Subgroups — D₈×C₂₇ #88378

Order 432.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₂₇	C₂	1	2	yes	maximal, complemented
2	C₈×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₈	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₂₇	—	2	2	no	—
5	C₄×C₂₇	C₂²	1	1	yes	characteristic
6	D₄×C₉	C₂×C₃	1	2	yes	—
7	C₈×C₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₂₇	—	4	2	no	—
9	C₂×C₂₇	D₄	1	1	yes	characteristic
10	C₃×D₈	C₉	1	1	yes	characteristic
11	C₂²×C₉	—	2	2	no	—
12	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
13	C₂₇	D₈	1	1	yes	characteristic, direct product factor, Sylow
14	C₃×D₄	C₂×C₉	1	2	yes	—
15	C₃×C₈	C₂×C₉	1	1	yes	characteristic
16	C₂×C₉	—	4	2	no	—
17	C₂×C₉	C₃×D₄	1	1	yes	characteristic
18	D₈	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²×C₃	—	2	2	no	—
20	C₃×C₄	C₂²×C₉	1	1	yes	characteristic
21	C₉	C₃×D₈	1	1	yes	characteristic
22	D₄	C₂×C₂₇	1	2	yes	complemented
23	C₈	C₂×C₂₇	1	1	yes	characteristic, complemented
24	C₂×C₃	—	4	2	no	—
25	C₂×C₃	D₄×C₉	1	1	yes	characteristic
26	C₂²	—	2	2	no	—
27	C₄	C₂²×C₂₇	1	1	yes	characteristic
28	C₃	C₉×D₈	1	1	yes	characteristic
29	C₂	—	4	2	no	—
30	C₂	D₄×C₂₇	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.