Subgroups — #34063751

Order 19232.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23751284	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₆₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	M₁₆×C₆₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₂₀₂	C₄	1	1	yes	characteristic, complemented
5	D₂₄₀₄	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊D₆₀₁	—	2	1	no	—
7	C₂×Dic₆₀₁	—	2	1	no	—
8	C₄×D₆₀₁	—	2	1	no	—
9	C₂×C₄×C₆₀₁	C₂²	1	1	yes	characteristic
10	C₈×C₆₀₁	—	2	1	no	—
11	C₂²×C₆₀₁	D₄	1	1	yes	characteristic
12	C₂×D₆₀₁	—	2	1	no	—
13	C₄×C₆₀₁	C₂×C₄	1	1	yes	characteristic
14	C₄×C₆₀₁	D₄	1	1	yes	characteristic
15	Dic₆₀₁	—	2	2	no	—
16	Dic₆₀₁	—	2	1	no	—
17	C₂×C₆₀₁	—	2	1	no	—
18	C₂×C₆₀₁	C₂²⋊C₄	1	1	yes	characteristic
19	D₆₀₁	—	4	1	no	—
20	C₆₀₁	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	601	1	no	maximal, Sylow
22	#41	—	601	1	no	—
23	M₁₆	D₆₀₁	1	1	yes	characteristic, complemented
24	C₄²	—	601	1	no	—
25	Q₈	—	601	1	no	—
26	D₄	—	601	1	no	—
27	D₄	—	1202	1	no	—
28	C₂×C₄	—	1202	1	no	—
29	C₂×C₄	—	1202	1	no	—
30	C₂×C₄	C₂×D₆₀₁	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₂²	—	1202	1	no	—
33	C₂²	D₂₄₀₄	1	1	yes	characteristic
34	C₄	—	1202	2	no	—
35	C₄	—	1202	1	no	—
36	C₄	C₄×D₆₀₁	1	1	yes	characteristic
37	C₄	C₂²⋊D₆₀₁	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	2404	1	no	—
40	C₂	#23751261	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.