	no	—
20	C₂²×C₄	—	9	14	no	—
21	C₂²×C₃	—	2	14	no	—
22	C₂×D₃	—	6	42	no	—
23	C₂×D₃	—	6	14	no	—
24	C₃²	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
25	C₂³	—	9	7	no	—
26	C₂³	—	9	7	no	—
27	C₂³	#157	1	1	yes	characteristic, direct product factor
28	C₂×C₄	—	9	28	no	—
29	C₂×C₃	—	2	14	no	—
30	D₃	—	6	14	no	—
31	D₃	—	6	2	no	—
32	C₂²	—	9	7	no	—
33	C₂²	—	9	21	no	—
34	C₂²	C₂×#157	1	7	yes	direct product factor
35	C₄	—	9	8	no	—
36	C₃	—	2	2	no	—
37	C₂	—	9	1	no	—
38	C₂	—	9	7	no	—
39	C₂	C₂²×#157	1	7	yes	direct product factor

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.