Subgroups — #7239

Order 256.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2166	C₂	1	2	yes	maximal
2	#2151	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂	C₄	1	1	yes	characteristic
4	C₂²×C₁₆	C₄	1	1	yes	characteristic
5	#405	C₂²	1	1	yes	characteristic
6	#364	—	2	2	no	—
7	C₄⋊C₁₆	—	2	2	no	—
8	#349	—	2	2	no	—
9	#347	C₄	1	4	yes	—
10	C₂×M₁₆	D₄	1	1	yes	characteristic
11	C₂²×C₈	C₂×C₄	1	1	yes	characteristic
12	#117	Q₈	1	1	yes	characteristic
13	M₃₂	—	2	4	no	—
14	M₃₂	—	4	1	no	—
15	C₂×C₁₆	—	2	1	no	—
16	C₂×C₁₆	—	2	1	no	—
17	C₂×C₁₆	—	4	1	no	—
18	#97	C₂×C₄	1	2	yes	—
19	C₄×C₈	D₄	1	2	yes	—
20	C₂²×C₄	C₄⋊C₄	1	1	yes	characteristic
21	M₁₆	—	4	1	no	—
22	C₂×C₈	—	2	1	no	—
23	C₂×C₈	—	2	1	no	—
24	C₂×C₈	C₄²	1	1	yes	characteristic
25	C₂×C₈	C₂²⋊C₄	1	2	yes	—
26	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₂²⋊C₄	—	2	1	no	—
29	C₄²	C₄⋊C₄	1	2	yes	—
30	C₁₆	—	4	4	no	—
31	C₁₆	—	4	1	no	—
32	C₁₆	—	4	1	no	—
33	C₂³	#108	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	—	2	2	no	—
37	C₂×C₄	#95	1	1	yes	characteristic
38	C₂×C₄	#108	1	1	yes	characteristic
39	C₈	—	2	2	no	—
40	C₈	—	2	1	no	—
41	C₈	#100	1	1	yes	characteristic
42	C₈	#101	1	1	yes	characteristic
43	C₂²	—	2	1	no	—
44	C₂²	—	4	1	no	—
45	C₂²	#341	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	4	2	no	—
48	C₄	H(3,ℤ/4)	1	1	yes	characteristic
49	C₄	#343	1	1	yes	characteristic
50	C₂	—	2	1	no	—
51	C₂	—	4	1	no	—
52	C₂	#1290	1	1	yes	characteristic

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

subgroup	index
#2166	2
#2151	2