Subgroups — #7365

Order 256.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2151	C₂	1	1	yes	maximal, characteristic
2	#1400	C₂	1	2	yes	maximal
3	C₂×M₃₂	C₂²	1	1	yes	characteristic
4	C₂²×C₁₆	C₄	1	1	yes	characteristic
5	#405	C₄	1	1	yes	characteristic
6	M₆₄	—	2	2	no	—
7	C₄⋊C₁₆	—	2	2	no	—
8	C₂×M₁₆	C₈	1	1	yes	characteristic
9	C₂²×C₈	C₂×C₄	1	1	yes	characteristic
10	#117	C₈	1	1	yes	characteristic
11	M₃₂	—	4	1	no	—
12	C₂×C₁₆	—	2	1	no	—
13	C₂×C₁₆	—	4	1	no	—
14	C₂×C₁₆	D₄	1	2	yes	—
15	#97	—	2	1	no	—
16	C₄×C₈	—	2	1	no	—
17	C₃₂	—	4	2	no	—
18	C₂²×C₄	C₂×C₈	1	1	yes	characteristic
19	M₁₆	—	4	1	no	—
20	C₂×C₈	—	2	1	no	—
21	C₂×C₈	—	2	1	no	—
22	C₂×C₈	—	2	1	no	—
23	C₂×C₈	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈	M₁₆	1	1	yes	characteristic
25	C₄⋊C₄	—	2	1	no	—
26	C₂²⋊C₄	C₁₆	1	2	yes	—
27	C₄²	—	2	1	no	—
28	C₁₆	—	2	2	no	—
29	C₁₆	—	4	1	no	—
30	C₂³	C₂×C₁₆	1	1	yes	characteristic
31	C₂×C₄	—	2	1	no	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	2	2	no	—
34	C₂×C₄	C₂²⋊C₈	1	1	yes	characteristic
35	C₂×C₄	M₃₂	1	1	yes	characteristic
36	C₈	—	2	1	no	—
37	C₈	—	4	1	no	—
38	C₈	#99	1	1	yes	characteristic
39	C₈	#101	1	1	yes	characteristic
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	2	no	—
45	C₄	#324	1	1	yes	characteristic
46	C₄	#349	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	4	1	no	—
49	C₂	#1322	1	1	yes	characteristic

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

subgroup	index
#2151	2
#1400	2