Subgroups — #43272864

Order 28736.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385395	C₂	1	1	yes	maximal, characteristic
2	#28385395	C₂	1	1	yes	maximal, characteristic
3	#28385331	C₂	1	1	yes	maximal, characteristic
4	C₂×#16813318	—	2	1	no	—
5	C₂×#16813318	—	2	1	no	—
6	C₄⋊Dic₄₄₉	—	2	1	no	—
7	C₄⋊Dic₄₄₉	C₄	1	1	yes	characteristic
8	#20297715	—	2	1	no	—
9	C₄×Dic₄₄₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₄₉	C₄	1	1	yes	characteristic
11	#16813318	—	2	2	no	—
12	#16813318	—	2	2	no	—
13	C₂×Dic₄₄₉	—	2	1	no	—
14	C₂×Dic₄₄₉	D₄	1	1	yes	characteristic
15	C₂×Dic₄₄₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₄₉	—	2	1	no	—
17	C₂×C₄×C₄₄₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₄₄₉	—	2	1	no	—
20	C₄×C₄₄₉	—	4	1	no	—
21	Dic₄₄₉	—	2	1	no	—
22	Dic₄₄₉	—	2	1	no	—
23	Dic₄₄₉	—	4	1	no	—
24	C₂×C₄₄₉	#101	1	1	yes	characteristic
25	C₂×C₄₄₉	#104	1	1	yes	characteristic
26	C₂×C₄₄₉	#104	1	1	yes	characteristic
27	C₄₄₉	#330	1	1	yes	characteristic, complemented, Sylow
28	#330	—	449	1	no	maximal, Sylow
29	#125	—	449	1	no	—
30	#97	—	449	1	no	—
31	#97	—	449	1	no	—
32	C₂×C₈	—	898	1	no	—
33	C₂×C₈	—	898	1	no	—
34	C₄⋊C₄	—	898	1	no	—
35	C₄⋊C₄	—	898	1	no	—
36	C₄⋊C₄	—	449	1	no	—
37	C₄⋊C₄	#14267798	1	1	yes	characteristic
38	C₄²	—	449	1	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	—	898	1	no	—
41	C₂×C₄	—	449	1	no	—
42	C₂×C₄	—	449	1	no	—
43	C₂×C₄	C₂×#14267798	1	1	yes	characteristic
44	C₈	—	898	2	no	—
45	C₈	—	898	2	no	—
46	C₂²	C₂²⋊#14267798	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	4	1	no	—
49	C₄	—	1796	1	no	—
50	C₄	—	898	1	no	—
51	C₄	—	898	1	no	—
52	C₂	#28385401	1	1	yes	characteristic
53	C₂	#28385404	1	1	yes	characteristic
54	C₂	#28385405	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#14267798
commutator	C₂×C₄×C₄₄₉	C₂×C₄
Frattini	C₂×C₄	C₂×#14267798
Fitting	C₄⋊C₄×C₄₄₉	C₄
socle, prime radical	C₂²×C₄₄₉	C₂²⋊C₄
cosocle	C₄×Dic₄₄₉	C₂²
hypercenter	C₄⋊C₄	#14267798
hypocenter	C₄₄₉	#330
LCS	G ▷ C₂×C₄×C₄₄₉ ▷ C₂²×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
27. C₄₄₉	#330	semidirect

Maximal subgroups

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

subgroup	index
#28385395	2
#28385331	2
#330	449