Subgroups — C₂×#28414028 #44442024

Order 29504.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16814779	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₆₁	C₂	1	1	yes	maximal, characteristic
3	#28414028	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₄₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₄₆₁	C₄	1	2	yes	—
6	C₂×#16814779	C₄	1	4	yes	complemented
7	C₂×#16814779	C₂²	1	2	yes	—
8	C₄×Dic₄₆₁	C₄	1	2	yes	—
9	C₄×Dic₄₆₁	C₂²	1	2	yes	—
10	C₂²×C₄×C₄₆₁	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₄₆₁	C₄	1	4	yes	complemented
12	C₂×C₈×C₄₆₁	C₂²	1	2	yes	—
13	C₂×Dic₄₆₁	—	2	4	no	—
14	C₂×Dic₄₆₁	C₂×C₄	1	4	yes	—
15	#16814779	C₂×C₄	1	4	yes	complemented
16	C₂³×C₄₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₆₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₄₆₁	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₄₆₁	C₂³	1	1	yes	characteristic
21	C₈×C₄₆₁	C₂×C₄	1	4	yes	complemented
22	C₂²×C₄₆₁	C₄²	1	2	yes	—
23	C₂²×C₄₆₁	M₁₆	1	4	yes	—
24	C₂²×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₄₆₁	C₄²	1	2	yes	—
26	C₄×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
28	Dic₄₆₁	—	2	4	no	—
29	C₂×C₄₆₁	#97	1	4	yes	complemented
30	C₂×C₄₆₁	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₄₆₁	C₂×M₁₆	1	2	yes	—
32	C₄₆₁	C₂×#97	1	1	yes	characteristic, complemented, Sylow
33	C₂×#97	—	461	1	no	maximal, Sylow
34	C₂²×C₈	—	461	1	no	—
35	C₂²×C₈	D₄₆₁	1	1	yes	characteristic
36	C₂×C₄²	—	461	1	no	—
37	#97	—	461	4	no	—
38	C₂²×C₄	—	461	2	no	—
39	C₂²×C₄	C₂×D₄₆₁	1	1	yes	characteristic
40	C₂×C₈	—	461	4	no	—
41	C₂×C₈	—	461	2	no	—
42	C₂×C₈	Dic₄₆₁	1	4	yes	complemented
43	C₂×C₈	C₂×D₄₆₁	1	2	yes	—
44	C₄²	—	461	2	no	—
45	C₄²	—	461	2	no	—
46	C₂³	C₄×D₄₆₁	1	1	yes	characteristic
47	C₂×C₄	—	922	4	no	—
48	C₂×C₄	—	461	4	no	—
49	C₂×C₄	C₄×D₄₆₁	1	1	yes	characteristic
50	C₂×C₄	C₄×D₄₆₁	1	2	yes	—
51	C₂×C₄	C₂×Dic₄₆₁	1	2	yes	—
52	C₂×C₄	C₂²×D₄₆₁	1	1	yes	characteristic
53	C₈	—	461	4	no	—
54	C₈	C₂×Dic₄₆₁	1	4	yes	complemented
55	C₂²	C₄×Dic₄₆₁	1	2	yes	—
56	C₂²	#20301484	1	4	yes	—
57	C₂²	C₂×C₄×D₄₆₁	1	1	yes	characteristic
58	C₄	—	922	4	no	—
59	C₄	C₄×Dic₄₆₁	1	2	yes	—
60	C₄	C₂×C₄×D₄₆₁	1	1	yes	characteristic
61	C₄	C₂²×Dic₄₆₁	1	1	yes	characteristic
62	C₂	#28414028	1	4	yes	direct product factor
63	C₂	C₂×C₄×Dic₄₆₁	1	1	yes	characteristic
64	C₂	C₂×#20301484	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₆₁
commutator	C₂×C₄₆₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₄₆₁
Fitting	C₂²×C₈×C₄₆₁	C₂
socle, prime radical	C₂³×C₄₆₁	C₂×C₄
cosocle	C₂×C₄×C₄₆₁	C₂³
hypercenter	C₂²×C₈	D₄₆₁
hypocenter	C₄₆₁	C₂×#97
LCS	G ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #28414028	C₂	direct (N × H)
6. C₂×#16814779	C₄	semidirect
11. C₂×C₈×C₄₆₁	C₄	semidirect
15. #16814779	C₂×C₄	semidirect
21. C₈×C₄₆₁	C₂×C₄	semidirect
29. C₂×C₄₆₁	#97	semidirect
32. C₄₆₁	C₂×#97	semidirect
42. C₂×C₈	Dic₄₆₁	semidirect
54. C₈	C₂×Dic₄₆₁	semidirect
62. C₂	#28414028	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#16814779	2
C₂×C₄×Dic₄₆₁	2
#28414028	2
C₂²×C₈×C₄₆₁	2
C₂×#97	461

Subgroups — C2×#28414028 #44442024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#28414028 #44442024