Subgroups — #8811

Order 256.

181 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1831	C₂	1	2	yes	maximal
2	#1744	C₂	1	1	yes	maximal, characteristic
3	C₂×#335	C₂	1	2	yes	maximal
4	C₂×#334	C₂	1	2	yes	maximal
5	C₂×C₄⋊C₈	C₂²	1	4	yes	—
6	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
8	C₄³	C₂²	1	1	yes	characteristic
9	#336	—	2	4	no	—
10	#336	C₄	1	4	yes	—
11	#335	—	2	4	no	—
12	#334	—	2	4	no	—
13	C₂²×C₈	—	2	4	no	—
14	C₂²×C₈	C₂×C₄	1	2	yes	—
15	C₂²×C₈	C₂×C₄	1	2	yes	—
16	C₂×C₄²	C₂×C₄	1	2	yes	—
17	C₂×C₄²	D₄	1	2	yes	—
18	C₂×C₄²	Q₈	1	2	yes	—
19	C₂×C₄²	C₂³	1	1	yes	characteristic
20	C₄⋊C₈	—	2	4	no	—
21	C₄⋊C₈	—	2	4	no	—
22	C₄×C₈	D₄	1	2	yes	—
23	C₄×C₈	D₄	1	2	yes	—
24	C₄×C₈	Q₈	1	2	yes	—
25	C₄×C₈	Q₈	1	2	yes	—
26	C₂²×C₄	C₄⋊C₄	1	4	yes	—
27	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₄	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₈	—	2	4	no	—
31	C₂×C₈	—	2	4	no	—
32	C₂×C₈	—	4	4	no	—
33	C₂×C₈	—	4	8	no	—
34	C₂×C₈	C₄⋊C₄	1	4	yes	—
35	C₂×C₈	C₄⋊C₄	1	4	yes	—
36	C₄²	—	2	4	no	—
37	C₄²	—	2	4	no	—
38	C₄²	—	4	2	no	—
39	C₄²	C₂×D₄	1	1	yes	characteristic
40	C₄²	C₂×D₄	1	1	yes	characteristic
41	C₄²	C₂×Q₈	1	1	yes	characteristic
42	C₄²	C₂×Q₈	1	1	yes	characteristic
43	C₂³	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄	—	2	2	no	—
45	C₂×C₄	—	2	4	no	—
46	C₂×C₄	—	2	4	no	—
47	C₂×C₄	—	2	4	no	—
48	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄	#127	1	1	yes	characteristic
51	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
52	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
53	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
54	C₂×C₄	#131	1	4	yes	—
55	C₂×C₄	#135	1	4	yes	—
56	C₈	—	2	4	no	—
57	C₈	—	2	4	no	—
58	C₈	—	8	4	no	—
59	C₂²	#384	1	1	yes	characteristic
60	C₂²	#424	1	2	yes	—
61	C₂²	#427	1	2	yes	—
62	C₂²	#430	1	2	yes	—
63	C₄	—	2	1	no	—
64	C₄	—	2	1	no	—
65	C₄	—	4	4	no	—
66	C₄	#424	1	2	yes	—
67	C₄	#424	1	2	yes	—
68	C₄	#495	1	2	yes	—
69	C₄	#499	1	2	yes	—
70	C₂	#1572	1	4	yes	—
71	C₂	#1843	1	1	yes	characteristic
72	C₂	#1846	1	1	yes	characteristic
73	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
#1831	2
#1744	2
C₂×#335	2
C₂×#334	2