Subgroups — C₄₂₁⋊#564 #41003595

Order 26944.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27212358	C₂	1	2	yes	maximal
2	#27212357	C₂	1	4	yes	maximal
3	#27212356	C₂	1	4	yes	maximal
4	#27212356	C₂	1	4	yes	maximal
5	#125×C₄₂₁	C₂	1	1	yes	maximal, characteristic
6	C₄⋊Dic₄₂₁	C₂²	1	2	yes	—
7	C₄⋊Dic₄₂₁	C₂²	1	4	yes	—
8	C₄⋊Dic₄₂₁	C₂²	1	2	yes	—
9	#20269750	C₂²	1	4	yes	—
10	#20269750	C₂²	1	4	yes	—
11	#20269750	C₂²	1	4	yes	—
12	#20269750	C₂²	1	4	yes	—
13	C₄×Dic₄₂₁	C₂²	1	4	yes	—
14	C₄⋊C₄×C₄₂₁	C₂²	1	2	yes	—
15	C₄⋊C₄×C₄₂₁	C₂²	1	4	yes	—
16	C₄²×C₄₂₁	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₂₁	C₂³	1	4	yes	—
18	C₂×Dic₄₂₁	C₂³	1	4	yes	—
19	C₂×C₄×C₄₂₁	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₄₂₁	C₂³	1	2	yes	—
21	C₂×C₄×C₄₂₁	C₂³	1	4	yes	—
22	C₂²×C₄₂₁	C₂⁴	1	1	yes	characteristic
23	C₄×C₄₂₁	—	2	2	no	—
24	C₄×C₄₂₁	—	2	4	no	—
25	C₄×C₄₂₁	—	2	1	no	—
26	Dic₄₂₁	—	2	4	no	—
27	Dic₄₂₁	—	2	4	no	—
28	C₂×C₄₂₁	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₄₂₁	2₋¹⁺⁴	1	1	yes	characteristic
30	C₄₂₁	#564	1	1	yes	characteristic, complemented, Sylow
31	#564	—	421	1	no	maximal, Sylow
32	#125	—	421	4	no	—
33	#125	—	421	4	no	—
34	#125	—	421	4	no	—
35	#125	—	421	2	no	—
36	#125	D₄₂₁	1	1	yes	characteristic
37	C₄⋊C₄	—	421	4	no	—
38	C₄⋊C₄	—	421	4	no	—
39	C₄⋊C₄	—	421	4	no	—
40	C₄⋊C₄	—	421	4	no	—
41	C₄⋊C₄	—	421	4	no	—
42	C₄⋊C₄	—	421	2	no	—
43	C₄⋊C₄	—	421	2	no	—
44	C₄⋊C₄	C₂×D₄₂₁	1	2	yes	—
45	C₄⋊C₄	C₂×D₄₂₁	1	4	yes	—
46	C₄²	—	421	4	no	—
47	C₄²	C₂×D₄₂₁	1	1	yes	characteristic
48	C₂×C₄	—	421	4	no	—
49	C₂×C₄	—	421	4	no	—
50	C₂×C₄	C₂²×D₄₂₁	1	4	yes	—
51	C₂×C₄	C₂²×D₄₂₁	1	2	yes	—
52	C₂×C₄	C₂²×D₄₂₁	1	1	yes	characteristic
53	C₂²	C₂³×D₄₂₁	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	842	4	no	—
58	C₄	—	842	4	no	—
59	C₂	#27212413	1	2	yes	—
60	C₂	#27212414	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₂₁
commutator, socle, prime radical, cosocle	C₂²×C₄₂₁	C₂⁴
Fitting	#125×C₄₂₁	C₂
hypercenter	#125	D₄₂₁
hypocenter	C₄₂₁	#564
LCS	G ▷ C₂²×C₄₂₁ ▷ C₄₂₁
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
30. C₄₂₁	#564	semidirect

Maximal subgroups

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

subgroup	index
#27212358	2
#27212357	2
#27212356	2
#125×C₄₂₁	2
#564	421

Subgroups — C421⋊#564 #41003595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₂₁⋊#564 #41003595