Subgroups — #8134

Order 256.

207 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1744	C₂	1	2	yes	maximal
2	C₄×#97	C₂	1	1	yes	maximal, characteristic
3	#1273	C₂	1	4	yes	maximal
4	C₂×#97	C₄	1	4	yes	—
5	C₂×C₄×C₈	C₂²	1	2	yes	—
6	C₂×C₄×C₈	C₂²	1	4	yes	—
7	C₄³	C₂²	1	1	yes	characteristic
8	#336	C₄	1	8	yes	—
9	C₂²×C₈	C₂×C₄	1	8	yes	—
10	C₂²×C₈	C₂×C₄	1	4	yes	—
11	C₂×C₄²	C₂×C₄	1	4	yes	—
12	C₂×C₄²	C₂×C₄	1	2	yes	—
13	C₂×C₄²	C₂³	1	1	yes	characteristic
14	#97	—	2	8	no	—
15	C₄×C₈	—	2	4	no	—
16	C₄×C₈	—	2	8	no	—
17	C₂²×C₄	C₄²	1	4	yes	—
18	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₄	C₂²×C₄	1	2	yes	—
20	C₂×C₈	—	2	4	no	—
21	C₂×C₈	—	2	4	no	—
22	C₂×C₈	—	2	8	no	—
23	C₂×C₈	—	2	16	no	—
24	C₂×C₈	M₁₆	1	8	yes	—
25	C₄²	—	2	4	no	—
26	C₄²	—	2	8	no	—
27	C₄²	#41	1	4	yes	—
28	C₂³	C₂×C₄²	1	1	yes	characteristic
29	C₂×C₄	—	2	4	no	—
30	C₂×C₄	—	2	8	no	—
31	C₂×C₄	#117	1	2	yes	—
32	C₂×C₄	#117	1	4	yes	—
33	C₂×C₄	C₂×M₁₆	1	4	yes	—
34	C₂×C₄	#131	1	8	yes	—
35	C₈	—	2	8	no	—
36	C₈	—	4	8	no	—
37	C₂²	#376	1	1	yes	characteristic
38	C₂²	C₄×M₁₆	1	2	yes	—
39	C₂²	#405	1	4	yes	—
40	C₄	—	4	4	no	—
41	C₄	#432	1	4	yes	—
42	C₄	#433	1	8	yes	—
43	C₂	#1453	1	4	yes	—
44	C₂	#1745	1	1	yes	characteristic
45	C₂	#1746	1	2	yes	—

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄²	C₂³
commutator, socle, prime radical	C₂³	C₂×C₄²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

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