Subgroups — #99291

Order 512.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#7846	C₂	1	1	yes	maximal, characteristic
2	#7019	C₂	1	6	yes	maximal
3	#1839	C₂²	1	4	yes	—
4	C₄×#97	C₂²	1	3	yes	—
5	C₂×#322	C₄	1	3	yes	—
6	C₂×C₈²	C₄	1	1	yes	characteristic
7	C₂×#97	—	2	6	no	—
8	C₂×C₄×C₈	C₂×C₄	1	3	yes	—
9	C₂×C₄×C₈	C₂×C₄	1	3	yes	—
10	C₄³	C₂³	1	1	yes	characteristic
11	#336	—	2	12	no	—
12	#322	—	2	6	no	—
13	C₈²	C₈	1	4	yes	complemented
14	C₂²×C₈	—	2	3	no	—
15	C₂²×C₈	—	2	3	no	—
16	C₂²×C₈	—	4	4	no	—
17	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄²	#41	1	6	yes	—
19	#97	—	4	12	no	—
20	C₄×C₈	—	2	3	no	—
21	C₄×C₈	—	2	3	no	—
22	C₄×C₈	C₂×C₈	1	6	yes	—
23	C₄×C₈	M₁₆	1	6	yes	—
24	C₂²×C₄	#117	1	3	yes	—
25	C₂²×C₄	#126	1	4	yes	—
26	C₂×C₈	—	2	12	no	—
27	C₂×C₈	—	2	6	no	—
28	C₂×C₈	—	2	6	no	—
29	C₂×C₈	—	4	6	no	—
30	C₂×C₈	—	8	12	no	—
31	C₄²	—	4	6	no	—
32	C₄²	C₂²×C₈	1	1	yes	characteristic
33	C₄²	C₂×M₁₆	1	3	yes	—
34	C₂³	#383	1	1	yes	characteristic
35	C₂×C₄	—	2	6	no	—
36	C₂×C₄	—	2	12	no	—
37	C₂×C₄	#431	1	3	yes	—
38	C₂×C₄	#432	1	3	yes	—
39	C₈	—	2	12	no	—
40	C₈	—	4	6	no	—
41	C₈	—	16	4	no	—
42	C₂²	#1839	1	1	yes	characteristic
43	C₂²	#1841	1	6	yes	—
44	C₄	—	2	3	no	—
45	C₄	—	2	3	no	—
46	C₄	—	4	4	no	—
47	C₂	#8800	1	3	yes	—
48	C₂	#8804	1	4	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. C₈²	C₈	semidirect

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

subgroup	index
#7846	2
#7019	2