Subgroups — C₄×C₂²⋊C₂₇ #88393

Order 432.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂²⋊C₂₇	C₄	1	1	yes	characteristic, direct product factor
4	C₄×C₂₇	—	4	1	no	maximal
5	C₂³×C₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₄×C₉	—	3	1	no	—
7	C₂×C₄×C₉	—	3	1	no	—
8	C₂×C₂₇	—	4	1	no	—
9	C₂²×C₃×C₄	C₉	1	1	yes	characteristic
10	C₂²×C₉	—	3	1	no	—
11	C₂²×C₉	—	3	1	no	—
12	C₂²×C₉	C₃×C₄	1	1	yes	characteristic
13	C₄×C₉	—	3	1	no	—
14	C₄×C₉	A₄	1	1	yes	characteristic
15	C₂₇	—	4	1	no	Sylow
16	C₂³×C₃	C₂×C₉	1	1	yes	characteristic
17	C₂×C₃×C₄	—	3	1	no	—
18	C₂×C₃×C₄	—	3	1	no	—
19	C₂×C₉	—	3	1	no	—
20	C₂×C₉	—	3	1	no	—
21	C₂×C₉	C₂×A₄	1	1	yes	characteristic
22	C₂²×C₄	C₂₇	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₃	—	3	1	no	—
24	C₂²×C₃	—	3	1	no	—
25	C₂²×C₃	C₄×C₉	1	1	yes	characteristic
26	C₃×C₄	—	3	1	no	—
27	C₃×C₄	C₂²⋊C₉	1	1	yes	characteristic
28	C₉	C₄×A₄	1	1	yes	characteristic
29	C₂³	C₂×C₂₇	1	1	yes	characteristic
30	C₂×C₄	—	3	1	no	—
31	C₂×C₄	—	3	1	no	—
32	C₂×C₃	—	3	1	no	—
33	C₂×C₃	—	3	1	no	—
34	C₂×C₃	C₂×C₂²⋊C₉	1	1	yes	characteristic
35	C₂²	—	3	1	no	—
36	C₂²	—	3	1	no	—
37	C₂²	C₄×C₂₇	1	1	yes	characteristic, complemented
38	C₄	—	3	1	no	—
39	C₄	C₂²⋊C₂₇	1	1	yes	characteristic, direct product factor
40	C₃	C₄×C₂²⋊C₉	1	1	yes	characteristic
41	C₂	—	3	1	no	—
42	C₂	—	3	1	no	—
43	C₂	C₂×C₂²⋊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.