Subgroups — #8788

Order 256.

161 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1831	C₂	1	2	yes	maximal
2	#1744	C₂	1	1	yes	maximal, characteristic
3	#1277	C₂	1	4	yes	maximal
4	C₂×C₄⋊C₈	C₂²	1	4	yes	—
5	C₂×C₄×C₈	C₂²	1	2	yes	—
6	C₄³	C₂²	1	1	yes	characteristic
7	#336	—	2	4	no	—
8	#336	C₄	1	4	yes	—
9	C₂²×C₈	—	2	4	no	—
10	C₂²×C₈	C₂×C₄	1	4	yes	—
11	C₂×C₄²	C₂×C₄	1	2	yes	—
12	C₂×C₄²	D₄	1	2	yes	—
13	C₂×C₄²	Q₈	1	2	yes	—
14	C₂×C₄²	C₂³	1	1	yes	characteristic
15	C₄⋊C₈	—	2	8	no	—
16	C₄×C₈	—	2	4	no	—
17	C₂²×C₄	C₄⋊C₄	1	4	yes	—
18	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
20	C₂²×C₄	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₈	—	2	4	no	—
22	C₂×C₈	—	2	8	no	—
23	C₂×C₈	—	4	4	no	—
24	C₂×C₈	—	4	8	no	—
25	C₄²	—	2	4	no	—
26	C₄²	—	2	4	no	—
27	C₄²	—	4	2	no	—
28	C₄²	#41	1	4	yes	—
29	C₂³	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄	—	2	2	no	—
31	C₂×C₄	—	2	4	no	—
32	C₂×C₄	—	2	4	no	—
33	C₂×C₄	—	2	4	no	—
34	C₂×C₄	#117	1	2	yes	—
35	C₂×C₄	#124	1	2	yes	—
36	C₂×C₄	#125	1	2	yes	—
37	C₂×C₄	#131	1	4	yes	—
38	C₂×C₄	#135	1	4	yes	—
39	C₈	—	4	4	no	—
40	C₈	—	8	4	no	—
41	C₂²	#382	1	1	yes	characteristic
42	C₂²	#424	1	2	yes	—
43	C₂²	#427	1	2	yes	—
44	C₂²	#430	1	2	yes	—
45	C₄	—	2	2	no	—
46	C₄	—	4	4	no	—
47	C₄	#433	1	4	yes	—
48	C₄	#488	1	4	yes	—
49	C₂	#1572	1	4	yes	—
50	C₂	#1832	1	1	yes	characteristic
51	C₂	#1835	1	1	yes	characteristic
52	C₂	#1838	1	1	yes	characteristic

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