Subgroups — #11416

Order 256.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2163	C₂	1	2	yes	maximal
2	#1450	C₂	1	1	yes	maximal, characteristic
3	#1313	C₂	1	4	yes	maximal, complemented
4	#431	C₄	1	2	yes	—
5	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
6	C₄⋊C₁₆	C₄	1	4	yes	—
7	C₂²⋊C₁₆	C₄	1	4	yes	—
8	#346	C₂²	1	4	yes	—
9	#322	C₂²	1	2	yes	—
10	C₈²	C₄	1	2	yes	—
11	C₂²×C₈	C₂×C₄	1	2	yes	—
12	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆	C₂×C₄	1	8	yes	—
14	C₄⋊C₈	—	2	2	no	—
15	C₂²⋊C₈	—	2	2	no	—
16	C₄×C₈	C₂×C₄	1	2	yes	—
17	C₄×C₈	C₂×C₄	1	4	yes	—
18	C₄×C₈	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈	C₂³	1	1	yes	characteristic
20	C₂²×C₄	C₄²	1	1	yes	characteristic
21	C₂²×C₄	M₁₆	1	2	yes	—
22	C₂×C₈	—	2	4	no	—
23	C₂×C₈	—	2	4	no	—
24	C₂×C₈	C₄²	1	2	yes	—
25	C₂×C₈	C₂²×C₄	1	2	yes	—
26	C₄²	C₄²	1	1	yes	characteristic
27	C₄²	M₁₆	1	2	yes	—
28	C₄²	C₂²×C₄	1	1	yes	characteristic
29	C₁₆	—	2	8	no	—
30	C₂³	#97	1	1	yes	characteristic
31	C₂×C₄	—	2	2	no	—
32	C₂×C₄	—	4	2	no	—
33	C₂×C₄	#97	1	2	yes	—
34	C₂×C₄	#97	1	1	yes	characteristic
35	C₂×C₄	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₄	C₂×M₁₆	1	2	yes	—
37	C₈	—	2	2	no	—
38	C₈	—	4	4	no	—
39	C₈	#131	1	4	yes	—
40	C₂²	—	2	2	no	—
41	C₂²	—	2	1	no	—
42	C₂²	C₂×#97	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	2	2	no	—
45	C₄	—	2	1	no	—
46	C₄	#405	1	2	yes	—
47	C₂	—	4	1	no	—
48	C₂	#1452	1	1	yes	characteristic
49	C₂	#2110	1	2	yes	—

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

N	H ≅ G/N	type
3. #1313	C₂	semidirect

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