Subgroups — #12902

Order 256.

139 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2153	C₂	1	3	yes	maximal
2	#2151	C₂	1	3	yes	maximal
3	#1747	C₂	1	1	yes	maximal, characteristic
4	C₂×M₃₂	C₂²	1	3	yes	—
5	C₂²×C₁₆	C₂²	1	1	yes	characteristic
6	#405	C₂²	1	3	yes	—
7	#364	—	2	6	no	—
8	C₄⋊C₁₆	—	2	6	no	—
9	#338	C₄	1	1	yes	characteristic
10	H(3,ℤ/4)	C₄	1	3	yes	—
11	C₂×M₁₆	C₂×C₄	1	3	yes	—
12	C₂²×C₈	C₂³	1	1	yes	characteristic
13	#117	C₂×C₄	1	3	yes	—
14	M₃₂	—	2	6	no	—
15	C₂×C₁₆	—	2	3	no	—
16	C₂×C₁₆	—	2	3	no	—
17	#97	Q₈	1	6	yes	—
18	C₄×C₈	D₄	1	6	yes	—
19	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
20	M₁₆	—	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	C₄⋊C₄	—	2	3	no	—
25	C₂²⋊C₄	—	2	3	no	—
26	C₄²	C₄⋊C₄	1	6	yes	—
27	C₁₆	—	4	1	no	—
28	C₁₆	—	4	3	no	—
29	C₂³	#131	1	1	yes	characteristic
30	C₂×C₄	—	2	6	no	—
31	C₂×C₄	C₂×C₄⋊C₄	1	3	yes	—
32	C₂×C₄	#131	1	3	yes	—
33	C₈	—	2	6	no	—
34	C₈	#127	1	1	yes	characteristic
35	C₈	C₄⋊Q₈	1	3	yes	—
36	C₂²	—	4	1	no	—
37	C₂²	#424	1	3	yes	—
38	C₄	—	4	6	no	—
39	C₄	#384	1	1	yes	characteristic
40	C₄	#424	1	3	yes	—
41	C₂	—	2	3	no	—
42	C₂	#1843	1	1	yes	characteristic

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