Subgroups — Q₈×D₂₇ #88402

Order 432.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₂₇	C₂	1	3	yes	maximal
3	Dic₅₄	C₂	1	3	yes	maximal, complemented
4	Q₈×D₉	—	3	1	no	maximal
5	C₂×D₂₇	C₂²	1	1	yes	characteristic
6	C₄×C₂₇	C₂²	1	3	yes	—
7	Dic₂₇	C₂²	1	3	yes	—
8	Q₈×C₉	D₃	1	1	yes	characteristic
9	C₄×D₉	—	3	3	no	—
10	Dic₁₈	—	3	3	no	—
11	C₂×C₂₇	C₂³	1	1	yes	characteristic
12	D₂₇	Q₈	1	2	yes	direct product factor
13	D₃×Q₈	—	9	1	no	—
14	C₂×D₉	—	3	1	no	—
15	C₄×C₉	C₂×D₃	1	3	yes	—
16	Dic₉	—	3	3	no	—
17	C₂₇	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₃×Q₈	D₉	1	1	yes	characteristic
19	C₄×D₃	—	9	3	no	—
20	Dic₆	—	9	3	no	—
21	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
22	D₉	—	3	2	no	—
23	C₂×Q₈	—	27	1	no	Sylow
24	C₂×D₃	—	9	1	no	—
25	C₃×C₄	C₂×D₉	1	3	yes	—
26	Dic₃	—	9	3	no	—
27	C₉	D₃×Q₈	1	1	yes	characteristic
28	Q₈	—	27	3	no	—
29	Q₈	D₂₇	1	1	yes	characteristic, direct product factor
30	C₂×C₄	—	27	3	no	—
31	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
32	D₃	—	9	2	no	—
33	C₂²	—	27	1	no	—
34	C₄	—	27	3	no	—
35	C₄	C₂×D₂₇	1	3	yes	—
36	C₃	Q₈×D₉	1	1	yes	characteristic
37	C₂	—	27	2	no	—
38	C₂	C₂²×D₂₇	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.