Subgroups — #8809

Order 256.

201 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1842	C₂	1	2	yes	maximal
2	#1744	C₂	1	1	yes	maximal, characteristic
3	C₂×#334	C₂	1	4	yes	maximal
4	C₂×C₄⋊C₈	—	2	4	no	—
5	C₂×C₄⋊C₈	C₂²	1	4	yes	—
6	C₂×C₄×C₈	C₂²	1	2	yes	—
7	C₄³	C₂²	1	1	yes	characteristic
8	#336	C₄	1	4	yes	—
9	#334	—	2	8	no	—
10	C₂²×C₈	—	2	4	no	—
11	C₂²×C₈	C₂×C₄	1	4	yes	—
12	C₂×C₄²	C₂×C₄	1	2	yes	—
13	C₂×C₄²	D₄	1	2	yes	—
14	C₂×C₄²	Q₈	1	2	yes	—
15	C₂×C₄²	C₂³	1	1	yes	characteristic
16	C₄⋊C₈	—	2	8	no	—
17	C₄⋊C₈	—	4	8	no	—
18	C₄×C₈	D₄	1	4	yes	—
19	C₄×C₈	Q₈	1	4	yes	—
20	C₂²×C₄	C₄⋊C₄	1	4	yes	—
21	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
23	C₂²×C₄	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₈	—	2	8	no	—
25	C₂×C₈	—	4	4	no	—
26	C₂×C₈	—	4	8	no	—
27	C₂×C₈	C₄⋊C₄	1	8	yes	—
28	C₄²	—	2	4	no	—
29	C₄²	—	4	2	no	—
30	C₄²	SD₁₆	1	8	yes	—
31	C₄²	C₂×D₄	1	2	yes	—
32	C₄²	C₂×Q₈	1	2	yes	—
33	C₂³	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄	—	2	4	no	—
35	C₂×C₄	—	2	4	no	—
36	C₂×C₄	—	2	2	no	—
37	C₂×C₄	#106	1	8	yes	—
38	C₂×C₄	C₂×C₄⋊C₄	1	2	yes	—
39	C₂×C₄	#127	1	1	yes	characteristic
40	C₂×C₄	C₄⋊Q₈	1	2	yes	—
41	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
42	C₂×C₄	#131	1	4	yes	—
43	C₂×C₄	C₂×SD₁₆	1	4	yes	—
44	C₈	—	2	8	no	—
45	C₈	—	8	4	no	—
46	C₂²	#384	1	1	yes	characteristic
47	C₂²	#424	1	2	yes	—
48	C₂²	C₂×#106	1	2	yes	—
49	C₂²	#430	1	2	yes	—
50	C₄	—	2	8	no	—
51	C₄	—	2	2	no	—
52	C₄	#424	1	4	yes	—
53	C₄	#492	1	2	yes	—
54	C₄	#498	1	2	yes	—
55	C₂	#1570	1	4	yes	—
56	C₂	#1843	1	1	yes	characteristic
57	C₂	#1844	1	1	yes	characteristic
58	C₂	#1849	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄
Frattini, cosocle	C₂×C₄²	C₂³
socle, prime radical	C₂³	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Maximal subgroups

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

subgroup	index
#1842	2
#1744	2
C₂×#334	2