Subgroups — C₂×#28385334 #43272532

Order 28736.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385334	C₂	1	8	yes	maximal, direct product factor
2	C₂×#20297715	C₂	1	3	yes	maximal, complemented
3	C₂×#20297713	C₂	1	3	yes	maximal
4	C₂×C₄²×C₄₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₄₄₉	C₂²	1	1	yes	characteristic
6	C₂²×Dic₄₄₉	C₂²	1	3	yes	—
7	#20297715	C₂²	1	12	yes	complemented
8	#20297713	C₂²	1	12	yes	—
9	C₂²×C₄×C₄₄₉	C₂²	1	3	yes	—
10	C₄²×C₄₄₉	C₂²	1	4	yes	complemented
11	C₂²×D₄₄₉	—	2	6	no	—
12	C₂²×D₄₄₉	C₂³	1	2	yes	—
13	C₂×Dic₄₄₉	—	2	6	no	—
14	C₂×Dic₄₄₉	C₂³	1	6	yes	—
15	C₂³×C₄₄₉	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₄₄₉	—	2	6	no	—
17	C₂×C₄×C₄₄₉	C₂³	1	6	yes	—
18	C₂²×C₄₄₉	#41	1	6	yes	—
19	C₂²×C₄₄₉	C₂⁴	1	1	yes	characteristic
20	C₂×D₄₄₉	—	2	6	no	—
21	C₂×D₄₄₉	—	4	4	no	—
22	C₄×C₄₄₉	—	2	6	no	—
23	Dic₄₄₉	—	2	6	no	—
24	C₂×C₄₄₉	#126	1	4	yes	complemented
25	C₂×C₄₄₉	C₂×#41	1	3	yes	—
26	D₄₄₉	—	4	2	no	—
27	C₄₄₉	C₂×#126	1	1	yes	characteristic, complemented, Sylow
28	C₂×#126	—	449	1	no	maximal, Sylow
29	#126	—	449	8	no	—
30	C₂×C₄⋊C₄	—	449	3	no	—
31	C₂×C₂²⋊C₄	—	449	3	no	—
32	C₂×C₄²	D₄₄₉	1	1	yes	characteristic, complemented
33	C₂⁴	—	449	1	no	—
34	C₂²×C₄	—	449	3	no	—
35	C₂²×C₄	C₂×D₄₄₉	1	3	yes	—
36	C₄⋊C₄	—	449	12	no	—
37	C₂²⋊C₄	—	449	12	no	—
38	C₄²	C₂×D₄₄₉	1	4	yes	complemented
39	C₂³	—	898	6	no	—
40	C₂³	—	449	2	no	—
41	C₂³	C₂²×D₄₄₉	1	1	yes	characteristic
42	C₂×C₄	—	2	6	no	—
43	C₂×C₄	—	898	6	no	—
44	C₂×C₄	—	449	6	no	—
45	C₂×C₄	C₂²×D₄₄₉	1	6	yes	—
46	C₂²	—	1796	4	no	—
47	C₂²	—	898	6	no	—
48	C₂²	#20297736	1	6	yes	—
49	C₂²	C₂³×D₄₄₉	1	1	yes	characteristic
50	C₄	—	2	6	no	—
51	C₄	—	898	6	no	—
52	C₂	—	1796	2	no	—
53	C₂	#28385334	1	4	yes	direct product factor
54	C₂	C₂×#20297736	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₄₄₉
commutator, cosocle	C₂²×C₄₄₉	C₂⁴
Frattini	C₂²	C₂³×D₄₄₉
Fitting	C₂×C₄²×C₄₄₉	C₂
socle	C₂³×C₄₄₉	C₂³
prime radical	C₂³×D₄₄₉	C₂²
hypercenter	C₂×C₄²	D₄₄₉
hypocenter	C₄₄₉	C₂×#126
LCS	G ▷ C₂²×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #28385334	C₂	direct (N × H)
2. C₂×#20297715	C₂	semidirect
4. C₂×C₄²×C₄₄₉	C₂	semidirect
7. #20297715	C₂²	semidirect
10. C₄²×C₄₄₉	C₂²	semidirect
24. C₂×C₄₄₉	#126	semidirect
27. C₄₄₉	C₂×#126	semidirect
32. C₂×C₄²	D₄₄₉	semidirect
38. C₄²	C₂×D₄₄₉	semidirect
53. C₂	#28385334	direct (N × H)

Maximal subgroups

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

subgroup	index
#28385334	2
C₂×#20297715	2
C₂×#20297713	2
C₂×C₄²×C₄₄₉	2
C₂×#126	449

Subgroups — C2×#28385334 #43272532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#28385334 #43272532