Subgroups — #44509739

Order 30848.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29507551	C₂	1	3	yes	maximal, complemented
2	C₂×#21440548	C₂	1	3	yes	maximal, complemented
3	#504×C₂₄₁	C₂	1	1	yes	maximal, characteristic
4	#21440548	C₂²	1	1	yes	characteristic
5	#21440548	C₂²	1	3	yes	—
6	#131×C₂₄₁	C₄	1	1	yes	characteristic
7	M₃₂×C₂₄₁	C₄	1	3	yes	—
8	C₂×C₁₆×C₂₄₁	C₂²	1	3	yes	—
9	#41×C₂₄₁	C₈	1	1	yes	characteristic
10	M₁₆×C₂₄₁	C₈	1	3	yes	—
11	C₂×C₈×C₂₄₁	C₂×C₄	1	3	yes	—
12	C₁₆×C₂₄₁	C₂×C₄	1	3	yes	—
13	C₁₆×C₂₄₁	C₂³	1	1	yes	characteristic
14	Q₈×C₂₄₁	C₁₆	1	1	yes	characteristic
15	D₄×C₂₄₁	C₁₆	1	3	yes	—
16	C₂×C₄×C₂₄₁	C₂×C₈	1	3	yes	—
17	C₈×C₂₄₁	C₂×C₈	1	3	yes	—
18	C₈×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₂₄₁	C₂×C₁₆	1	3	yes	—
20	C₄×C₂₄₁	C₂×C₁₆	1	3	yes	—
21	C₄×C₂₄₁	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₂₄₁	—	2	3	no	—
23	C₂×C₂₄₁	C₂²×C₁₆	1	1	yes	characteristic
24	C₂₄₁	#2258	1	1	yes	characteristic, complemented, Sylow
25	#2258	—	241	1	no	maximal, Sylow
26	#504	D₂₄₁	1	1	yes	characteristic
27	M₆₄	—	241	3	no	—
28	C₂×C₃₂	—	241	3	no	—
29	#131	Dic₂₄₁	1	1	yes	characteristic
30	M₃₂	Dic₂₄₁	1	3	yes	—
31	C₂×C₁₆	C₂×D₂₄₁	1	3	yes	—
32	C₃₂	—	241	1	no	—
33	C₃₂	—	241	3	no	—
34	#41	#14515349	1	1	yes	characteristic
35	M₁₆	#14515349	1	3	yes	—
36	C₂×C₈	C₂×Dic₂₄₁	1	3	yes	—
37	C₁₆	C₂×Dic₂₄₁	1	3	yes	—
38	C₁₆	C₂²×D₂₄₁	1	1	yes	characteristic
39	Q₈	#16838745	1	1	yes	characteristic
40	D₄	#16838745	1	3	yes	—
41	C₂×C₄	C₂×#14515349	1	3	yes	—
42	C₈	C₂×#14515349	1	3	yes	—
43	C₈	C₂²×Dic₂₄₁	1	1	yes	characteristic
44	C₂²	C₂×#16838745	1	3	yes	—
45	C₄	C₂×#16838745	1	3	yes	—
46	C₄	C₂²×#14515349	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#16838745	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₂₄₁
commutator, socle	C₂×C₂₄₁	C₂²×C₁₆
Fitting	#504×C₂₄₁	C₂
prime radical	#41×C₂₄₁	C₈
cosocle	C₁₆×C₂₄₁	C₂³
hypercenter	#504	D₂₄₁
hypocenter	C₂₄₁	#2258
LCS	G ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #29507551	C₂	semidirect
2. C₂×#21440548	C₂	semidirect
24. C₂₄₁	#2258	semidirect

Maximal subgroups

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

subgroup	index
#29507551	2
C₂×#21440548	2
#504×C₂₄₁	2
#2258	241