Subgroups — #8803

Order 256.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1455	C₂	1	1	yes	maximal, characteristic
2	#1291	C₂	1	3	yes	maximal
3	#1288	C₂	1	3	yes	maximal
4	#432	C₂²	1	3	yes	—
5	C₄×M₁₆	C₂²	1	3	yes	—
6	#383	C₂²	1	1	yes	characteristic
7	#322	C₄	1	3	yes	complemented
8	C₈²	C₄	1	1	yes	characteristic, complemented
9	C₂×M₁₆	—	2	3	no	—
10	C₂×C₄²	C₂³	1	1	yes	characteristic
11	C₄⋊C₈	—	2	3	no	—
12	C₂²⋊C₈	—	2	3	no	—
13	#97	—	2	3	no	—
14	#97	—	2	3	no	—
15	C₄×C₈	C₂×C₄	1	3	yes	—
16	C₄×C₈	C₂×C₄	1	3	yes	—
17	#95	—	2	3	no	—
18	C₂²×C₄	—	4	1	no	—
19	C₂²×C₄	#41	1	3	yes	—
20	M₁₆	—	4	6	no	—
21	C₂×C₈	—	2	3	no	—
22	C₂×C₈	—	2	3	no	—
23	C₂×C₈	—	4	3	no	—
24	C₄²	C₂²×C₄	1	1	yes	characteristic
25	C₄²	#41	1	3	yes	—
26	C₂³	#126	1	1	yes	characteristic
27	C₂×C₄	—	4	3	no	—
28	C₂×C₄	—	8	3	no	—
29	C₂×C₄	#117	1	3	yes	—
30	C₂×C₄	#126	1	3	yes	—
31	C₈	—	2	6	no	—
32	C₈	—	4	3	no	—
33	C₈	—	8	3	no	—
34	C₂²	—	2	3	no	—
35	C₂²	#383	1	1	yes	characteristic
36	C₄	—	2	3	no	—
37	C₄	—	2	3	no	—
38	C₄	—	16	1	no	—
39	C₂	—	4	1	no	—
40	C₂	#1841	1	3	yes	—

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

N	H ≅ G/N	type
7. #322	C₄	semidirect
8. C₈²	C₄	semidirect

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