Subgroups — #7097

Order 256.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1713	C₂	1	1	yes	maximal, characteristic
2	#1370	C₂	1	1	yes	maximal, characteristic
3	#1370	C₂	1	1	yes	maximal, characteristic
4	#500	—	2	1	no	—
5	#500	C₄	1	2	yes	—
6	#494	—	2	1	no	—
7	C₄⋊C₁₆	—	2	1	no	—
8	C₄⋊C₁₆	—	2	1	no	—
9	C₈²	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆	—	4	1	no	—
11	C₂×Q₁₆	—	4	1	no	—
12	C₄⋊Q₈	—	2	2	no	—
13	C₂×C₁₆	—	4	1	no	—
14	C₂×C₁₆	—	4	1	no	—
15	#107	—	4	1	no	—
16	#107	—	4	1	no	—
17	#107	—	4	2	no	—
18	C₄×C₈	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈	D₄	1	1	yes	characteristic
20	C₄×C₈	D₄	1	1	yes	characteristic
21	C₂×Q₈	—	4	2	no	—
22	Q₁₆	—	8	2	no	—
23	Q₁₆	—	8	1	no	—
24	Q₁₆	—	8	1	no	—
25	C₂×C₈	—	2	1	no	—
26	C₂×C₈	D₈	1	1	yes	characteristic
27	C₂×C₈	D₈	1	1	yes	characteristic
28	C₂×C₈	SD₁₆	1	1	yes	characteristic
29	C₂×C₈	SD₁₆	1	1	yes	characteristic
30	C₄⋊C₄	—	4	2	no	—
31	C₄⋊C₄	—	4	2	no	—
32	C₄²	C₂²⋊C₄	1	1	yes	characteristic
33	C₁₆	—	8	1	no	—
34	C₁₆	—	8	1	no	—
35	Q₈	—	8	2	no	—
36	Q₈	—	8	2	no	—
37	C₂×C₄	—	8	2	no	—
38	C₂×C₄	#100	1	1	yes	characteristic
39	C₂×C₄	#102	1	1	yes	characteristic
40	C₂×C₄	#102	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	—	2	1	no	—
43	C₈	—	2	1	no	—
44	C₈	D₁₆	1	1	yes	characteristic
45	C₈	SD₃₂	1	1	yes	characteristic
46	C₈	SD₃₂	1	1	yes	characteristic
47	C₈	Q₃₂	1	1	yes	characteristic
48	C₂²	#331	1	1	yes	characteristic
49	C₄	—	2	1	no	—
50	C₄	—	16	2	no	—
51	C₄	#357	1	1	yes	characteristic
52	C₄	#358	1	1	yes	characteristic
53	C₄	#361	1	1	yes	characteristic
54	C₄	#362	1	1	yes	characteristic
55	C₂	#1358	1	1	yes	characteristic
56	C₂	#1361	1	1	yes	characteristic
57	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
#1713	2
#1370	2