Subgroups — #12901

Order 256.

171 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#364	C₂	1	4	yes	maximal
2	#2150	C₂	1	2	yes	maximal
3	#1726	C₂	1	1	yes	maximal, characteristic
4	C₂×M₃₂	C₂²	1	4	yes	—
5	C₂×#97	C₄	1	2	yes	—
6	C₂×#97	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈	C₂²	1	2	yes	—
8	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
9	#376	C₄	1	1	yes	characteristic
10	#364	—	2	8	no	—
11	C₄⋊C₁₆	—	2	4	no	—
12	C₂²×C₈	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈	C₂×C₄	1	2	yes	—
14	C₂²×C₈	C₂³	1	1	yes	characteristic
15	C₂×C₄²	C₂×C₄	1	2	yes	—
16	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
17	M₃₂	—	2	8	no	—
18	C₂×C₁₆	—	2	4	no	—
19	#97	—	2	4	no	—
20	#97	C₈	1	4	yes	—
21	C₄×C₈	D₄	1	4	yes	—
22	C₄×C₈	D₄	1	2	yes	—
23	C₄×C₈	Q₈	1	4	yes	—
24	C₄×C₈	Q₈	1	2	yes	—
25	#95	—	2	2	no	—
26	C₂²×C₄	—	2	2	no	—
27	C₂²×C₄	M₁₆	1	2	yes	—
28	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈	—	2	2	no	—
30	C₂×C₈	C₄⋊C₄	1	2	yes	—
31	C₂×C₈	C₄⋊C₄	1	4	yes	—
32	C₂×C₈	C₂×C₈	1	4	yes	—
33	C₂×C₈	M₁₆	1	4	yes	—
34	C₂×C₈	C₂×D₄	1	2	yes	—
35	C₂×C₈	C₂×D₄	1	1	yes	characteristic
36	C₂×C₈	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₈	C₂×Q₈	1	2	yes	—
38	C₄²	—	2	2	no	—
39	C₄²	C₄⋊C₄	1	4	yes	—
40	C₄²	C₄⋊C₄	1	2	yes	—
41	C₄²	C₂×C₈	1	2	yes	—
42	C₁₆	—	4	4	no	—
43	C₂³	C₂×M₁₆	1	1	yes	characteristic
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	—	4	2	no	—
46	C₂×C₄	—	4	4	no	—
47	C₂×C₄	C₄⋊C₈	1	4	yes	—
48	C₂×C₄	C₂×C₄⋊C₄	1	2	yes	—
49	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
51	C₂×C₄	C₂×M₁₆	1	2	yes	—
52	C₈	—	2	2	no	—
53	C₈	C₄⋊C₈	1	8	yes	—
54	C₈	#127	1	1	yes	characteristic
55	C₈	C₄⋊Q₈	1	2	yes	—
56	C₈	C₄⋊Q₈	1	1	yes	characteristic
57	C₂²	—	2	2	no	—
58	C₂²	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₂²	#423	1	2	yes	—
60	C₄	—	2	4	no	—
61	C₄	—	4	4	no	—
62	C₄	#384	1	1	yes	characteristic
63	C₄	C₂×C₄⋊C₈	1	2	yes	—
64	C₄	#423	1	1	yes	characteristic
65	C₂	—	2	2	no	—
66	C₂	#1842	1	1	yes	characteristic
67	C₂	#2153	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₄
commutator	C₂×C₄	C₂²×C₈
Frattini, cosocle	C₂²×C₈	C₂³
socle	C₂²	C₂×C₄⋊C₈
prime radical	C₂³	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Maximal subgroups

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

subgroup	index
C₂×#364	2
#2150	2
#1726	2