Subgroups — #8783

Order 256.

131 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1746	C₂	1	1	yes	maximal, characteristic
2	#1564	C₂	1	2	yes	maximal
3	#1281	C₂	1	2	yes	maximal
4	#1274	C₂	1	2	yes	maximal
5	#431	C₂²	1	4	yes	—
6	C₂×#97	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
8	#376	C₂²	1	1	yes	characteristic
9	#336	C₄	1	4	yes	—
10	#335	—	2	2	no	—
11	#334	—	2	2	no	—
12	C₂²×C₈	C₂×C₄	1	2	yes	—
13	C₂²×C₈	C₂×C₄	1	2	yes	—
14	C₂×C₄²	C₂×C₄	1	2	yes	—
15	C₂×C₄²	C₂³	1	1	yes	characteristic
16	C₄⋊C₈	—	2	4	no	—
17	C₂²⋊C₈	—	2	4	no	—
18	#97	—	2	2	no	—
19	C₄×C₈	—	2	4	no	—
20	C₄×C₈	D₄	1	2	yes	—
21	C₄×C₈	Q₈	1	2	yes	—
22	#95	—	2	2	no	—
23	C₂²×C₄	—	2	2	no	—
24	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
25	C₂²×C₄	#41	1	2	yes	—
26	C₂×C₈	—	2	4	no	—
27	C₂×C₈	—	2	2	no	—
28	C₂×C₈	—	2	4	no	—
29	C₂×C₈	—	4	4	no	—
30	C₂×C₈	C₄⋊C₄	1	4	yes	—
31	C₄²	—	2	4	no	—
32	C₄²	C₂×D₄	1	1	yes	characteristic
33	C₄²	C₂×Q₈	1	1	yes	characteristic
34	C₄²	#41	1	2	yes	—
35	C₂³	#117	1	1	yes	characteristic
36	C₂×C₄	—	4	2	no	—
37	C₂×C₄	—	4	4	no	—
38	C₂×C₄	—	4	2	no	—
39	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₄	#117	1	1	yes	characteristic
41	C₂×C₄	#124	1	2	yes	—
42	C₂×C₄	#125	1	2	yes	—
43	C₂×C₄	#131	1	4	yes	—
44	C₈	—	2	4	no	—
45	C₈	—	4	2	no	—
46	C₈	—	8	4	no	—
47	C₂²	—	2	2	no	—
48	C₂²	#382	1	1	yes	characteristic
49	C₂²	#433	1	2	yes	—
50	C₄	—	2	2	no	—
51	C₄	—	2	2	no	—
52	C₄	—	8	2	no	—
53	C₄	#424	1	2	yes	—
54	C₄	#433	1	2	yes	—
55	C₂	—	2	2	no	—
56	C₂	#1832	1	1	yes	characteristic
57	C₂	#1833	1	2	yes	—

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