Subgroups — C₄⋊C₄×D₂₇₁ #22576113

Order 8672.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₂₇₁	C₂	1	2	yes	maximal
2	C₂×C₄×D₂₇₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₂₇₁⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₄×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₂₇₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₂₇₁	C₂²	1	2	yes	—
8	C₂×Dic₂₇₁	C₂²	1	1	yes	characteristic
9	C₄×D₂₇₁	—	2	4	no	—
10	C₄×D₂₇₁	C₄	1	4	yes	complemented
11	C₂×C₄×C₂₇₁	C₂²	1	2	yes	—
12	C₂×C₄×C₂₇₁	C₂²	1	1	yes	characteristic
13	C₂²×C₂₇₁	C₂³	1	1	yes	characteristic
14	C₂×D₂₇₁	C₂×C₄	1	2	yes	—
15	C₂×D₂₇₁	D₄	1	2	yes	—
16	C₂×D₂₇₁	Q₈	1	2	yes	—
17	C₄×C₂₇₁	—	2	2	no	—
18	C₄×C₂₇₁	C₂×C₄	1	2	yes	complemented
19	Dic₂₇₁	—	2	2	no	—
20	Dic₂₇₁	C₂×C₄	1	2	yes	complemented
21	C₂×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₂₇₁	C₂×D₄	1	1	yes	characteristic
23	C₂×C₂₇₁	C₂×Q₈	1	1	yes	characteristic
24	D₂₇₁	C₄⋊C₄	1	4	yes	direct product factor
25	C₂₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄⋊C₄	—	271	1	no	maximal, Sylow
27	C₂²×C₄	—	271	1	no	—
28	C₂²×C₄	—	271	2	no	—
29	C₄⋊C₄	—	271	2	no	—
30	C₄⋊C₄	—	271	1	no	—
31	C₄⋊C₄	D₂₇₁	1	1	yes	characteristic, direct product factor
32	C₂³	—	271	1	no	—
33	C₂×C₄	—	271	1	no	—
34	C₂×C₄	—	271	4	no	—
35	C₂×C₄	—	271	2	no	—
36	C₂×C₄	—	542	4	no	—
37	C₂×C₄	C₂×D₂₇₁	1	2	yes	—
38	C₂×C₄	C₂×D₂₇₁	1	1	yes	characteristic
39	C₂²	—	271	2	no	—
40	C₂²	—	271	2	no	—
41	C₂²	—	271	2	no	—
42	C₂²	C₂²×D₂₇₁	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	271	2	no	—
45	C₄	—	542	2	no	—
46	C₄	C₄×D₂₇₁	1	2	yes	complemented
47	C₂	—	271	4	no	—
48	C₂	C₂×C₄×D₂₇₁	1	1	yes	characteristic
49	C₂	D₄×D₂₇₁	1	1	yes	characteristic
50	C₂	Q₈×D₂₇₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₂₇₁
commutator	C₂×C₂₇₁	C₂²×C₄
Fitting	C₄⋊C₄×C₂₇₁	C₂
socle	C₂²×C₂₇₁	C₂³
hypercenter	C₄⋊C₄	D₂₇₁
hypocenter	C₂₇₁	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₄⋊Dic₂₇₁	C₂	semidirect
4. Dic₂₇₁⋊C₄	C₂	semidirect
5. C₄⋊C₄×C₂₇₁	C₂	semidirect
10. C₄×D₂₇₁	C₄	semidirect
18. C₄×C₂₇₁	C₂×C₄	semidirect
20. Dic₂₇₁	C₂×C₄	semidirect
24. D₂₇₁	C₄⋊C₄	direct (N × H)
25. C₂₇₁	C₂×C₄⋊C₄	semidirect
31. C₄⋊C₄	D₂₇₁	direct (N × H)
46. C₄	C₄×D₂₇₁	semidirect

Subgroups — C4⋊C4×D271 #22576113

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊C₄×D₂₇₁ #22576113