Subgroups — C₄×Dic₂₇ #88364

Order 432.

60 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	C₄	1	4	yes	direct product factor
7	C₂×C₄×C₉	D₃	1	1	yes	characteristic
8	C₂×Dic₉	—	3	2	no	—
9	C₂×C₂₇	C₂×C₄	1	2	yes	—
10	C₂×C₂₇	C₂×C₄	1	1	yes	characteristic
11	C₄×Dic₃	—	9	1	no	—
12	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
13	C₄×C₉	Dic₃	1	2	yes	—
14	Dic₉	—	3	4	no	—
15	C₂₇	C₄²	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×C₄	D₉	1	1	yes	characteristic
17	C₂×Dic₃	—	9	2	no	—
18	C₂×C₉	C₄×D₃	1	2	yes	—
19	C₂×C₉	C₂×Dic₃	1	1	yes	characteristic
20	C₄²	—	27	1	no	Sylow
21	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
22	C₃×C₄	Dic₉	1	2	yes	—
23	Dic₃	—	9	4	no	—
24	C₉	C₄×Dic₃	1	1	yes	characteristic
25	C₂×C₄	—	27	2	no	—
26	C₂×C₄	D₂₇	1	1	yes	characteristic
27	C₂×C₃	C₄×D₉	1	2	yes	—
28	C₂×C₃	C₂×Dic₉	1	1	yes	characteristic
29	C₂²	C₂×D₂₇	1	1	yes	characteristic
30	C₄	—	27	4	no	—
31	C₄	Dic₂₇	1	2	yes	direct product factor
32	C₃	C₄×Dic₉	1	1	yes	characteristic
33	C₂	C₄×D₂₇	1	2	yes	—
34	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.