Subgroups — #8797

Order 256.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1568	C₂	1	2	yes	maximal
2	#1450	C₂	1	1	yes	maximal, characteristic
3	#1287	C₂	1	4	yes	maximal
4	#432	C₂²	1	4	yes	—
5	#431	C₂²	1	2	yes	—
6	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
7	#335	—	2	2	no	—
8	#334	—	2	2	no	—
9	#322	C₄	1	2	yes	—
10	C₈²	C₄	1	2	yes	—
11	C₂²×C₈	Q₈	1	2	yes	—
12	C₂×C₄²	C₂³	1	1	yes	characteristic
13	C₄⋊C₈	—	2	4	no	—
14	C₄⋊C₈	—	2	2	no	—
15	C₂²⋊C₈	—	2	2	no	—
16	C₂²⋊C₈	—	2	4	no	—
17	#97	—	2	4	no	—
18	C₄×C₈	C₂×C₄	1	4	yes	—
19	C₄×C₈	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈	D₄	1	2	yes	—
22	C₂²×C₄	C₂×Q₈	1	1	yes	characteristic
23	C₂²×C₄	#41	1	2	yes	—
24	C₂×C₈	—	2	4	no	—
25	C₂×C₈	—	2	4	no	—
26	C₂×C₈	—	4	4	no	—
27	C₂×C₈	C₄⋊C₄	1	2	yes	—
28	C₂×C₈	C₄⋊C₄	1	2	yes	—
29	C₄²	C₂²×C₄	1	1	yes	characteristic
30	C₄²	C₂×D₄	1	1	yes	characteristic
31	C₄²	#41	1	2	yes	—
32	C₂³	#125	1	1	yes	characteristic
33	C₂×C₄	—	2	2	no	—
34	C₂×C₄	—	4	2	no	—
35	C₂×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄	#117	1	2	yes	—
37	C₂×C₄	#124	1	2	yes	—
38	C₂×C₄	#125	1	1	yes	characteristic
39	C₈	—	2	2	no	—
40	C₈	—	4	4	no	—
41	C₈	—	8	4	no	—
42	C₈	#108	1	4	yes	—
43	C₂²	—	2	2	no	—
44	C₂²	—	2	1	no	—
45	C₂²	#382	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	—	2	2	no	—
48	C₄	—	2	1	no	—
49	C₄	C₂×#108	1	2	yes	—
50	C₂	—	4	1	no	—
51	C₂	#1833	1	2	yes	—
52	C₂	#1837	1	1	yes	characteristic

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