Subgroups — #88369

Order 432.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₀₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#3673	—	3	1	no	maximal
5	C₂²×C₂₇	—	2	1	no	—
6	C₂×D₂₇	—	2	1	no	—
7	C₄×C₂₇	C₂²	1	1	yes	characteristic
8	D₄×C₉	D₃	1	1	yes	characteristic
9	D₃₆	—	3	1	no	—
10	C₉⋊C₈	—	3	1	no	—
11	C₂×C₂₇	—	4	1	no	—
12	C₂×C₂₇	D₄	1	1	yes	characteristic
13	D₂₇	—	4	1	no	—
14	#213	—	9	1	no	—
15	C₂²×C₉	—	2	1	no	—
16	C₂×D₉	—	6	1	no	—
17	C₄×C₉	C₂×D₃	1	1	yes	characteristic
18	C₂₇	D₈	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₄	D₉	1	1	yes	characteristic
20	D₁₂	—	9	1	no	—
21	C₃⋊C₈	—	9	1	no	—
22	C₂×C₉	—	4	1	no	—
23	C₂×C₉	#67	1	1	yes	characteristic
24	D₉	—	12	1	no	—
25	D₈	—	27	1	no	Sylow
26	C₂²×C₃	—	2	1	no	—
27	C₂×D₃	—	18	1	no	—
28	C₃×C₄	C₂×D₉	1	1	yes	characteristic
29	C₉	#213	1	1	yes	characteristic
30	D₄	—	27	1	no	—
31	D₄	D₂₇	1	1	yes	characteristic, complemented
32	C₈	—	27	1	no	—
33	C₂×C₃	—	4	1	no	—
34	C₂×C₃	#611	1	1	yes	characteristic
35	D₃	—	36	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	54	1	no	—
38	C₄	C₂×D₂₇	1	1	yes	characteristic
39	C₃	#3673	1	1	yes	characteristic
40	C₂	—	4	1	no	—
41	C₂	—	108	1	no	—
42	C₂	#6171	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.