Subgroups — C₄⋊Dic₂₇ #88366

Order 432.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₇	C₂	1	2	yes	maximal
3	C₄⋊Dic₉	—	3	1	no	maximal
4	C₂²×C₂₇	C₂²	1	1	yes	characteristic
5	C₄×C₂₇	C₄	1	2	yes	complemented
6	Dic₂₇	—	2	2	no	—
7	C₂×C₄×C₉	D₃	1	1	yes	characteristic
8	C₂×Dic₉	—	3	2	no	—
9	C₂×C₂₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₂₇	D₄	1	1	yes	characteristic
11	C₂×C₂₇	Q₈	1	1	yes	characteristic
12	C₄⋊Dic₃	—	9	1	no	—
13	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
14	C₄×C₉	Dic₃	1	2	yes	—
15	Dic₉	—	6	2	no	—
16	C₂₇	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₄	D₉	1	1	yes	characteristic
18	C₂×Dic₃	—	9	2	no	—
19	C₂×C₉	Dic₆	1	1	yes	characteristic
20	C₂×C₉	D₁₂	1	1	yes	characteristic
21	C₂×C₉	C₂×Dic₃	1	1	yes	characteristic
22	C₄⋊C₄	—	27	1	no	Sylow
23	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
24	C₃×C₄	Dic₉	1	2	yes	—
25	Dic₃	—	18	2	no	—
26	C₉	C₄⋊Dic₃	1	1	yes	characteristic
27	C₂×C₄	—	27	2	no	—
28	C₂×C₄	D₂₇	1	1	yes	characteristic
29	C₂×C₃	Dic₁₈	1	1	yes	characteristic
30	C₂×C₃	D₃₆	1	1	yes	characteristic
31	C₂×C₃	C₂×Dic₉	1	1	yes	characteristic
32	C₂²	C₂×D₂₇	1	1	yes	characteristic
33	C₄	—	54	2	no	—
34	C₄	Dic₂₇	1	2	yes	complemented
35	C₃	C₄⋊Dic₉	1	1	yes	characteristic
36	C₂	Dic₅₄	1	1	yes	characteristic
37	C₂	D₁₀₈	1	1	yes	characteristic
38	C₂	C₂×Dic₂₇	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.