Subgroups — #12898

Order 256.

207 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₁₆	C₂	1	6	yes	maximal
2	C₄²×C₈	C₂	1	1	yes	maximal, characteristic
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	C₄⋊C₁₆	—	2	12	no	—
8	C₂²×C₈	C₂×C₄	1	3	yes	—
9	C₂²×C₈	C₂³	1	1	yes	characteristic
10	C₂×C₄²	C₈	1	3	yes	—
11	C₂×C₄²	C₈	1	1	yes	characteristic
12	C₂×C₄²	C₂×C₄	1	3	yes	—
13	C₂×C₁₆	—	2	12	no	—
14	C₄×C₈	—	2	6	no	—
15	C₄×C₈	D₄	1	6	yes	—
16	C₄×C₈	Q₈	1	6	yes	—
17	C₂²×C₄	C₂×C₈	1	3	yes	—
18	C₂²×C₄	C₂×C₈	1	3	yes	—
19	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
20	C₂×C₈	—	2	6	no	—
21	C₂×C₈	C₄⋊C₄	1	6	yes	—
22	C₂×C₈	C₂×D₄	1	3	yes	—
23	C₂×C₈	C₂×Q₈	1	3	yes	—
24	C₄²	—	2	6	no	—
25	C₄²	C₁₆	1	4	yes	complemented
26	C₄²	C₄⋊C₄	1	6	yes	—
27	C₄²	M₁₆	1	6	yes	—
28	C₁₆	—	4	4	no	—
29	C₂³	C₂²×C₈	1	1	yes	characteristic
30	C₂×C₄	—	2	6	no	—
31	C₂×C₄	C₄⋊C₈	1	6	yes	—
32	C₂×C₄	C₄⋊C₈	1	6	yes	—
33	C₂×C₄	C₂×C₁₆	1	6	yes	—
34	C₂×C₄	M₃₂	1	6	yes	—
35	C₂×C₄	C₂×C₄⋊C₄	1	3	yes	—
36	C₂×C₄	C₂×M₁₆	1	3	yes	—
37	C₈	—	2	6	no	—
38	C₈	#127	1	1	yes	characteristic
39	C₈	C₄⋊Q₈	1	3	yes	—
40	C₂²	C₂×C₄⋊C₈	1	3	yes	—
41	C₂²	C₂²×C₁₆	1	1	yes	characteristic
42	C₂²	C₂×M₃₂	1	3	yes	—
43	C₄	—	2	6	no	—
44	C₄	C₄⋊C₁₆	1	12	yes	complemented
45	C₄	#384	1	1	yes	characteristic
46	C₄	#423	1	3	yes	—
47	C₂	#1842	1	1	yes	characteristic
48	C₂	C₂×C₄⋊C₁₆	1	3	yes	—
49	C₂	#2150	1	3	yes	—

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

N	H ≅ G/N	type
25. C₄²	C₁₆	semidirect
44. C₄	C₄⋊C₁₆	semidirect

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

subgroup	index
C₂×C₄⋊C₁₆	2
C₄²×C₈	2