Subgroups — #28385373

Order 14368.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20297736	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₈₉₈	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₁₇₉₆	C₂	1	2	yes	maximal, complemented
4	#20297725	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₄₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₈₉₈	—	2	1	no	—
7	Dic₈₉₈	C₂²	1	2	yes	—
8	Dic₈₉₈	C₂²	1	1	yes	characteristic
9	D₁₇₉₆	C₂²	1	1	yes	characteristic
10	C₂²⋊D₄₄₉	—	2	1	no	—
11	C₂×Dic₄₄₉	—	2	1	no	—
12	C₄×D₄₄₉	—	2	1	no	—
13	C₂×C₄×C₄₄₉	C₂²	1	1	yes	characteristic
14	C₈×C₄₄₉	C₂²	1	2	yes	—
15	C₂²×C₄₄₉	D₄	1	1	yes	characteristic
16	C₂×D₄₄₉	—	2	1	no	—
17	C₄×C₄₄₉	D₄	1	1	yes	characteristic
18	C₄×C₄₄₉	C₂³	1	1	yes	characteristic
19	Dic₄₄₉	—	2	1	no	—
20	Dic₄₄₉	—	2	2	no	—
21	C₂×C₄₄₉	—	2	1	no	—
22	C₂×C₄₄₉	C₂×D₄	1	1	yes	characteristic
23	D₄₄₉	—	4	1	no	—
24	C₄₄₉	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	449	1	no	maximal, Sylow
26	#41	—	449	1	no	—
27	C₂×Q₈	—	449	1	no	—
28	Q₁₆	—	449	2	no	—
29	SD₁₆	—	449	2	no	—
30	M₁₆	D₄₄₉	1	1	yes	characteristic, complemented
31	Q₈	—	898	1	no	—
32	Q₈	—	449	2	no	—
33	Q₈	—	449	1	no	—
34	D₄	—	898	1	no	—
35	D₄	—	449	1	no	—
36	C₂×C₄	—	898	1	no	—
37	C₂×C₄	—	898	1	no	—
38	C₂×C₄	C₂×D₄₄₉	1	1	yes	characteristic
39	C₈	C₂×D₄₄₉	1	2	yes	—
40	C₂²	—	898	1	no	—
41	C₂²	D₁₇₉₆	1	1	yes	characteristic
42	C₄	—	898	1	no	—
43	C₄	—	898	2	no	—
44	C₄	D₁₇₉₆	1	1	yes	characteristic
45	C₄	C₂²×D₄₄₉	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	1796	1	no	—
48	C₂	C₂×D₁₇₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₁₇₉₆
commutator, cosocle	C₄×C₄₄₉	C₂³
Frattini	C₄	C₂²×D₄₄₉
Fitting	M₁₆×C₄₄₉	C₂
socle	C₂×C₄₄₉	C₂×D₄
prime radical	#20297736	C₂
hypercenter	M₁₆	D₄₄₉
hypocenter	C₄₄₉	#137
LCS	G ▷ C₄×C₄₄₉ ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₈₉₈	C₂	semidirect
3. Dic₁₇₉₆	C₂	semidirect
4. #20297725	C₂	semidirect
5. M₁₆×C₄₄₉	C₂	semidirect
24. C₄₄₉	#137	semidirect
30. M₁₆	D₄₄₉	semidirect

Maximal subgroups

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

subgroup	index
#20297736	2
C₂×Dic₈₉₈	2
Dic₁₇₉₆	2
#20297725	2
M₁₆×C₄₄₉	2
#137	449