Subgroups — #29508616

Order 15424.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21440716	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16838773	C₂	1	1	yes	maximal, characteristic, complemented
3	#21440650	C₂	1	1	yes	maximal, characteristic
4	#16838773	—	2	1	no	—
5	#16838773	—	2	1	no	—
6	#16838770	C₄	1	1	yes	characteristic
7	#16838753	—	2	1	no	—
8	C₂×#14515349	C₂²	1	1	yes	characteristic
9	C₈×D₂₄₁	—	2	1	no	—
10	M₁₆×C₂₄₁	C₄	1	1	yes	characteristic
11	Dic₄₈₂	C₈	1	1	yes	characteristic
12	D₉₆₄	C₈	1	1	yes	characteristic
13	C₂²⋊D₂₄₁	—	2	1	no	—
14	C₄×D₂₄₁	—	2	1	no	—
15	#14515349	D₄	1	1	yes	characteristic
16	#14515349	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₂₄₁	—	2	1	no	—
19	C₂²×C₂₄₁	M₁₆	1	1	yes	characteristic
20	C₂×D₂₄₁	—	2	1	no	—
21	C₄×C₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₂₄₁	C₂×C₈	1	1	yes	characteristic
23	Dic₂₄₁	—	2	1	no	—
24	C₂×C₂₄₁	—	2	1	no	—
25	C₂×C₂₄₁	C₂²⋊C₈	1	1	yes	characteristic
26	D₂₄₁	—	4	1	no	—
27	C₂₄₁	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	241	1	no	maximal, Sylow
29	#131	—	241	1	no	—
30	M₃₂	—	241	1	no	—
31	C₂×C₁₆	—	241	1	no	—
32	#41	—	241	1	no	—
33	M₁₆	—	482	1	no	—
34	M₁₆	#11757210	1	1	yes	characteristic
35	C₂×C₈	—	482	1	no	—
36	C₂×C₈	—	241	1	no	—
37	C₁₆	—	482	1	no	—
38	C₁₆	—	482	1	no	—
39	Q₈	—	241	1	no	—
40	D₄	—	482	1	no	—
41	D₄	—	241	1	no	—
42	C₂×C₄	—	482	1	no	—
43	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	241	1	no	—
46	C₈	—	241	1	no	—
47	C₂²	—	482	1	no	—
48	C₂²	#16838780	1	1	yes	characteristic
49	C₄	—	482	1	no	—
50	C₄	C₂²⋊#11757210	1	1	yes	characteristic
51	C₄	#16838778	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	964	1	no	—
54	C₂	#21440699	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#11757210
commutator	C₄×C₂₄₁	C₂×C₈
Frattini	C₂×C₄	C₂×#11757210
Fitting	M₁₆×C₂₄₁	C₄
socle	C₂×C₂₄₁	C₂²⋊C₈
prime radical	#16838770	C₄
cosocle	C₂×#14515349	C₂²
hypercenter	M₁₆	#11757210
hypocenter	C₂₄₁	#350
LCS	G ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #21440716	C₂	semidirect
2. C₂×#16838773	C₂	semidirect
27. C₂₄₁	#350	semidirect

Maximal subgroups

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

subgroup	index
#21440716	2
C₂×#16838773	2
#21440650	2
#350	241