Subgroups — C₂²×C₄×C₂₇ #88406

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×C₄×C₂₇	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₉	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₂₇	C₄	1	4	yes	direct product factor
5	C₂²×C₂₇	C₂²	1	3	yes	—
6	C₄×C₂₇	C₂²	1	4	yes	direct product factor
7	C₂³×C₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₄×C₉	C₂×C₃	1	6	yes	—
9	C₂×C₂₇	C₂×C₄	1	6	yes	direct product factor
10	C₂×C₂₇	C₂³	1	1	yes	characteristic
11	C₂²×C₃×C₄	C₉	1	1	yes	characteristic
12	C₂²×C₉	C₃×C₄	1	4	yes	—
13	C₂²×C₉	C₂²×C₃	1	3	yes	—
14	C₄×C₉	C₂²×C₃	1	4	yes	—
15	C₂₇	C₂²×C₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂³×C₃	C₂×C₉	1	1	yes	characteristic
17	C₂×C₃×C₄	C₂×C₉	1	6	yes	—
18	C₂×C₉	C₂×C₃×C₄	1	6	yes	—
19	C₂×C₉	C₂³×C₃	1	1	yes	characteristic
20	C₂²×C₄	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₃	C₄×C₉	1	4	yes	—
22	C₂²×C₃	C₂²×C₉	1	3	yes	—
23	C₃×C₄	C₂²×C₉	1	4	yes	—
24	C₉	C₂²×C₃×C₄	1	1	yes	characteristic
25	C₂³	C₂×C₂₇	1	1	yes	characteristic
26	C₂×C₄	C₂×C₂₇	1	6	yes	direct product factor
27	C₂×C₃	C₂×C₄×C₉	1	6	yes	—
28	C₂×C₃	C₂³×C₉	1	1	yes	characteristic
29	C₂²	C₄×C₂₇	1	4	yes	direct product factor
30	C₂²	C₂²×C₂₇	1	3	yes	—
31	C₄	C₂²×C₂₇	1	4	yes	direct product factor
32	C₃	C₂²×C₄×C₉	1	1	yes	characteristic
33	C₂	C₂×C₄×C₂₇	1	6	yes	direct product factor
34	C₂	C₂³×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂³×C₃
socle, prime radical	C₂³×C₃	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄×C₂₇	C₂	direct (N × H)
4. C₂²×C₂₇	C₄	direct (N × H)
6. C₄×C₂₇	C₂²	direct (N × H)
9. C₂×C₂₇	C₂×C₄	direct (N × H)
15. C₂₇	C₂²×C₄	direct (N × H)
20. C₂²×C₄	C₂₇	direct (N × H)
26. C₂×C₄	C₂×C₂₇	direct (N × H)
29. C₂²	C₄×C₂₇	direct (N × H)
31. C₄	C₂²×C₂₇	direct (N × H)
33. C₂	C₂×C₄×C₂₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₂₇	2
C₂×C₄×C₂₇	2
C₂²×C₄×C₉	3

Subgroups — C22×C4×C27 #88406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₂₇ #88406