Subgroups — C₄×#376 #13746

Order 256.

1151 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#376	C₂	1	4	yes	maximal
2	C₂×C₄³	C₂	1	3	yes	maximal
3	C₄×#95	C₂	1	8	yes	maximal
4	C₂²×C₄²	C₂²	1	12	yes	—
5	C₂²×C₄²	C₂²	1	6	yes	—
6	C₂²×C₄²	C₂²	1	1	yes	characteristic
7	#376	C₄	1	32	yes	direct product factor
8	C₂×#95	C₂²	1	16	yes	—
9	C₄³	C₄	1	24	yes	complemented
10	C₂³×C₄	C₂³	1	12	yes	—
11	C₂³×C₄	C₂³	1	1	yes	characteristic
12	C₂³×C₄	C₂³	1	2	yes	—
13	C₂×C₄²	—	2	48	no	—
14	C₂×C₄²	C₂×C₄	1	48	yes	—
15	C₂×C₄²	C₂×C₄	1	12	yes	—
16	C₂×C₄²	C₂×C₄	1	24	yes	—
17	C₂×C₄²	C₂×C₄	1	48	yes	—
18	#95	C₂×C₄	1	64	yes	—
19	C₂⁴	C₂⁴	1	1	yes	characteristic
20	C₂²×C₄	—	2	48	no	—
21	C₂²×C₄	C₂²×C₄	1	48	yes	—
22	C₂²×C₄	C₂²×C₄	1	24	yes	—
23	C₂²×C₄	C₂²×C₄	1	6	yes	—
24	C₂²×C₄	C₂²×C₄	1	8	yes	—
25	C₂²×C₄	C₂²×C₄	1	12	yes	—
26	C₂²×C₄	#41	1	16	yes	—
27	C₄²	—	2	96	no	—
28	C₄²	C₄²	1	16	yes	—
29	C₄²	C₄²	1	96	yes	complemented
30	C₂³	C₂³×C₄	1	3	yes	—
31	C₂³	C₂³×C₄	1	4	yes	—
32	C₂³	C₂×#41	1	8	yes	—
33	C₂×C₄	—	2	48	no	—
34	C₂×C₄	—	2	96	no	—
35	C₂×C₄	C₂×C₄²	1	48	yes	—
36	C₂×C₄	C₂×C₄²	1	4	yes	—
37	C₂×C₄	C₂×C₄²	1	24	yes	—
38	C₂×C₄	C₂×C₄²	1	8	yes	—
39	C₂×C₄	#117	1	48	yes	—
40	C₂²	C₂²×C₄²	1	1	yes	characteristic
41	C₂²	C₂²×C₄²	1	6	yes	—
42	C₂²	C₂×#117	1	12	yes	—
43	C₂²	C₄×#41	1	16	yes	—
44	C₄	—	2	48	no	—
45	C₄	C₄³	1	8	yes	—
46	C₄	#376	1	16	yes	direct product factor
47	C₂	C₂×C₄³	1	1	yes	characteristic
48	C₂	C₂×#376	1	2	yes	—
49	C₂	C₄×#117	1	12	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂²
commutator	C₂	C₂×C₄³
Frattini, socle, prime radical, cosocle	C₂⁴	C₂⁴
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂⁴ ▷ C₁

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

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