Subgroups — C₄×#401 #13866

Order 256.

611 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#401	C₂	1	1	yes	maximal, characteristic
2	#1443	C₂	1	7	yes	maximal
3	C₄×#95	C₂	1	7	yes	maximal
4	C₂²×C₄²	C₂²	1	7	yes	—
5	#401	C₄	1	8	yes	direct product factor
6	C₂×#95	C₂²	1	21	yes	—
7	C₂×#95	C₂²	1	7	yes	—
8	C₂³×C₄	C₂³	1	7	yes	—
9	C₂³×C₄	C₂³	1	7	yes	—
10	C₂³×C₄	C₂³	1	1	yes	characteristic
11	C₂×C₄²	—	2	42	no	—
12	#95	—	2	42	no	—
13	#95	C₂×C₄	1	28	yes	—
14	C₂⁴	C₂⁴	1	1	yes	characteristic
15	C₂²×C₄	—	2	21	no	—
16	C₂²×C₄	—	2	21	no	—
17	C₂²×C₄	—	2	21	no	—
18	C₂²×C₄	—	2	21	no	—
19	C₂²×C₄	C₂²×C₄	1	14	yes	—
20	C₂²×C₄	#41	1	14	yes	—
21	C₂²×C₄	#41	1	14	yes	—
22	C₄²	—	4	28	no	—
23	C₂³	C₂³×C₄	1	1	yes	characteristic
24	C₂³	C₂×#41	1	7	yes	—
25	C₂³	C₂×#41	1	7	yes	—
26	C₂×C₄	—	2	42	no	—
27	C₂×C₄	—	2	42	no	—
28	C₂×C₄	—	4	7	no	—
29	C₂×C₄	—	4	7	no	—
30	C₂×C₄	—	4	21	no	—
31	C₂×C₄	—	4	21	no	—
32	C₂×C₄	#126	1	28	yes	—
33	C₂²	C₄×#41	1	7	yes	—
34	C₂²	C₂×#126	1	7	yes	—
35	C₂²	#529	1	21	yes	—
36	C₄	—	4	14	no	—
37	C₄	—	4	14	no	—
38	C₄	#401	1	8	yes	direct product factor
39	C₂	C₄×#126	1	7	yes	—
40	C₂	C₂×#401	1	1	yes	characteristic
41	C₂	#2401	1	7	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂³
commutator	C₂³	C₂³×C₄
Frattini, socle, prime radical, cosocle	C₂⁴	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄ ◁ G
LECS	G ▷ C₂⁴ ▷ C₁

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

N	H ≅ G/N	type
5. #401	C₄	direct (N × H)
38. C₄	#401	direct (N × H)

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