Subgroups — Q₈×#272 #88747

Order 432.

209 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#272	C₂	1	3	yes	maximal
3	#6229	C₂	1	3	yes	maximal, complemented
4	C₃×D₃×Q₈	—	3	4	no	maximal
5	C₂×#272	C₂²	1	1	yes	characteristic
6	C₄×H(3,𝔽₃)	C₂²	1	3	yes	—
7	#1084	C₂²	1	3	yes	—
8	C₃²×Q₈	D₃	1	4	yes	complemented
9	C₃×C₄×D₃	—	3	12	no	—
10	C₃×Dic₆	—	3	12	no	—
11	C₂×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
12	#272	Q₈	1	2	yes	direct product factor
13	C₂×C₃×Q₈	—	9	1	no	—
14	D₃×Q₈	—	3	4	no	—
15	C₂×C₃×D₃	—	3	4	no	—
16	C₃²×C₄	C₂×D₃	1	12	yes	—
17	C₃×Dic₃	—	3	12	no	—
18	H(3,𝔽₃)	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
19	C₃×Q₈	—	6	4	no	—
20	C₃×Q₈	—	9	3	no	—
21	C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic
22	C₂×C₃×C₄	—	9	3	no	—
23	C₄×D₃	—	3	12	no	—
24	Dic₆	—	3	12	no	—
25	C₂×C₃²	C₂²×D₃	1	4	yes	—
26	C₃×D₃	—	3	8	no	—
27	C₂×Q₈	—	9	1	no	Sylow
28	C₂²×C₃	—	9	1	no	—
29	C₂×D₃	—	3	4	no	—
30	C₃×C₄	—	6	12	no	—
31	C₃×C₄	—	9	3	no	—
32	C₃×C₄	C₂×C₃⋊D₃	1	3	yes	—
33	Dic₃	—	3	12	no	—
34	C₃²	D₃×Q₈	1	4	yes	complemented
35	Q₈	—	9	3	no	—
36	Q₈	#272	1	1	yes	characteristic, direct product factor
37	C₂×C₄	—	9	3	no	—
38	C₂×C₃	—	6	4	no	—
39	C₂×C₃	—	9	2	no	—
40	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
41	D₃	—	3	8	no	—
42	C₂²	—	9	1	no	—
43	C₄	—	9	3	no	—
44	C₄	C₂×#272	1	3	yes	—
45	C₃	—	6	4	no	—
46	C₃	Q₈×C₃⋊D₃	1	1	yes	characteristic
47	C₂	—	9	2	no	—
48	C₂	C₂²×#272	1	1	yes	characteristic

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.