Subgroups — #99306

Order 512.

366 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#8806	C₂	1	6	yes	maximal
2	#8131	C₂	1	1	yes	maximal, characteristic
3	#1842	C₂²	1	4	yes	—
4	C₄²×C₈	C₂²	1	3	yes	—
5	C₂×#335	—	2	12	no	—
6	#1273	C₄	1	4	yes	—
7	C₂×C₄⋊C₈	—	2	12	no	—
8	C₂×C₄×C₈	C₂×C₄	1	6	yes	—
9	C₂×C₄×C₈	D₄	1	6	yes	—
10	C₂×C₄×C₈	Q₈	1	6	yes	—
11	C₄³	C₂³	1	1	yes	characteristic
12	#335	—	4	24	no	—
13	C₂²×C₈	—	4	4	no	—
14	C₂²×C₈	C₄⋊C₄	1	12	yes	—
15	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄²	C₂×D₄	1	3	yes	—
17	C₂×C₄²	C₂×Q₈	1	3	yes	—
18	C₄⋊C₈	—	4	24	no	—
19	C₄×C₈	—	2	12	no	—
20	C₄×C₈	—	4	6	no	—
21	C₄×C₈	D₈	1	12	yes	—
22	C₄×C₈	Q₁₆	1	12	yes	—
23	C₂²×C₄	C₂×C₄⋊C₄	1	3	yes	—
24	C₂²×C₄	#127	1	1	yes	characteristic
25	C₂²×C₄	C₄⋊Q₈	1	3	yes	—
26	C₂×C₈	—	2	12	no	—
27	C₂×C₈	—	2	12	no	—
28	C₂×C₈	—	8	12	no	—
29	C₂×C₈	#107	1	24	yes	—
30	C₄²	—	2	6	no	—
31	C₄²	#131	1	4	yes	—
32	C₄²	C₂×D₈	1	6	yes	—
33	C₄²	C₂×Q₁₆	1	6	yes	—
34	C₂³	#384	1	1	yes	characteristic
35	C₂×C₄	—	2	6	no	—
36	C₂×C₄	#424	1	6	yes	—
37	C₂×C₄	C₂×#107	1	6	yes	—
38	C₂×C₄	#430	1	6	yes	—
39	C₂×C₄	#493	1	3	yes	—
40	C₂×C₄	#494	1	3	yes	—
41	C₂×C₄	#500	1	6	yes	—
42	C₈	—	2	24	no	—
43	C₈	—	16	4	no	—
44	C₂²	#1843	1	1	yes	characteristic
45	C₂²	#1845	1	3	yes	—
46	C₂²	#1849	1	3	yes	—
47	C₄	—	2	6	no	—
48	C₄	#1571	1	12	yes	—
49	C₄	#1712	1	1	yes	characteristic
50	C₄	#1713	1	3	yes	—
51	C₂	#8810	1	3	yes	—
52	C₂	#8818	1	1	yes	characteristic
53	C₂	#8826	1	3	yes	—

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

subgroup	index
#8806	2
#8131	2