Subgroups — #12894

Order 256.

171 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₈	C₂	1	1	yes	maximal, characteristic
2	#1374	C₂	1	6	yes	maximal
3	C₂²×C₁₆	C₂²	1	4	yes	—
4	C₂×C₄×C₈	C₄	1	3	yes	—
5	C₂×C₄×C₈	C₂²	1	3	yes	—
6	C₄³	C₄	1	1	yes	characteristic
7	C₂²×C₈	C₂×C₄	1	3	yes	—
8	C₂²×C₈	C₂³	1	1	yes	characteristic
9	C₂×C₄²	C₈	1	3	yes	—
10	C₂×C₄²	C₈	1	1	yes	characteristic
11	C₂×C₄²	C₂×C₄	1	3	yes	—
12	C₂×C₁₆	—	2	12	no	—
13	C₄×C₈	—	2	6	no	—
14	C₄×C₈	—	2	6	no	—
15	C₂²×C₄	C₂×C₈	1	3	yes	—
16	C₂²×C₄	C₂×C₈	1	3	yes	—
17	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₈	—	2	3	no	—
19	C₂×C₈	—	2	3	no	—
20	C₂×C₈	M₁₆	1	6	yes	—
21	C₂×C₈	#41	1	6	yes	—
22	C₄²	—	2	6	no	—
23	C₄²	—	2	3	no	—
24	C₄²	—	2	3	no	—
25	C₄²	C₁₆	1	4	yes	complemented
26	C₁₆	—	4	4	no	—
27	C₂³	C₂²×C₈	1	1	yes	characteristic
28	C₂×C₄	—	2	3	no	—
29	C₂×C₄	—	2	3	no	—
30	C₂×C₄	—	2	3	no	—
31	C₂×C₄	—	2	3	no	—
32	C₂×C₄	C₂×C₁₆	1	6	yes	—
33	C₂×C₄	M₃₂	1	6	yes	—
34	C₂×C₄	#117	1	3	yes	—
35	C₂×C₄	C₂×M₁₆	1	3	yes	—
36	C₈	—	2	6	no	—
37	C₈	#126	1	4	yes	—
38	C₂²	#431	1	3	yes	—
39	C₂²	C₂²×C₁₆	1	1	yes	characteristic
40	C₂²	C₂×M₃₂	1	3	yes	—
41	C₄	—	2	6	no	—
42	C₄	—	2	6	no	—
43	C₄	#383	1	1	yes	characteristic
44	C₄	#432	1	3	yes	—
45	C₂	#1839	1	1	yes	characteristic
46	C₂	#2162	1	3	yes	—
47	C₂	#2163	1	3	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
25. C₄²	C₁₆	semidirect

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

subgroup	index
C₄²×C₈	2
#1374	2