Subgroups — SD₁₆×C₂₇ #88379

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	D₄×C₂₇	C₂	1	1	yes	maximal, characteristic
3	C₈×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×SD₁₆	C₃	1	1	yes	maximal, characteristic
5	C₂²×C₂₇	—	2	1	no	—
6	C₄×C₂₇	—	2	1	no	—
7	C₄×C₂₇	C₂²	1	1	yes	characteristic
8	Q₈×C₉	C₂×C₃	1	1	yes	characteristic
9	D₄×C₉	C₂×C₃	1	1	yes	characteristic
10	C₈×C₉	C₂×C₃	1	1	yes	characteristic
11	C₂×C₂₇	—	4	1	no	—
12	C₂×C₂₇	D₄	1	1	yes	characteristic
13	C₃×SD₁₆	C₉	1	1	yes	characteristic
14	C₂²×C₉	—	2	1	no	—
15	C₄×C₉	—	2	1	no	—
16	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
17	C₂₇	SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×Q₈	C₂×C₉	1	1	yes	characteristic
19	C₃×D₄	C₂×C₉	1	1	yes	characteristic
20	C₃×C₈	C₂×C₉	1	1	yes	characteristic
21	C₂×C₉	—	4	1	no	—
22	C₂×C₉	C₃×D₄	1	1	yes	characteristic
23	SD₁₆	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃	—	2	1	no	—
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	C₂²×C₉	1	1	yes	characteristic
27	C₉	C₃×SD₁₆	1	1	yes	characteristic
28	Q₈	C₂×C₂₇	1	1	yes	characteristic, complemented
29	D₄	C₂×C₂₇	1	1	yes	characteristic
30	C₈	C₂×C₂₇	1	1	yes	characteristic, complemented
31	C₂×C₃	—	4	1	no	—
32	C₂×C₃	D₄×C₉	1	1	yes	characteristic
33	C₂²	—	2	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂²×C₂₇	1	1	yes	characteristic
36	C₃	C₉×SD₁₆	1	1	yes	characteristic
37	C₂	—	4	1	no	—
38	C₂	D₄×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.