Subgroups — #88371

Order 432.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₀₈	C₂	1	1	yes	maximal, characteristic
3	C₂₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#3675	—	3	1	no	maximal
5	C₂×D₂₇	—	2	1	no	—
6	C₄×C₂₇	—	2	1	no	—
7	C₄×C₂₇	C₂²	1	1	yes	characteristic
8	Q₈×C₉	D₃	1	1	yes	characteristic
9	D₃₆	—	3	1	no	—
10	C₉⋊C₈	—	3	1	no	—
11	C₂×C₂₇	D₄	1	1	yes	characteristic
12	D₂₇	—	4	1	no	—
13	#215	—	9	1	no	—
14	C₂×D₉	—	6	1	no	—
15	C₄×C₉	—	2	1	no	—
16	C₄×C₉	C₂×D₃	1	1	yes	characteristic
17	C₂₇	SD₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₃×Q₈	D₉	1	1	yes	characteristic
19	D₁₂	—	9	1	no	—
20	C₃⋊C₈	—	9	1	no	—
21	C₂×C₉	#67	1	1	yes	characteristic
22	D₉	—	12	1	no	—
23	SD₁₆	—	27	1	no	Sylow
24	C₂×D₃	—	18	1	no	—
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	C₂×D₉	1	1	yes	characteristic
27	C₉	#215	1	1	yes	characteristic
28	Q₈	D₂₇	1	1	yes	characteristic, complemented
29	D₄	—	27	1	no	—
30	C₈	—	27	1	no	—
31	C₂×C₃	#611	1	1	yes	characteristic
32	D₃	—	36	1	no	—
33	C₂²	—	54	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂×D₂₇	1	1	yes	characteristic
36	C₃	#3675	1	1	yes	characteristic
37	C₂	—	108	1	no	—
38	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.