Subgroups — C₄⋊C₄×C₂₇ #88375

Order 432.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₇	C₂	1	2	yes	maximal
2	C₂×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic
3	C₉×C₄⋊C₄	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₂₇	C₂²	1	1	yes	characteristic
5	C₄×C₂₇	—	2	2	no	—
6	C₄×C₂₇	C₄	1	2	yes	complemented
7	C₂×C₄×C₉	C₂×C₃	1	2	yes	—
8	C₂×C₄×C₉	C₂×C₃	1	1	yes	characteristic
9	C₂×C₂₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₂₇	D₄	1	1	yes	characteristic
11	C₂×C₂₇	Q₈	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₉	1	1	yes	characteristic
13	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
14	C₄×C₉	—	2	2	no	—
15	C₄×C₉	C₃×C₄	1	2	yes	—
16	C₂₇	C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃×C₄	C₂×C₉	1	2	yes	—
18	C₂×C₃×C₄	C₂×C₉	1	1	yes	characteristic
19	C₂×C₉	C₂×C₃×C₄	1	1	yes	characteristic
20	C₂×C₉	C₃×D₄	1	1	yes	characteristic
21	C₂×C₉	C₃×Q₈	1	1	yes	characteristic
22	C₄⋊C₄	C₂₇	1	1	yes	characteristic, direct product factor, Sylow
23	C₂²×C₃	C₂²×C₉	1	1	yes	characteristic
24	C₃×C₄	—	2	2	no	—
25	C₃×C₄	C₄×C₉	1	2	yes	—
26	C₉	C₃×C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄	C₂×C₂₇	1	2	yes	—
28	C₂×C₄	C₂×C₂₇	1	1	yes	characteristic
29	C₂×C₃	C₂×C₄×C₉	1	1	yes	characteristic
30	C₂×C₃	D₄×C₉	1	1	yes	characteristic
31	C₂×C₃	Q₈×C₉	1	1	yes	characteristic
32	C₂²	C₂²×C₂₇	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	C₄×C₂₇	1	2	yes	complemented
35	C₃	C₉×C₄⋊C₄	1	1	yes	characteristic
36	C₂	C₂×C₄×C₂₇	1	1	yes	characteristic
37	C₂	D₄×C₂₇	1	1	yes	characteristic
38	C₂	Q₈×C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₂₇	C₂²
commutator	C₂	C₂×C₄×C₂₇
Frattini, cosocle	C₂²×C₉	C₂²×C₃
socle, prime radical	C₂²×C₃	C₂²×C₉
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄×C₂₇	C₄	semidirect
16. C₂₇	C₄⋊C₄	direct (N × H)
22. C₄⋊C₄	C₂₇	direct (N × H)
34. C₄	C₄×C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₂₇	2
C₉×C₄⋊C₄	3

Subgroups — C4⋊C4×C27 #88375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×C₂₇ #88375