Subgroups — #46831099

Order 34624.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772698	C₂	1	1	yes	maximal, characteristic
2	#31772696	C₂	1	1	yes	maximal, characteristic
3	#31772567	C₂	1	1	yes	maximal, characteristic
4	#22575846	—	2	1	no	—
5	C₄⋊#14524194	—	2	1	no	—
6	C₈×D₅₄₁	C₂²	1	1	yes	characteristic
7	#22575811	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₅₄₁	C₄	1	1	yes	characteristic, complemented
9	C₂×#14524194	—	4	1	no	—
10	#16864520	—	4	1	no	—
11	C₄×D₅₄₁	D₄	1	1	yes	characteristic
12	#16864513	Q₈	1	1	yes	characteristic
13	C₈×C₅₄₁	C₂×C₄	1	1	yes	characteristic
14	C₂×D₅₄₁	SD₁₆	1	1	yes	characteristic
15	#14524194	—	8	1	no	—
16	C₄×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
17	Dic₅₄₁	SD₁₆	1	1	yes	characteristic
18	C₂×C₅₄₁	#106	1	1	yes	characteristic
19	D₅₄₁	—	2	1	no	—
20	C₅₄₁	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	541	1	no	maximal, Sylow
22	M₃₂	—	541	1	no	—
23	#108	—	541	1	no	—
24	#106	—	541	1	no	—
25	M₁₆	—	1082	1	no	—
26	C₂×C₈	—	541	1	no	—
27	C₄⋊C₄	—	1082	1	no	—
28	C₁₆	—	541	1	no	—
29	C₁₆	#14524194	1	1	yes	characteristic, complemented
30	C₂×C₄	—	541	1	no	—
31	C₂×C₄	—	2164	1	no	—
32	C₈	—	541	1	no	—
33	C₈	—	2164	1	no	—
34	C₈	C₂×#14524194	1	1	yes	characteristic
35	C₂²	—	541	1	no	—
36	C₄	—	541	1	no	—
37	C₄	—	4328	1	no	—
38	C₄	C₄⋊#14524194	1	1	yes	characteristic
39	C₂	—	1082	1	no	—
40	C₂	#31772696	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.