Subgroups — #44442917

Order 29504.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#16814786	C₂	1	2	yes	maximal
2	C₈×Dic₄₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#16814786	C₄	1	4	yes	—
4	C₂×#16814779	C₄	1	1	yes	characteristic
5	C₄×Dic₄₆₁	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₆₁	C₄	1	1	yes	characteristic
7	#16814786	—	2	4	no	—
8	C₂×Dic₄₆₁	C₂×C₄	1	2	yes	—
9	#16814779	C₈	1	2	yes	complemented
10	C₂×C₄×C₄₆₁	C₂×C₄	1	1	yes	characteristic
11	C₈×C₄₆₁	C₈	1	2	yes	complemented
12	C₂²×C₄₆₁	C₄²	1	1	yes	characteristic
13	C₄×C₄₆₁	C₂×C₈	1	1	yes	characteristic
14	C₄×C₄₆₁	C₂×C₈	1	1	yes	characteristic
15	Dic₄₆₁	M₁₆	1	4	yes	—
16	C₂×C₄₆₁	C₄×C₈	1	1	yes	characteristic
17	C₂×C₄₆₁	#97	1	2	yes	—
18	C₄₆₁	#322	1	1	yes	characteristic, complemented, Sylow
19	#322	—	461	1	no	maximal, Sylow
20	C₄×C₈	—	461	2	no	—
21	C₄×C₈	—	461	1	no	—
22	C₂×C₈	—	461	4	no	—
23	C₂×C₈	—	461	1	no	—
24	C₂×C₈	#14270406	1	1	yes	characteristic
25	C₄²	—	461	1	no	—
26	C₂×C₄	—	461	2	no	—
27	C₂×C₄	C₂×#14270406	1	1	yes	characteristic
28	C₈	—	922	4	no	—
29	C₈	—	461	2	no	—
30	C₈	#16814786	1	2	yes	complemented
31	C₂²	C₄×#14270406	1	1	yes	characteristic
32	C₄	—	461	4	no	—
33	C₄	C₂×#16814786	1	1	yes	characteristic
34	C₄	D₄₆₁⋊C₈	1	1	yes	characteristic
35	C₂	C₄×#16814786	1	1	yes	characteristic
36	C₂	#28414172	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.