Subgroups — C₂₇×C₄₃⋊C₂₇ #44531883

Order 31347.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₄₃⋊C₂₇	C₃	1	3	yes	maximal
2	C₉×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₃⋊C₂₇	C₉	1	9	yes	—
4	C₃×C₂₇×C₄₃	C₉	1	3	yes	—
5	C₉²×C₄₃	C₃²	1	1	yes	characteristic
6	C₄₃⋊C₂₇	C₂₇	1	27	yes	direct product factor
7	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
8	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
9	C₂₇×C₄₃	C₂₇	1	9	yes	complemented
10	C₂₇²	—	43	1	no	maximal, Sylow
11	C₃²×C₄₃	C₉²	1	1	yes	characteristic
12	C₉×C₄₃	C₃×C₂₇	1	9	yes	—
13	C₉×C₄₃	C₃×C₂₇	1	3	yes	—
14	C₉×C₂₇	—	43	3	no	—
15	C₉×C₂₇	C₄₃⋊C₃	1	1	yes	characteristic
16	C₃×C₄₃	C₉×C₂₇	1	3	yes	—
17	C₃×C₄₃	C₉×C₂₇	1	1	yes	characteristic
18	C₃×C₂₇	—	43	9	no	—
19	C₃×C₂₇	C₄₃⋊C₉	1	3	yes	—
20	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
21	C₄₃	C₂₇²	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
23	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
24	C₂₇	—	43	27	no	—
25	C₂₇	C₄₃⋊C₂₇	1	9	yes	direct product factor
26	C₃²	C₉×C₄₃⋊C₉	1	1	yes	characteristic
27	C₉	C₂₇×C₄₃⋊C₃	1	9	yes	—
28	C₉	C₃×C₄₃⋊C₂₇	1	3	yes	—
29	C₃	C₂₇×C₄₃⋊C₉	1	3	yes	—
30	C₃	C₉×C₄₃⋊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.