Subgroups — #7095

Order 256.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1707	C₂	1	1	yes	maximal, characteristic
2	#1370	C₂	1	1	yes	maximal, characteristic
3	#1367	C₂	1	1	yes	maximal, characteristic
4	#500	C₄	1	1	yes	characteristic
5	#498	—	2	1	no	—
6	#494	C₄	1	1	yes	characteristic
7	#487	—	2	1	no	—
8	C₄⋊C₁₆	—	2	1	no	—
9	C₄⋊C₁₆	—	2	1	no	—
10	C₈²	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆	—	4	1	no	—
12	C₄⋊Q₈	—	2	1	no	—
13	C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₆	—	4	1	no	—
15	C₂×C₁₆	—	4	1	no	—
16	#107	—	4	1	no	—
17	#106	—	4	1	no	—
18	#106	—	4	1	no	—
19	#103	—	4	1	no	—
20	#103	—	4	1	no	—
21	C₄×C₈	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈	D₄	1	1	yes	characteristic
23	C₄×C₈	D₄	1	1	yes	characteristic
24	C₂×Q₈	—	4	1	no	—
25	C₂×Q₈	—	4	1	no	—
26	Q₁₆	—	8	2	no	—
27	C₂×C₈	—	2	1	no	—
28	C₂×C₈	D₈	1	1	yes	characteristic
29	C₂×C₈	D₈	1	1	yes	characteristic
30	C₂×C₈	SD₁₆	1	1	yes	characteristic
31	C₂×C₈	SD₁₆	1	1	yes	characteristic
32	C₄⋊C₄	—	4	1	no	—
33	C₄⋊C₄	—	4	1	no	—
34	C₄⋊C₄	—	4	1	no	—
35	C₄⋊C₄	—	4	1	no	—
36	C₄²	C₂²⋊C₄	1	1	yes	characteristic
37	C₁₆	—	8	1	no	—
38	C₁₆	—	8	1	no	—
39	Q₈	—	8	2	no	—
40	Q₈	—	8	1	no	—
41	Q₈	—	8	1	no	—
42	C₂×C₄	—	8	1	no	—
43	C₂×C₄	—	8	1	no	—
44	C₂×C₄	#100	1	1	yes	characteristic
45	C₂×C₄	#102	1	1	yes	characteristic
46	C₂×C₄	#102	1	1	yes	characteristic
47	C₈	—	2	2	no	—
48	C₈	—	2	1	no	—
49	C₈	—	2	1	no	—
50	C₈	—	2	1	no	—
51	C₈	SD₃₂	1	1	yes	characteristic
52	C₈	Q₃₂	1	1	yes	characteristic
53	C₂²	#331	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	16	1	no	—
56	C₄	—	16	1	no	—
57	C₄	#358	1	1	yes	characteristic
58	C₄	#359	1	1	yes	characteristic
59	C₄	#360	1	1	yes	characteristic
60	C₄	#362	1	1	yes	characteristic
61	C₂	#1359	1	1	yes	characteristic
62	C₂	#1360	1	1	yes	characteristic
63	C₂	#1362	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²	#331
commutator	C₄×C₈	C₂×C₄
Frattini, cosocle	C₈²	C₂²
LCS	G ▷ C₄×C₈ ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ G
LECS	G ▷ C₈² ▷ C₄² ▷ C₂² ▷ C₁

Maximal subgroups

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

subgroup	index
#1707	2
#1370	2
#1367	2