Subgroups — #7198

Order 256.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2162	C₂	1	2	yes	maximal
2	#1452	C₂	1	1	yes	maximal, characteristic
3	#431	C₄	1	2	yes	—
4	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
5	C₄⋊C₁₆	—	2	2	no	—
6	C₂²⋊C₁₆	C₄	1	4	yes	—
7	C₄×C₁₆	—	2	2	no	—
8	#322	—	2	2	no	—
9	C₂²×C₈	C₂×C₄	1	2	yes	—
10	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₆	—	2	4	no	—
12	C₄⋊C₈	C₈	1	4	yes	—
13	C₂²⋊C₈	—	2	2	no	—
14	C₄×C₈	—	2	2	no	—
15	C₄×C₈	D₄	1	2	yes	—
16	C₄×C₈	D₄	1	1	yes	characteristic
17	C₄×C₈	Q₈	1	1	yes	characteristic
18	C₂²×C₄	C₄²	1	1	yes	characteristic
19	C₂²×C₄	M₁₆	1	2	yes	—
20	C₂×C₈	—	2	4	no	—
21	C₂×C₈	—	4	2	no	—
22	C₂×C₈	C₂²⋊C₄	1	2	yes	—
23	C₂×C₈	C₄⋊C₄	1	2	yes	—
24	C₄²	C₂²⋊C₄	1	1	yes	characteristic
25	C₄²	C₄⋊C₄	1	1	yes	characteristic
26	C₄²	C₂×C₈	1	2	yes	—
27	C₁₆	—	4	4	no	—
28	C₂³	#97	1	1	yes	characteristic
29	C₂×C₄	—	2	2	no	—
30	C₂×C₄	—	2	4	no	—
31	C₂×C₄	#95	1	1	yes	characteristic
32	C₂×C₄	C₄×C₈	1	1	yes	characteristic
33	C₂×C₄	C₂²⋊C₈	1	2	yes	—
34	C₂×C₄	C₄⋊C₈	1	2	yes	—
35	C₈	—	2	2	no	—
36	C₈	—	2	2	no	—
37	C₈	—	4	4	no	—
38	C₂²	—	2	1	no	—
39	C₂²	—	2	2	no	—
40	C₂²	#336	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	—	2	2	no	—
43	C₄	#344	1	2	yes	—
44	C₄	#350	1	4	yes	—
45	C₂	—	4	1	no	—
46	C₂	#1281	1	1	yes	characteristic
47	C₂	#1379	1	2	yes	—

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

subgroup	index
#2162	2
#1452	2