Subgroups — C₂×#28414189 #44443090

Order 29504.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20301511	C₂	1	2	yes	maximal
2	#28414189	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₄₆₁	C₂	1	1	yes	maximal, characteristic
4	#20301511	—	2	2	no	—
5	#20301511	C₂²	1	4	yes	—
6	C₂×#16814786	—	2	2	no	—
7	C₂×C₄×D₄₆₁	C₂²	1	1	yes	characteristic
8	C₂×#16814779	C₄	1	1	yes	characteristic
9	C₈×D₄₆₁	C₄	1	2	yes	—
10	C₈×D₄₆₁	C₂²	1	2	yes	—
11	C₂×C₈×C₄₆₁	C₄	1	1	yes	characteristic
12	#16814786	—	2	4	no	—
13	C₂²×D₄₆₁	Q₈	1	1	yes	characteristic
14	C₂×Dic₄₆₁	D₄	1	1	yes	characteristic
15	C₄×D₄₆₁	C₂×C₄	1	1	yes	characteristic
16	C₄×D₄₆₁	D₄	1	1	yes	characteristic
17	C₄×D₄₆₁	Q₈	1	1	yes	characteristic
18	C₄×D₄₆₁	C₂³	1	1	yes	characteristic
19	#16814779	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₄₆₁	C₂×C₄	1	1	yes	characteristic
21	C₈×C₄₆₁	C₂×C₄	1	2	yes	—
22	C₂²×C₄₆₁	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₄₆₁	—	2	2	no	—
24	C₂×D₄₆₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₄₆₁	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₄₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
28	Dic₄₆₁	C₄⋊C₄	1	1	yes	characteristic
29	Dic₄₆₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄₆₁	#108	1	2	yes	complemented
31	C₂×C₄₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₄₆₁	—	2	1	no	—
33	D₄₆₁	—	2	1	no	—
34	C₄₆₁	C₂×#108	1	1	yes	characteristic, complemented, Sylow
35	C₂×#108	—	461	1	no	maximal, Sylow
36	C₂×M₁₆	—	461	2	no	—
37	C₂²×C₈	—	461	1	no	—
38	#108	—	461	4	no	—
39	C₂²×C₄	—	461	1	no	—
40	M₁₆	—	922	2	no	—
41	M₁₆	—	461	4	no	—
42	C₂×C₈	—	922	2	no	—
43	C₂×C₈	—	461	1	no	—
44	C₂×C₈	—	461	2	no	—
45	C₂×C₈	—	461	2	no	—
46	C₂×C₈	#14270406	1	1	yes	characteristic
47	C₂³	—	461	1	no	—
48	C₂×C₄	—	461	1	no	—
49	C₂×C₄	—	461	1	no	—
50	C₂×C₄	—	461	1	no	—
51	C₂×C₄	—	461	1	no	—
52	C₂×C₄	—	461	1	no	—
53	C₂×C₄	C₂×#14270406	1	1	yes	characteristic
54	C₈	—	922	4	no	—
55	C₈	—	461	2	no	—
56	C₈	C₂×#14270406	1	2	yes	—
57	C₂²	—	922	2	no	—
58	C₂²	—	461	1	no	—
59	C₂²	—	461	1	no	—
60	C₂²	C₄⋊#14270406	1	1	yes	characteristic
61	C₄	—	461	1	no	—
62	C₄	—	461	1	no	—
63	C₄	C₄⋊#14270406	1	1	yes	characteristic
64	C₄	C₂²×#14270406	1	1	yes	characteristic
65	C₂	—	922	1	no	—
66	C₂	—	922	1	no	—
67	C₂	#28414189	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#14270406	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#14270406
commutator	C₄×C₄₆₁	C₂²×C₄
Frattini	C₄	C₂²×#14270406
Fitting	C₂×C₈×C₄₆₁	C₄
socle	C₂²×C₄₆₁	C₄⋊C₄
prime radical	C₂²×D₄₆₁	Q₈
cosocle	C₄×D₄₆₁	C₂³
hypercenter	C₂×C₈	#14270406
hypocenter	C₄₆₁	C₂×#108
LCS	G ▷ C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #28414189	C₂	direct (N × H)
30. C₂×C₄₆₁	#108	semidirect
34. C₄₆₁	C₂×#108	semidirect
67. C₂	#28414189	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#20301511	2
#28414189	2
C₂×C₈×D₄₆₁	2
C₂×#108	461

Subgroups — C2×#28414189 #44443090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#28414189 #44443090