Subgroups — C₂×#22575846 #31772714

Order 17312.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575846	C₂	1	4	yes	maximal, direct product factor
2	C₂×#16864520	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₅₄₁	C₂	1	1	yes	maximal, characteristic
4	#16864520	C₂²	1	4	yes	complemented
5	C₂²×D₅₄₁	C₄	1	1	yes	characteristic
6	C₂×Dic₅₄₁	C₂²	1	1	yes	characteristic
7	C₄×D₅₄₁	C₄	1	2	yes	—
8	C₄×D₅₄₁	C₂²	1	2	yes	—
9	C₂×C₄×C₅₄₁	C₄	1	1	yes	characteristic
10	C₂²×C₅₄₁	C₂×C₄	1	1	yes	characteristic
11	C₂×D₅₄₁	—	2	2	no	—
12	C₂×D₅₄₁	C₂×C₄	1	2	yes	—
13	C₄×C₅₄₁	C₂×C₄	1	2	yes	—
14	Dic₅₄₁	C₂×C₄	1	1	yes	characteristic
15	Dic₅₄₁	C₂³	1	1	yes	characteristic
16	C₂×C₅₄₁	M₁₆	1	2	yes	complemented
17	C₂×C₅₄₁	C₂²×C₄	1	1	yes	characteristic
18	D₅₄₁	—	2	2	no	—
19	C₅₄₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂×M₁₆	—	541	1	no	maximal, Sylow
21	C₂²×C₄	—	541	1	no	—
22	M₁₆	—	541	4	no	—
23	C₂×C₈	—	541	2	no	—
24	C₂³	—	541	1	no	—
25	C₂×C₄	—	541	1	no	—
26	C₂×C₄	—	541	2	no	—
27	C₂×C₄	—	541	2	no	—
28	C₂×C₄	#14524194	1	1	yes	characteristic
29	C₈	—	541	4	no	—
30	C₂²	—	541	2	no	—
31	C₂²	—	1082	2	no	—
32	C₂²	C₂×#14524194	1	1	yes	characteristic
33	C₄	—	541	1	no	—
34	C₄	—	541	1	no	—
35	C₄	C₂×#14524194	1	2	yes	—
36	C₂	—	1082	2	no	—
37	C₂	#22575846	1	2	yes	direct product factor
38	C₂	C₂²×#14524194	1	1	yes	characteristic

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.