Subgroups — #28385402

Order 14368.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20297744	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#14267798	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₄₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#14267798	—	2	1	no	—
5	#16813318	—	2	1	no	—
6	C₂²×D₄₄₉	—	2	1	no	—
7	D₁₇₉₆	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊D₄₄₉	—	2	1	no	—
9	C₄×D₄₄₉	C₂²	1	1	yes	characteristic
10	D₄×C₄₄₉	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₄₄₉	—	2	1	no	—
12	C₂×D₄₄₉	—	2	1	no	—
13	C₂×D₄₄₉	—	4	1	no	—
14	C₂×D₄₄₉	—	4	1	no	—
15	C₂×D₄₄₉	D₄	1	1	yes	characteristic
16	#14267798	—	4	1	no	—
17	C₄×C₄₄₉	C₂×C₄	1	1	yes	characteristic
18	Dic₄₄₉	D₄	1	1	yes	characteristic
19	C₂×C₄₄₉	—	4	1	no	—
20	C₂×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
21	D₄₄₉	—	4	1	no	—
22	D₄₄₉	D₈	1	1	yes	characteristic
23	D₄₄₉	SD₁₆	1	1	yes	characteristic
24	C₄₄₉	#102	1	1	yes	characteristic, complemented, Sylow
25	#102	—	449	1	no	maximal, Sylow
26	C₂×D₄	—	449	1	no	—
27	C₂×C₈	—	449	1	no	—
28	C₄⋊C₄	—	449	1	no	—
29	C₂³	—	898	1	no	—
30	D₄	—	898	1	no	—
31	D₄	—	449	1	no	—
32	D₄	#14267798	1	1	yes	characteristic, complemented
33	C₂×C₄	—	898	1	no	—
34	C₂×C₄	—	449	1	no	—
35	C₈	—	898	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	1796	1	no	—
38	C₂²	—	1796	1	no	—
39	C₂²	—	898	1	no	—
40	C₂²	—	449	1	no	—
41	C₄	—	1796	1	no	—
42	C₄	—	449	1	no	—
43	C₄	C₂×#14267798	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	1796	1	no	—
46	C₂	—	449	1	no	—
47	C₂	—	449	1	no	—
48	C₂	C₂²⋊#14267798	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#14267798
commutator	C₄×C₄₄₉	C₂×C₄
Frattini	C₄	C₂×#14267798
Fitting	D₄×C₄₄₉	C₄
socle	C₂×C₄₄₉	C₂²⋊C₄
prime radical	D₄×D₄₄₉	C₂
cosocle	C₄×D₄₄₉	C₂²
hypercenter	D₄	#14267798
hypocenter	C₄₄₉	#102
LCS	G ▷ C₄×C₄₄₉ ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #20297744	C₂	semidirect
2. C₄⋊#14267798	C₂	semidirect
7. D₁₇₉₆	C₄	semidirect
10. D₄×C₄₄₉	C₄	semidirect
24. C₄₄₉	#102	semidirect
32. D₄	#14267798	semidirect

Maximal subgroups

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

subgroup	index
#20297744	2
C₄⋊#14267798	2
D₄×D₄₄₉	2
#102	449