Subgroups — #8825

Order 256.

169 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1848	C₂	1	2	yes	maximal
2	#1566	C₂	1	4	yes	maximal
3	C₂×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×#108	—	2	4	no	—
5	#423	C₂²	1	4	yes	—
6	C₂×C₄×C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
8	#334	—	2	8	no	—
9	#322	C₄	1	4	yes	—
10	C₂×M₁₆	—	2	4	no	—
11	C₂²×C₈	D₄	1	2	yes	—
12	C₂²×C₈	Q₈	1	4	yes	—
13	C₂×C₄²	C₂³	1	1	yes	characteristic
14	#108	—	4	8	no	—
15	C₄⋊C₈	—	2	8	no	—
16	C₄×C₈	C₂×C₄	1	4	yes	—
17	C₄×C₈	C₂×C₄	1	2	yes	—
18	C₄×C₈	D₄	1	4	yes	—
19	C₄×C₈	Q₈	1	2	yes	—
20	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₄	C₂×Q₈	1	2	yes	—
22	M₁₆	—	4	8	no	—
23	C₂×C₈	—	4	4	no	—
24	C₂×C₈	—	4	4	no	—
25	C₂×C₈	C₄⋊C₄	1	8	yes	—
26	C₂×C₈	C₄⋊C₄	1	4	yes	—
27	C₂×C₈	SD₁₆	1	8	yes	—
28	C₄²	C₂²×C₄	1	1	yes	characteristic
29	C₄²	C₂×D₄	1	2	yes	—
30	C₄²	C₂×Q₈	1	1	yes	characteristic
31	C₂³	C₄⋊Q₈	1	1	yes	characteristic
32	C₂×C₄	—	2	4	no	—
33	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄	C₂×C₄⋊C₄	1	2	yes	—
35	C₂×C₄	#127	1	1	yes	characteristic
36	C₂×C₄	C₄⋊Q₈	1	2	yes	—
37	C₂×C₄	C₂×SD₁₆	1	4	yes	—
38	C₈	—	2	8	no	—
39	C₈	—	8	4	no	—
40	C₈	#106	1	8	yes	—
41	C₂²	—	2	2	no	—
42	C₂²	#384	1	1	yes	characteristic
43	C₂²	#498	1	2	yes	—
44	C₄	—	2	2	no	—
45	C₄	C₂×#106	1	2	yes	—
46	C₄	#430	1	4	yes	—
47	C₄	#492	1	2	yes	—
48	C₂	—	2	2	no	—
49	C₂	#1844	1	1	yes	characteristic
50	C₂	#1849	1	2	yes	—

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