Subgroups — #14580713

Order 2624.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₂₈	C₂	1	4	yes	maximal, complemented
2	#13050161	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆₄	—	2	4	no	—
5	C₂×D₁₆₄	C₂²	1	4	yes	—
6	C₂×C₈×C₄₁	C₂²	1	2	yes	—
7	C₄²×C₄₁	C₂²	1	1	yes	characteristic
8	D₃₂₈	—	2	8	no	—
9	C₂²×D₄₁	—	2	4	no	—
10	C₂×C₄×C₄₁	D₄	1	2	yes	—
11	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
12	D₁₆₄	—	2	8	no	—
13	D₁₆₄	—	4	8	no	—
14	C₈×C₄₁	D₄	1	4	yes	complemented
15	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
16	C₂×D₄₁	—	4	4	no	—
17	C₂×D₄₁	—	4	8	no	—
18	C₄×C₄₁	D₈	1	4	yes	complemented
19	C₄×C₄₁	C₂×D₄	1	2	yes	—
20	C₂×C₄₁	#127	1	1	yes	characteristic
21	C₂×C₄₁	C₂×D₈	1	2	yes	—
22	D₄₁	—	8	4	no	—
23	#493	—	41	1	no	maximal, Sylow
24	C₄₁	#493	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₈	—	41	4	no	—
26	#127	—	41	2	no	—
27	C₄×C₈	D₄₁	1	1	yes	characteristic, complemented
28	C₂×D₄	—	41	4	no	—
29	C₂×D₄	—	82	4	no	—
30	D₈	—	82	8	no	—
31	C₂×C₈	C₂×D₄₁	1	2	yes	—
32	C₄²	C₂×D₄₁	1	1	yes	characteristic
33	C₂³	—	82	4	no	—
34	D₄	—	82	8	no	—
35	D₄	—	164	8	no	—
36	C₂×C₄	D₁₆₄	1	2	yes	—
37	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
38	C₈	D₁₆₄	1	4	yes	complemented
39	C₂²	—	164	4	no	—
40	C₂²	—	164	8	no	—
41	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
42	C₄	D₃₂₈	1	4	yes	complemented
43	C₄	C₂×D₁₆₄	1	2	yes	—
44	C₂	—	328	4	no	—
45	C₂	#13050161	1	1	yes	characteristic
46	C₂	C₂×D₃₂₈	1	2	yes	—

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

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