Subgroups — #88372

Order 432.

68 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	2	yes	maximal, complemented
3	#3676	—	3	1	no	maximal
4	C₂²×C₂₇	—	2	2	no	—
5	C₂²×C₂₇	C₄	1	2	yes	complemented
6	C₂²×C₂₇	C₂²	1	1	yes	characteristic
7	Dic₂₇	—	2	2	no	—
8	C₂³×C₉	D₃	1	1	yes	characteristic
9	C₂×Dic₉	—	3	2	no	—
10	C₂×C₂₇	—	2	2	no	—
11	C₂×C₂₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₂₇	D₄	1	2	yes	—
13	#217	—	9	1	no	—
14	C₂²×C₉	—	2	2	no	—
15	C₂²×C₉	Dic₃	1	2	yes	—
16	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
17	Dic₉	—	6	2	no	—
18	C₂₇	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₃	D₉	1	1	yes	characteristic
20	C₂×Dic₃	—	9	2	no	—
21	C₂×C₉	—	2	2	no	—
22	C₂×C₉	C₂×Dic₃	1	1	yes	characteristic
23	C₂×C₉	#67	1	2	yes	—
24	C₂²⋊C₄	—	27	1	no	Sylow
25	C₂²×C₃	—	2	2	no	—
26	C₂²×C₃	Dic₉	1	2	yes	—
27	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
28	Dic₃	—	18	2	no	—
29	C₉	#217	1	1	yes	characteristic
30	C₂³	D₂₇	1	1	yes	characteristic
31	C₂×C₄	—	27	2	no	—
32	C₂×C₃	—	2	2	no	—
33	C₂×C₃	C₂×Dic₉	1	1	yes	characteristic
34	C₂×C₃	#611	1	2	yes	—
35	C₂²	—	2	2	no	—
36	C₂²	Dic₂₇	1	2	yes	complemented
37	C₂²	C₂×D₂₇	1	1	yes	characteristic
38	C₄	—	54	2	no	—
39	C₃	#3676	1	1	yes	characteristic
40	C₂	—	2	2	no	—
41	C₂	C₂×Dic₂₇	1	1	yes	characteristic
42	C₂	#6171	1	2	yes	—

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.