Subgroups — #13636

Order 256.

89 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#368	C₂	1	2	yes	maximal
3	#1425	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₆	C₂²	1	1	yes	characteristic
5	C₂×#108	—	2	2	no	—
6	M₆₄	C₄	1	4	yes	—
7	C₂×C₃₂	C₂²	1	2	yes	—
8	#368	—	2	2	no	—
9	#368	C₂²	1	4	yes	—
10	C₂×M₁₆	—	4	2	no	—
11	C₂²×C₈	D₄	1	1	yes	characteristic
12	C₂×C₁₆	C₂×C₄	1	2	yes	—
13	C₂×C₁₆	D₄	1	1	yes	characteristic
14	C₂×C₁₆	Q₈	1	2	yes	—
15	C₂×C₁₆	C₂³	1	1	yes	characteristic
16	#108	—	2	4	no	—
17	#108	—	4	2	no	—
18	C₃₂	C₂×C₄	1	4	yes	—
19	C₂²×C₄	D₈	1	1	yes	characteristic
20	M₁₆	—	4	4	no	—
21	M₁₆	—	8	2	no	—
22	C₂×C₈	—	8	2	no	—
23	C₂×C₈	C₄⋊C₄	1	2	yes	—
24	C₂×C₈	D₈	1	1	yes	characteristic
25	C₂×C₈	Q₁₆	1	2	yes	—
26	C₂×C₈	C₂×D₄	1	1	yes	characteristic
27	C₁₆	C₄⋊C₄	1	2	yes	—
28	C₁₆	C₂²×C₄	1	1	yes	characteristic
29	C₁₆	C₂×Q₈	1	1	yes	characteristic
30	C₂³	Q₃₂	1	1	yes	characteristic
31	C₂×C₄	#107	1	2	yes	—
32	C₂×C₄	D₁₆	1	2	yes	—
33	C₂×C₄	Q₃₂	1	1	yes	characteristic
34	C₂×C₄	C₂×D₈	1	1	yes	characteristic
35	C₈	—	8	4	no	—
36	C₈	#107	1	2	yes	—
37	C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₈	C₂×Q₁₆	1	1	yes	characteristic
39	C₂²	—	4	1	no	—
40	C₂²	#366	1	2	yes	—
41	C₂²	C₂×Q₃₂	1	1	yes	characteristic
42	C₄	#366	1	2	yes	—
43	C₄	C₂×#107	1	1	yes	characteristic
44	C₄	C₂×D₁₆	1	1	yes	characteristic
45	C₂	—	2	2	no	—
46	C₂	—	2	1	no	—
47	C₂	C₂×#366	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #1425	C₂	semidirect

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