Subgroups — C₂²×Dic₂₇ #88404

Order 432.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₇	C₂	1	6	yes	maximal, direct product factor
3	C₂²×Dic₉	—	3	1	no	maximal
4	C₂²×C₂₇	C₄	1	4	yes	complemented
5	C₂²×C₂₇	C₂²	1	3	yes	—
6	Dic₂₇	C₂²	1	4	yes	direct product factor
7	C₂³×C₉	D₃	1	1	yes	characteristic
8	C₂×Dic₉	—	3	6	no	—
9	C₂×C₂₇	C₂×C₄	1	6	yes	complemented
10	C₂×C₂₇	C₂³	1	1	yes	characteristic
11	C₂²×Dic₃	—	9	1	no	—
12	C₂²×C₉	Dic₃	1	4	yes	—
13	C₂²×C₉	C₂×D₃	1	3	yes	—
14	Dic₉	—	3	4	no	—
15	C₂₇	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂³×C₃	D₉	1	1	yes	characteristic
17	C₂×Dic₃	—	9	6	no	—
18	C₂×C₉	C₂×Dic₃	1	6	yes	—
19	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
20	C₂²×C₄	—	27	1	no	Sylow
21	C₂²×C₃	Dic₉	1	4	yes	—
22	C₂²×C₃	C₂×D₉	1	3	yes	—
23	Dic₃	—	9	4	no	—
24	C₉	C₂²×Dic₃	1	1	yes	characteristic
25	C₂³	D₂₇	1	1	yes	characteristic
26	C₂×C₄	—	27	6	no	—
27	C₂×C₃	C₂×Dic₉	1	6	yes	—
28	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
29	C₂²	Dic₂₇	1	4	yes	direct product factor
30	C₂²	C₂×D₂₇	1	3	yes	—
31	C₄	—	27	4	no	—
32	C₃	C₂²×Dic₉	1	1	yes	characteristic
33	C₂	C₂×Dic₂₇	1	6	yes	direct product factor
34	C₂	C₂²×D₂₇	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.