Subgroups — #44505646

Order 30848.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21440548	C₂	1	1	yes	maximal, characteristic
2	#29507543	C₂	1	1	yes	maximal, characteristic
3	#366×C₂₄₁	C₂	1	1	yes	maximal, characteristic
4	#21440576	—	2	1	no	—
5	#21440548	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₂₄₁	C₂²	1	1	yes	characteristic
7	#107×C₂₄₁	—	2	1	no	—
8	C₄⋊Dic₂₄₁	—	4	1	no	—
9	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₂₄₁	—	4	1	no	—
11	C₁₆×C₂₄₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₄₁	Q₈	1	1	yes	characteristic
13	C₂×Dic₂₄₁	—	8	1	no	—
14	C₂×C₄×C₂₄₁	—	8	1	no	—
15	C₂×C₄×C₂₄₁	D₈	1	1	yes	characteristic
16	C₈×C₂₄₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₄₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₄₁	D₁₆	1	1	yes	characteristic
19	C₄×C₂₄₁	—	16	1	no	—
20	C₄×C₂₄₁	#107	1	1	yes	characteristic
21	C₄×C₂₄₁	Q₃₂	1	1	yes	characteristic
22	Dic₂₄₁	—	16	1	no	—
23	C₂×C₂₄₁	#366	1	1	yes	characteristic
24	C₂×C₂₄₁	SD₆₄	1	1	yes	characteristic
25	C₂×C₂₄₁	SD₆₄	1	1	yes	characteristic
26	C₂₄₁	#1424	1	1	yes	characteristic, complemented, Sylow
27	#1424	—	241	1	no	maximal, Sylow
28	C₂×C₃₂	—	241	1	no	—
29	#366	—	241	1	no	—
30	#366	D₂₄₁	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₂₄₁	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	482	1	no	—
34	C₃₂	—	241	2	no	—
35	C₂×C₈	C₂²⋊D₂₄₁	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	964	1	no	—
38	C₁₆	C₄×D₂₄₁	1	1	yes	characteristic
39	C₁₆	Dic₄₈₂	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	1928	1	no	—
42	C₂×C₄	#16838755	1	1	yes	characteristic
43	C₈	#16838749	1	1	yes	characteristic
44	C₈	#16838760	1	1	yes	characteristic
45	C₂²	#21440583	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	3856	1	no	—
48	C₄	#21440575	1	1	yes	characteristic
49	C₄	#21440588	1	1	yes	characteristic
50	C₂	#29507542	1	1	yes	characteristic
51	C₂	#29507554	1	1	yes	characteristic
52	C₂	#29507555	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#21440583
commutator	C₁₆×C₂₄₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₄₁
Fitting	#366×C₂₄₁	C₂
socle, prime radical	C₂²×C₂₄₁	D₁₆
cosocle	C₂×C₁₆×C₂₄₁	C₂²
hypercenter	#366	D₂₄₁
hypocenter	C₂₄₁	#1424
LCS	G ▷ C₁₆×C₂₄₁ ▷ C₈×C₂₄₁ ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. #21440548	C₄	semidirect
26. C₂₄₁	#1424	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21440548	2
#29507543	2
#366×C₂₄₁	2
#1424	241