Subgroups — C₂×Dic₅₄ #88396

Order 432.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₇	C₂	1	2	yes	maximal
3	Dic₅₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₁₈	—	3	1	no	maximal
5	C₂²×C₂₇	C₂²	1	1	yes	characteristic
6	C₄×C₂₇	C₂²	1	2	yes	—
7	Dic₂₇	C₂²	1	4	yes	—
8	C₂×C₄×C₉	D₃	1	1	yes	characteristic
9	C₂×Dic₉	—	3	2	no	—
10	Dic₁₈	—	3	4	no	—
11	C₂×C₂₇	Q₈	1	2	yes	complemented
12	C₂×C₂₇	C₂³	1	1	yes	characteristic
13	C₂×Dic₆	—	9	1	no	—
14	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
15	C₄×C₉	C₂×D₃	1	2	yes	—
16	Dic₉	—	3	4	no	—
17	C₂₇	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₄	D₉	1	1	yes	characteristic
19	C₂×Dic₃	—	9	2	no	—
20	Dic₆	—	9	4	no	—
21	C₂×C₉	Dic₆	1	2	yes	—
22	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
23	C₂×Q₈	—	27	1	no	Sylow
24	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
25	C₃×C₄	C₂×D₉	1	2	yes	—
26	Dic₃	—	9	4	no	—
27	C₉	C₂×Dic₆	1	1	yes	characteristic
28	Q₈	—	27	4	no	—
29	C₂×C₄	—	27	2	no	—
30	C₂×C₄	D₂₇	1	1	yes	characteristic
31	C₂×C₃	Dic₁₈	1	2	yes	—
32	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
33	C₂²	C₂×D₂₇	1	1	yes	characteristic
34	C₄	—	27	4	no	—
35	C₄	C₂×D₂₇	1	2	yes	—
36	C₃	C₂×Dic₁₈	1	1	yes	characteristic
37	C₂	Dic₅₄	1	2	yes	direct product factor
38	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.