Subgroups — #93866

Order 512.

123 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#12515	C₂	1	1	yes	maximal, characteristic
2	#7459	C₂	1	2	yes	maximal, complemented
3	#2246	—	2	2	no	—
4	#1712	C₄	1	2	yes	—
5	#1422	—	2	2	no	—
6	C₈×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×D₁₆	—	4	2	no	—
8	C₂×D₁₆	—	4	2	no	—
9	#493	—	2	2	no	—
10	#493	—	4	2	no	—
11	M₆₄	—	4	2	no	—
12	C₄×C₁₆	D₄	1	2	yes	—
13	C₈²	C₂×C₄	1	1	yes	characteristic
14	C₂×D₈	—	4	4	no	—
15	C₂×D₈	—	8	4	no	—
16	#127	—	4	2	no	—
17	D₁₆	—	8	4	no	—
18	D₁₆	—	8	2	no	—
19	D₁₆	—	8	2	no	—
20	C₂×C₁₆	D₈	1	2	yes	—
21	C₂×C₁₆	SD₁₆	1	2	yes	—
22	C₄×C₈	—	2	1	no	—
23	C₄×C₈	C₂²⋊C₄	1	1	yes	characteristic
24	C₃₂	—	8	2	no	—
25	C₂×D₄	—	8	4	no	—
26	C₂×D₄	—	8	2	no	—
27	D₈	—	8	4	no	—
28	D₈	—	8	4	no	—
29	D₈	—	16	8	no	—
30	C₂×C₈	—	2	2	no	—
31	C₂×C₈	#102	1	2	yes	—
32	C₄²	#100	1	1	yes	characteristic
33	C₁₆	—	2	2	no	—
34	C₁₆	D₁₆	1	2	yes	—
35	C₁₆	SD₃₂	1	2	yes	—
36	C₂³	—	16	2	no	—
37	D₄	—	16	8	no	—
38	D₄	—	16	4	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	#331	1	1	yes	characteristic
41	C₈	—	2	4	no	—
42	C₈	#357	1	2	yes	—
43	C₈	#361	1	2	yes	—
44	C₂²	—	32	4	no	—
45	C₂²	—	32	2	no	—
46	C₂²	#1357	1	1	yes	characteristic
47	C₄	—	2	2	no	—
48	C₄	#1361	1	2	yes	—
49	C₂	—	2	1	no	—
50	C₂	—	64	2	no	—
51	C₂	#7096	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #7459	C₂	semidirect

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

subgroup	index
#12515	2
#7459	2