Subgroups — #44442975

Order 29504.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28414192	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#20301504	C₂	1	1	yes	maximal, characteristic, complemented
3	#28414126	C₂	1	1	yes	maximal, characteristic
4	#20301504	—	2	1	no	—
5	#20301504	—	2	1	no	—
6	#20301501	C₄	1	1	yes	characteristic
7	#20301484	—	2	1	no	—
8	C₂×#16814779	C₂²	1	1	yes	characteristic
9	C₈×D₄₆₁	—	2	1	no	—
10	M₁₆×C₄₆₁	C₄	1	1	yes	characteristic
11	Dic₉₂₂	C₈	1	1	yes	characteristic
12	D₁₈₄₄	C₈	1	1	yes	characteristic
13	C₂²⋊D₄₆₁	—	2	1	no	—
14	C₄×D₄₆₁	—	2	1	no	—
15	#16814779	D₄	1	1	yes	characteristic
16	#16814779	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₆₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₄₆₁	—	2	1	no	—
19	C₂²×C₄₆₁	M₁₆	1	1	yes	characteristic
20	C₂×D₄₆₁	—	2	1	no	—
21	C₄×C₄₆₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₄₆₁	C₂×C₈	1	1	yes	characteristic
23	Dic₄₆₁	—	2	1	no	—
24	C₂×C₄₆₁	—	2	1	no	—
25	C₂×C₄₆₁	C₂²⋊C₈	1	1	yes	characteristic
26	D₄₆₁	—	4	1	no	—
27	C₄₆₁	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	461	1	no	maximal, Sylow
29	#131	—	461	1	no	—
30	M₃₂	—	461	1	no	—
31	C₂×C₁₆	—	461	1	no	—
32	#41	—	461	1	no	—
33	M₁₆	—	922	1	no	—
34	M₁₆	#14270406	1	1	yes	characteristic
35	C₂×C₈	—	922	1	no	—
36	C₂×C₈	—	461	1	no	—
37	C₁₆	—	922	1	no	—
38	C₁₆	—	922	1	no	—
39	Q₈	—	461	1	no	—
40	D₄	—	922	1	no	—
41	D₄	—	461	1	no	—
42	C₂×C₄	—	922	1	no	—
43	C₂×C₄	C₂×#14270406	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	461	1	no	—
46	C₈	—	461	1	no	—
47	C₂²	—	922	1	no	—
48	C₂²	#20301511	1	1	yes	characteristic
49	C₄	—	922	1	no	—
50	C₄	C₂²⋊#14270406	1	1	yes	characteristic
51	C₄	D₄₆₁⋊C₈	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	1844	1	no	—
54	C₂	#28414175	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#14270406
commutator	C₄×C₄₆₁	C₂×C₈
Frattini	C₂×C₄	C₂×#14270406
Fitting	M₁₆×C₄₆₁	C₄
socle	C₂×C₄₆₁	C₂²⋊C₈
prime radical	#20301501	C₄
cosocle	C₂×#16814779	C₂²
hypercenter	M₁₆	#14270406
hypocenter	C₄₆₁	#350
LCS	G ▷ C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #28414192	C₂	semidirect
2. C₂×#20301504	C₂	semidirect
27. C₄₆₁	#350	semidirect

Maximal subgroups

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

subgroup	index
#28414192	2
C₂×#20301504	2
#28414126	2
#350	461