Subgroups — #44443123

Order 29504.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28414205	C₂	1	2	yes	maximal, complemented
2	#28414188	C₂	1	1	yes	maximal, characteristic, complemented
3	#28414182	C₂	1	2	yes	maximal, complemented
4	#28414172	C₂	1	1	yes	maximal, characteristic, complemented
5	#28414137	C₂	1	1	yes	maximal, characteristic
6	#20301511	C₂²	1	2	yes	—
7	#20301510	—	2	2	no	—
8	D₄₆₁⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×#16814786	—	2	2	no	—
10	C₄×#14270406	C₂²	1	1	yes	characteristic
11	#20301500	C₂²	1	2	yes	—
12	Dic₁₈₄₄	C₄	1	1	yes	characteristic, complemented
13	#20301489	C₄	1	2	yes	complemented
14	C₈×D₄₆₁	C₂²	1	1	yes	characteristic
15	D₈×C₄₆₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#14270406	—	2	1	no	—
17	#16814786	—	2	2	no	—
18	#16814786	D₄	1	2	yes	—
19	Dic₉₂₂	C₂×C₄	1	2	yes	—
20	C₂²⋊D₄₆₁	—	2	2	no	—
21	C₂×Dic₄₆₁	—	2	2	no	—
22	C₄×D₄₆₁	C₂³	1	1	yes	characteristic
23	#16814779	C₂×C₄	1	1	yes	characteristic
24	D₄×C₄₆₁	C₂×C₄	1	2	yes	—
25	C₈×C₄₆₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₆₁	—	2	2	no	—
27	C₂×D₄₆₁	#41	1	1	yes	characteristic
28	#14270406	—	4	1	no	—
29	C₄×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
30	Dic₄₆₁	—	2	2	no	—
31	Dic₄₆₁	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄₆₁	—	4	2	no	—
33	C₂×C₄₆₁	C₄×D₄	1	1	yes	characteristic
34	D₄₆₁	—	2	1	no	—
35	C₄₆₁	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	461	1	no	maximal, Sylow
37	#135	—	461	1	no	—
38	#131	—	461	2	no	—
39	#108	—	461	1	no	—
40	#104	—	461	2	no	—
41	#97	—	461	1	no	—
42	#41	—	461	2	no	—
43	Q₁₆	—	461	1	no	—
44	SD₁₆	—	461	2	no	—
45	D₈	#14270406	1	1	yes	characteristic, complemented
46	M₁₆	—	922	2	no	—
47	M₁₆	—	461	2	no	—
48	C₂×C₈	—	922	2	no	—
49	C₂×C₈	—	461	1	no	—
50	C₂×C₈	—	461	1	no	—
51	C₄²	—	461	1	no	—
52	Q₈	—	461	2	no	—
53	D₄	—	922	2	no	—
54	D₄	C₂×#14270406	1	2	yes	—
55	C₂×C₄	—	922	1	no	—
56	C₂×C₄	—	922	2	no	—
57	C₂×C₄	—	461	1	no	—
58	C₈	—	922	2	no	—
59	C₈	—	461	2	no	—
60	C₈	—	461	1	no	—
61	C₈	C₂×#14270406	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	461	1	no	—
64	C₄	—	1844	1	no	—
65	C₄	—	922	2	no	—
66	C₄	—	461	1	no	—
67	C₄	C₂²×#14270406	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	922	1	no	—
70	C₂	D₄×#14270406	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#14270406
commutator	C₄×C₄₆₁	C₂²×C₄
Frattini	C₄	C₂²×#14270406
Fitting	D₈×C₄₆₁	C₄
socle	C₂×C₄₆₁	C₄×D₄
prime radical	#28414137	C₂
cosocle	C₄×D₄₆₁	C₂³
hypercenter	D₈	#14270406
hypocenter	C₄₆₁	#444
LCS	G ▷ C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #28414205	C₂	semidirect
2. #28414188	C₂	semidirect
3. #28414182	C₂	semidirect
4. #28414172	C₂	semidirect
12. Dic₁₈₄₄	C₄	semidirect
13. #20301489	C₄	semidirect
15. D₈×C₄₆₁	C₄	semidirect
35. C₄₆₁	#444	semidirect
45. D₈	#14270406	semidirect

Maximal subgroups

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

subgroup	index
#28414205	2
#28414188	2
#28414182	2
#28414172	2
#28414137	2
#444	461