Subgroups — #28385296

Order 14368.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₄₉	C₂	1	1	yes	maximal, characteristic
2	#20297715	C₂	1	2	yes	maximal, complemented
3	C₂²⋊Dic₄₄₉	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₄₄₉	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₄×C₄₄₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₄₄₉	C₄	1	4	yes	complemented
7	C₂×Dic₄₄₉	C₂²	1	2	yes	—
8	C₂×Dic₄₄₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₄₉	C₂²	1	1	yes	characteristic
10	C₂³×C₄₄₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₄₄₉	C₂²	1	2	yes	—
12	C₂²×C₄₄₉	—	2	2	no	—
13	C₂²×C₄₄₉	C₂×C₄	1	2	yes	—
14	C₂²×C₄₄₉	C₂³	1	1	yes	characteristic
15	C₄×C₄₄₉	—	2	2	no	—
16	Dic₄₄₉	—	2	2	no	—
17	Dic₄₄₉	C₂×C₄	1	2	yes	—
18	Dic₄₄₉	C₂×C₄	1	2	yes	—
19	C₂×C₄₄₉	—	2	2	no	—
20	C₂×C₄₄₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄₄₉	#41	1	2	yes	—
22	C₄₄₉	#117	1	1	yes	characteristic, complemented, Sylow
23	#117	—	449	1	no	maximal, Sylow
24	C₂²×C₄	—	449	1	no	—
25	C₄⋊C₄	—	449	2	no	—
26	C₂²⋊C₄	—	449	1	no	—
27	C₂²⋊C₄	D₄₄₉	1	1	yes	characteristic
28	C₄²	—	449	2	no	—
29	C₂³	C₂×D₄₄₉	1	1	yes	characteristic
30	C₂×C₄	—	449	2	no	—
31	C₂×C₄	—	449	4	no	—
32	C₂×C₄	—	449	1	no	—
33	C₂×C₄	—	449	1	no	—
34	C₂×C₄	C₂×D₄₄₉	1	2	yes	—
35	C₂²	—	2	2	no	—
36	C₂²	C₄×D₄₄₉	1	2	yes	—
37	C₂²	C₂²×D₄₄₉	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	—	898	2	no	—
40	C₄	—	449	2	no	—
41	C₄	—	449	2	no	—
42	C₂	—	2	2	no	—
43	C₂	C₂×C₄×D₄₄₉	1	1	yes	characteristic
44	C₂	#20297735	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₄₄₉
commutator	C₂×C₄₄₉	C₂²×C₄
Fitting	C₂²⋊C₄×C₄₄₉	C₂
socle, cosocle	C₂²×C₄₄₉	C₂³
prime radical	C₂³×C₄₄₉	C₂²
hypercenter	C₂²⋊C₄	D₄₄₉
hypocenter	C₄₄₉	#117
LCS	G ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. #20297715	C₂	semidirect
4. C₄×Dic₄₄₉	C₂	semidirect
6. C₂×Dic₄₄₉	C₄	semidirect
22. C₄₄₉	#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₄₄₉	2
#20297715	2
C₂²⋊Dic₄₄₉	2
C₄×Dic₄₄₉	2
C₂²⋊C₄×C₄₄₉	2
#117	449