Subgroups — #8802

Order 256.

129 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1745	C₂	1	1	yes	maximal, characteristic
2	#1281	C₂	1	2	yes	maximal
3	#1276	C₂	1	2	yes	maximal
4	#1275	C₂	1	2	yes	maximal
5	#431	C₂²	1	4	yes	—
6	C₂×#97	C₂²	1	1	yes	characteristic
7	C₂×#97	C₂²	1	1	yes	characteristic
8	C₄³	C₂²	1	1	yes	characteristic
9	#336	C₄	1	4	yes	—
10	C₂²×C₈	C₂×C₄	1	2	yes	—
11	C₂²×C₈	C₂×C₄	1	2	yes	—
12	C₂×C₄²	—	2	2	no	—
13	C₂×C₄²	C₂×C₄	1	2	yes	—
14	C₂×C₄²	C₂³	1	1	yes	characteristic
15	C₄⋊C₈	—	2	4	no	—
16	C₂²⋊C₈	—	2	4	no	—
17	#97	—	2	2	no	—
18	#97	—	2	2	no	—
19	C₄×C₈	—	2	4	no	—
20	C₂²×C₄	—	2	2	no	—
21	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄	#41	1	2	yes	—
23	C₂×C₈	—	2	2	no	—
24	C₂×C₈	—	2	2	no	—
25	C₂×C₈	—	2	4	no	—
26	C₂×C₈	—	2	4	no	—
27	C₂×C₈	—	4	4	no	—
28	C₄²	—	2	4	no	—
29	C₄²	—	4	4	no	—
30	C₄²	#41	1	2	yes	—
31	C₄²	#41	1	2	yes	—
32	C₂³	#117	1	1	yes	characteristic
33	C₂×C₄	—	2	4	no	—
34	C₂×C₄	—	4	2	no	—
35	C₂×C₄	—	4	2	no	—
36	C₂×C₄	—	4	2	no	—
37	C₂×C₄	#117	1	1	yes	characteristic
38	C₂×C₄	#117	1	1	yes	characteristic
39	C₂×C₄	#126	1	4	yes	—
40	C₂×C₄	#131	1	4	yes	—
41	C₈	—	4	2	no	—
42	C₈	—	4	2	no	—
43	C₈	—	8	4	no	—
44	C₂²	—	2	2	no	—
45	C₂²	#383	1	1	yes	characteristic
46	C₂²	#433	1	2	yes	—
47	C₄	—	2	4	no	—
48	C₄	—	4	4	no	—
49	C₄	#433	1	2	yes	—
50	C₄	#433	1	2	yes	—
51	C₂	—	2	2	no	—
52	C₂	#1840	1	1	yes	characteristic
53	C₂	#1841	1	2	yes	—

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