Subgroups — #35203091

Order 20288.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23778687	C₂	1	6	yes	maximal
2	C₂×C₄²×C₃₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₃₁₇	C₂²	1	4	yes	—
4	C₂²×C₄×C₃₁₇	C₂²	1	3	yes	—
5	C₄²×C₃₁₇	C₄	1	4	yes	complemented
6	C₂×Dic₃₁₇	—	2	12	no	—
7	C₂³×C₃₁₇	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₃₁₇	—	2	6	no	—
9	C₂×C₄×C₃₁₇	C₂×C₄	1	6	yes	—
10	C₂²×C₃₁₇	C₂²×C₄	1	1	yes	characteristic
11	C₂²×C₃₁₇	#41	1	6	yes	—
12	C₄×C₃₁₇	—	2	6	no	—
13	Dic₃₁₇	—	4	4	no	—
14	C₂×C₃₁₇	#117	1	3	yes	—
15	C₂×C₃₁₇	#126	1	4	yes	—
16	C₃₁₇	#383	1	1	yes	characteristic, complemented, Sylow
17	#383	—	317	1	no	maximal, Sylow
18	C₂×C₄²	D₃₁₇	1	1	yes	characteristic
19	#95	—	317	6	no	—
20	C₂²×C₄	—	317	4	no	—
21	C₂²×C₄	C₂×D₃₁₇	1	3	yes	—
22	C₄²	Dic₃₁₇	1	4	yes	complemented
23	C₂³	C₂²×D₃₁₇	1	1	yes	characteristic
24	C₂×C₄	—	2	6	no	—
25	C₂×C₄	—	634	12	no	—
26	C₂×C₄	C₂×Dic₃₁₇	1	6	yes	—
27	C₂²	C₂²×Dic₃₁₇	1	1	yes	characteristic
28	C₂²	#19099574	1	6	yes	—
29	C₄	—	2	6	no	—
30	C₄	—	1268	4	no	—
31	C₂	#23778739	1	3	yes	—
32	C₂	#23778774	1	4	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.