Subgroups — #7452

Order 256.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2253	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	#1372	C₂	1	1	yes	maximal, characteristic
4	#499	—	2	1	no	—
5	C₂×C₃₂	—	2	1	no	—
6	#367	—	2	1	no	—
7	#366	C₄	1	1	yes	characteristic
8	#366	C₄	1	1	yes	characteristic
9	C₄×C₁₆	C₂²	1	1	yes	characteristic
10	#335	—	2	1	no	—
11	#125	—	4	1	no	—
12	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆	D₄	1	1	yes	characteristic
14	#107	—	2	1	no	—
15	#107	—	2	1	no	—
16	#106	—	4	1	no	—
17	C₄⋊C₈	—	4	1	no	—
18	C₄×C₈	D₄	1	1	yes	characteristic
19	C₃₂	—	4	1	no	—
20	C₂×C₈	—	8	1	no	—
21	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₈	SD₁₆	1	1	yes	characteristic
23	C₄⋊C₄	—	4	1	no	—
24	C₄⋊C₄	—	4	1	no	—
25	C₄⋊C₄	—	8	1	no	—
26	C₄⋊C₄	—	8	1	no	—
27	C₄²	D₈	1	1	yes	characteristic
28	C₁₆	—	2	1	no	—
29	C₁₆	SD₁₆	1	1	yes	characteristic
30	C₁₆	Q₁₆	1	1	yes	characteristic
31	C₂×C₄	—	8	1	no	—
32	C₂×C₄	—	8	1	no	—
33	C₂×C₄	#102	1	1	yes	characteristic
34	C₂×C₄	D₁₆	1	1	yes	characteristic
35	C₂×C₄	SD₃₂	1	1	yes	characteristic
36	C₈	—	2	1	no	—
37	C₈	—	16	1	no	—
38	C₈	#101	1	1	yes	characteristic
39	C₈	#103	1	1	yes	characteristic
40	C₂²	#357	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	—	2	1	no	—
43	C₄	—	16	1	no	—
44	C₄	—	16	1	no	—
45	C₄	#332	1	1	yes	characteristic
46	C₄	#362	1	1	yes	characteristic
47	C₂	#1364	1	1	yes	characteristic
48	C₂	#1417	1	1	yes	characteristic
49	C₂	#1418	1	1	yes	characteristic

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