Subgroups — #43273104

Order 28736.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20297748	C₂	1	2	yes	maximal, complemented
2	C₂×#20297744	C₂	1	1	yes	maximal, characteristic
3	#20297748	—	2	2	no	—
4	#20297744	—	2	2	no	—
5	C₂×#16813318	C₄	1	1	yes	characteristic
6	C₂×#16813318	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄₄₉	C₄	1	1	yes	characteristic
8	#16813318	—	2	1	no	—
9	#16813318	D₄	1	2	yes	—
10	C₂²×D₄₄₉	C₈	1	1	yes	characteristic
11	C₂×Dic₄₄₉	C₂×C₄	1	1	yes	characteristic
12	C₄×D₄₄₉	—	2	1	no	—
13	C₄×D₄₄₉	—	2	1	no	—
14	C₂×C₄×C₄₄₉	C₈	1	1	yes	characteristic
15	C₂²×C₄₄₉	C₂×C₈	1	1	yes	characteristic
16	C₂×D₄₄₉	—	2	1	no	—
17	C₂×D₄₄₉	—	2	1	no	—
18	C₂×D₄₄₉	C₁₆	1	2	yes	complemented
19	C₄×C₄₄₉	—	2	1	no	—
20	Dic₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
21	Dic₄₄₉	M₁₆	1	1	yes	characteristic
22	C₂×C₄₄₉	C₂²⋊C₈	1	1	yes	characteristic
23	C₂×C₄₄₉	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₄₄₉	M₃₂	1	1	yes	characteristic
25	D₄₄₉	—	2	2	no	—
26	C₄₄₉	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	449	1	no	maximal, Sylow
28	C₂²×C₈	—	449	1	no	—
29	C₂×C₁₆	—	449	2	no	—
30	C₂²×C₄	—	449	1	no	—
31	C₂×C₈	—	898	2	no	—
32	C₂×C₈	—	449	1	no	—
33	C₂×C₈	—	449	1	no	—
34	C₁₆	—	898	2	no	—
35	C₂³	—	449	1	no	—
36	C₂×C₄	—	898	1	no	—
37	C₂×C₄	—	898	1	no	—
38	C₂×C₄	—	449	1	no	—
39	C₂×C₄	#16813320	1	1	yes	characteristic
40	C₈	—	898	1	no	—
41	C₈	—	449	2	no	—
42	C₂²	—	898	1	no	—
43	C₂²	—	898	1	no	—
44	C₂²	—	449	2	no	—
45	C₂²	C₂×#16813320	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	449	1	no	—
48	C₄	—	449	1	no	—
49	C₂	—	898	2	no	—
50	C₂	C₂²⋊#16813320	1	1	yes	characteristic
51	C₂	#28385435	1	1	yes	characteristic
52	C₂	#28385437	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#16813320
commutator	C₂×C₄₄₉	C₂×C₁₆
Fitting	C₂×C₄×C₄₄₉	C₈
socle	C₂²×C₄₄₉	C₂×C₈
prime radical	C₂²×D₄₄₉	C₈
cosocle	C₂×#16813318	C₂²
hypercenter	C₂×C₄	#16813320
hypocenter	C₄₄₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#20297748	C₂	semidirect
18. C₂×D₄₄₉	C₁₆	semidirect
26. C₄₄₉	C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20297748	2
C₂×#20297744	2
C₂²⋊C₁₆	449