Subgroups — #46831068

Order 34624.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772702	C₂	1	2	yes	maximal
2	#31772538	C₂	1	1	yes	maximal, characteristic
3	#22575839	C₄	1	4	yes	complemented
4	C₂×#16864513	C₂²	1	1	yes	characteristic
5	C₄×Dic₅₄₁	C₄	1	1	yes	characteristic
6	C₂×C₈×C₅₄₁	C₄	1	1	yes	characteristic
7	C₂×Dic₅₄₁	—	2	1	no	—
8	#16864513	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
10	C₈×C₅₄₁	—	2	1	no	—
11	C₂²×C₅₄₁	M₁₆	1	1	yes	characteristic
12	C₄×C₅₄₁	C₄²	1	1	yes	characteristic
13	C₄×C₅₄₁	M₁₆	1	1	yes	characteristic
14	Dic₅₄₁	—	4	1	no	—
15	C₂×C₅₄₁	—	2	1	no	—
16	C₂×C₅₄₁	#97	1	1	yes	characteristic
17	C₅₄₁	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	541	1	no	maximal, Sylow
19	M₃₂	—	541	2	no	—
20	#97	—	541	1	no	—
21	C₂×C₈	—	541	1	no	—
22	C₂×C₈	#14524194	1	1	yes	characteristic
23	C₄²	—	541	1	no	—
24	C₁₆	—	541	4	no	—
25	C₂×C₄	—	1082	1	no	—
26	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	541	2	no	—
29	C₂²	#22575846	1	1	yes	characteristic
30	C₄	—	2164	1	no	—
31	C₄	C₄×#14524194	1	1	yes	characteristic
32	C₄	#22575845	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#31772683	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #22575839	C₄	semidirect
17. C₅₄₁	#347	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.