Subgroups — #8782

Order 256.

131 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1746	C₂	1	1	yes	maximal, characteristic
2	#1564	C₂	1	2	yes	maximal
3	#1281	C₂	1	2	yes	maximal
4	#1274	C₂	1	2	yes	maximal
5	#431	C₂²	1	4	yes	—
6	C₂×#97	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
8	#376	C₂²	1	1	yes	characteristic
9	#336	C₄	1	4	yes	—
10	#335	—	2	2	no	—
11	#334	—	2	2	no	—
12	C₂²×C₈	C₂×C₄	1	2	yes	—
13	C₂²×C₈	C₂×C₄	1	2	yes	—
14	C₂×C₄²	C₂×C₄	1	2	yes	—
15	C₂×C₄²	C₂³	1	1	yes	characteristic
16	C₄⋊C₈	—	2	4	no	—
17	C₂²⋊C₈	—	2	4	no	—
18	#97	—	2	2	no	—
19	C₄×C₈	—	2	4	no	—
20	C₄×C₈	D₄	1	1	yes	characteristic
21	C₄×C₈	D₄	1	1	yes	characteristic
22	C₄×C₈	Q₈	1	2	yes	—
23	#95	—	2	2	no	—
24	C₂²×C₄	—	2	2	no	—
25	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄	#41	1	2	yes	—
27	C₂×C₈	—	2	4	no	—
28	C₂×C₈	—	2	2	no	—
29	C₂×C₈	—	2	4	no	—
30	C₂×C₈	—	4	4	no	—
31	C₂×C₈	C₄⋊C₄	1	2	yes	—
32	C₂×C₈	C₄⋊C₄	1	2	yes	—
33	C₄²	—	2	4	no	—
34	C₄²	C₂×D₄	1	1	yes	characteristic
35	C₄²	C₂×Q₈	1	1	yes	characteristic
36	C₄²	#41	1	2	yes	—
37	C₂³	#117	1	1	yes	characteristic
38	C₂×C₄	—	4	2	no	—
39	C₂×C₄	—	4	4	no	—
40	C₂×C₄	—	4	2	no	—
41	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄	#117	1	1	yes	characteristic
43	C₂×C₄	#124	1	2	yes	—
44	C₂×C₄	#125	1	2	yes	—
45	C₂×C₄	#131	1	4	yes	—
46	C₈	—	2	2	no	—
47	C₈	—	2	2	no	—
48	C₈	—	4	2	no	—
49	C₈	—	8	4	no	—
50	C₂²	—	2	2	no	—
51	C₂²	#382	1	1	yes	characteristic
52	C₂²	#433	1	2	yes	—
53	C₄	—	2	2	no	—
54	C₄	—	2	2	no	—
55	C₄	—	8	2	no	—
56	C₄	#424	1	2	yes	—
57	C₄	#433	1	2	yes	—
58	C₂	—	2	2	no	—
59	C₂	#1832	1	1	yes	characteristic
60	C₂	#1833	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#117
commutator	C₂²×C₄	C₂²×C₄
Frattini, cosocle	C₂×C₄²	C₂³
socle	C₂²	#382
prime radical	C₂³	#117
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #376 ◁ 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
#1746	2
#1564	2
#1281	2
#1274	2