Subgroups — #41×C₂₇ #88409

Order 432.

80 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	D₄×C₂₇	C₂	1	3	yes	maximal, complemented
3	C₂×C₄×C₂₇	C₂	1	3	yes	maximal, complemented
4	C₉×#41	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₂₇	C₂²	1	3	yes	—
6	C₄×C₂₇	C₂²	1	3	yes	—
7	C₄×C₂₇	C₂²	1	1	yes	characteristic
8	Q₈×C₉	C₂×C₃	1	1	yes	characteristic
9	D₄×C₉	C₂×C₃	1	3	yes	—
10	C₂×C₄×C₉	C₂×C₃	1	3	yes	—
11	C₂×C₂₇	—	2	3	no	—
12	C₂×C₂₇	C₂³	1	1	yes	characteristic
13	C₃×#41	C₉	1	1	yes	characteristic
14	C₂²×C₉	C₂²×C₃	1	3	yes	—
15	C₄×C₉	C₂²×C₃	1	3	yes	—
16	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
17	C₂₇	#41	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×Q₈	C₂×C₉	1	1	yes	characteristic
19	C₃×D₄	C₂×C₉	1	3	yes	—
20	C₂×C₃×C₄	C₂×C₉	1	3	yes	—
21	C₂×C₉	—	2	3	no	—
22	C₂×C₉	C₂³×C₃	1	1	yes	characteristic
23	#41	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃	C₂²×C₉	1	3	yes	—
25	C₃×C₄	C₂²×C₉	1	1	yes	characteristic
26	C₃×C₄	C₂²×C₉	1	3	yes	—
27	C₉	C₃×#41	1	1	yes	characteristic
28	Q₈	C₂×C₂₇	1	1	yes	characteristic, complemented
29	D₄	C₂×C₂₇	1	3	yes	complemented
30	C₂×C₄	C₂×C₂₇	1	3	yes	complemented
31	C₂×C₃	—	2	3	no	—
32	C₂×C₃	C₂³×C₉	1	1	yes	characteristic
33	C₂²	C₂²×C₂₇	1	3	yes	—
34	C₄	C₂²×C₂₇	1	1	yes	characteristic
35	C₄	C₂²×C₂₇	1	3	yes	—
36	C₃	C₉×#41	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂³×C₂₇	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.