Subgroups — #7099

Order 256.

49 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1367	C₂	1	2	yes	maximal
2	#1311	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆	—	2	2	no	—
4	C₄×C₁₆	C₄	1	1	yes	characteristic
5	C₄×C₁₆	C₄	1	1	yes	characteristic
6	C₈²	C₂²	1	1	yes	characteristic
7	C₂×C₁₆	—	2	1	no	—
8	C₂×C₁₆	—	4	2	no	—
9	C₂×C₁₆	C₈	1	1	yes	characteristic
10	C₂×C₁₆	C₈	1	1	yes	characteristic
11	C₄×C₈	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈	D₄	1	1	yes	characteristic
13	C₄×C₈	Q₈	1	1	yes	characteristic
14	C₂×C₈	—	2	1	no	—
15	C₂×C₈	C₂×C₈	1	1	yes	characteristic
16	C₂×C₈	M₁₆	1	1	yes	characteristic
17	C₂×C₈	SD₁₆	1	2	yes	—
18	C₄²	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆	—	2	2	no	—
20	C₁₆	—	2	1	no	—
21	C₁₆	—	8	2	no	—
22	C₁₆	C₁₆	1	2	yes	complemented
23	C₂×C₄	C₄⋊C₈	1	1	yes	characteristic
24	C₂×C₄	#106	1	1	yes	characteristic
25	C₂×C₄	#108	1	1	yes	characteristic
26	C₈	—	2	1	no	—
27	C₈	—	2	2	no	—
28	C₈	—	4	1	no	—
29	C₈	C₂×C₁₆	1	1	yes	characteristic
30	C₈	M₃₂	1	1	yes	characteristic
31	C₂²	#334	1	1	yes	characteristic
32	C₄	—	2	1	no	—
33	C₄	C₄⋊C₁₆	1	1	yes	characteristic
34	C₄	#364	1	1	yes	characteristic
35	C₄	#365	1	2	yes	—
36	C₂	#1367	1	1	yes	characteristic
37	C₂	#1368	1	1	yes	characteristic
38	C₂	#1369	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₁₆	C₁₆	semidirect

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

subgroup	index
#1367	2
#1311	2