Subgroups — #14580716

Order 2624.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₆₄	C₂	1	4	yes	maximal
2	#13050164	C₂	1	2	yes	maximal
3	C₄×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₂	C₂²	1	4	yes	—
5	C₂×C₈×C₄₁	C₂²	1	2	yes	—
6	C₄²×C₄₁	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₄₁	—	2	4	no	—
8	Dic₁₆₄	—	2	8	no	—
9	C₂×C₄×C₄₁	D₄	1	2	yes	—
10	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
11	C₂×Dic₄₁	—	2	4	no	—
12	Dic₈₂	—	2	8	no	—
13	C₈×C₄₁	D₄	1	4	yes	—
14	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
15	C₄×C₄₁	Q₁₆	1	4	yes	complemented
16	C₄×C₄₁	C₂×D₄	1	2	yes	—
17	Dic₄₁	—	4	4	no	—
18	C₂×C₄₁	#127	1	1	yes	characteristic
19	C₂×C₄₁	C₂×Q₁₆	1	2	yes	—
20	#494	—	41	1	no	maximal, Sylow
21	C₄₁	#494	1	1	yes	characteristic, complemented, Sylow
22	C₂×Q₁₆	—	41	4	no	—
23	C₄⋊Q₈	—	41	2	no	—
24	C₄×C₈	D₄₁	1	1	yes	characteristic
25	C₂×Q₈	—	41	4	no	—
26	Q₁₆	—	82	8	no	—
27	C₂×C₈	C₂×D₄₁	1	2	yes	—
28	C₄⋊C₄	—	82	4	no	—
29	C₄²	C₂×D₄₁	1	1	yes	characteristic
30	Q₈	—	82	8	no	—
31	C₂×C₄	—	82	4	no	—
32	C₂×C₄	D₁₆₄	1	2	yes	—
33	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
34	C₈	D₁₆₄	1	4	yes	—
35	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
36	C₄	—	164	4	no	—
37	C₄	Dic₁₆₄	1	4	yes	complemented
38	C₄	C₂×D₁₆₄	1	2	yes	—
39	C₂	#13050161	1	1	yes	characteristic
40	C₂	C₂×Dic₁₆₄	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.