Subgroups — #88359

Order 432.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₂₇	C₂	1	1	yes	maximal, characteristic
2	C₈×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#3663	—	3	1	no	maximal
5	C₂×D₂₇	C₄	1	1	yes	characteristic
6	C₄×C₂₇	C₂²	1	1	yes	characteristic
7	Dic₂₇	C₄	1	1	yes	characteristic
8	C₄×D₉	—	3	1	no	—
9	C₈×C₉	D₃	1	1	yes	characteristic
10	C₉⋊C₈	—	3	1	no	—
11	C₂×C₂₇	C₂×C₄	1	1	yes	characteristic
12	D₂₇	—	2	1	no	—
13	ΓL(1,𝔽₂₅)	—	9	1	no	—
14	C₂×D₉	—	3	1	no	—
15	C₄×C₉	C₂×D₃	1	1	yes	characteristic
16	Dic₉	—	3	1	no	—
17	C₂₇	M₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×D₃	—	9	1	no	—
19	C₃×C₈	D₉	1	1	yes	characteristic
20	C₃⋊C₈	—	9	1	no	—
21	C₂×C₉	C₄×D₃	1	1	yes	characteristic
22	D₉	—	6	1	no	—
23	M₁₆	—	27	1	no	Sylow
24	C₂×D₃	—	9	1	no	—
25	C₃×C₄	C₂×D₉	1	1	yes	characteristic
26	Dic₃	—	9	1	no	—
27	C₉	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
28	C₂×C₄	—	27	1	no	—
29	C₈	—	27	1	no	—
30	C₈	D₂₇	1	1	yes	characteristic, complemented
31	C₂×C₃	C₄×D₉	1	1	yes	characteristic
32	D₃	—	18	1	no	—
33	C₂²	—	27	1	no	—
34	C₄	—	27	1	no	—
35	C₄	C₂×D₂₇	1	1	yes	characteristic
36	C₃	#3663	1	1	yes	characteristic
37	C₂	—	54	1	no	—
38	C₂	C₄×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.