Subgroups — #43272926

Order 28736.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385415	C₂	1	1	yes	maximal, characteristic
2	#28385410	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₄₄₉	C₂	1	1	yes	maximal, characteristic
4	#20297746	—	2	1	no	—
5	#20297739	—	2	1	no	—
6	Q₈×D₄₄₉	—	2	1	no	—
7	Dic₁₇₉₆	C₄	1	1	yes	characteristic
8	#20297726	—	2	1	no	—
9	C₈×D₄₄₉	C₂²	1	1	yes	characteristic
10	Q₁₆×C₄₄₉	C₄	1	1	yes	characteristic
11	#16813318	—	4	1	no	—
12	Dic₈₉₈	—	2	1	no	—
13	Dic₈₉₈	—	4	1	no	—
14	C₄×D₄₄₉	—	4	1	no	—
15	C₄×D₄₄₉	D₄	1	1	yes	characteristic
16	#16813311	D₄	1	1	yes	characteristic
17	Q₈×C₄₄₉	—	2	1	no	—
18	C₈×C₄₄₉	C₂×C₄	1	1	yes	characteristic
19	C₂×D₄₄₉	SD₁₆	1	1	yes	characteristic
20	C₄×C₄₄₉	—	4	1	no	—
21	C₄×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₄₄₉	—	4	1	no	—
23	Dic₄₄₉	D₈	1	1	yes	characteristic
24	C₂×C₄₄₉	#102	1	1	yes	characteristic
25	D₄₄₉	—	2	1	no	—
26	C₄₄₉	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	449	1	no	maximal, Sylow
28	C₂×Q₁₆	—	449	1	no	—
29	M₃₂	—	449	1	no	—
30	#108	—	449	1	no	—
31	C₂×Q₈	—	898	1	no	—
32	Q₁₆	—	898	1	no	—
33	Q₁₆	—	449	1	no	—
34	Q₁₆	#14267798	1	1	yes	characteristic
35	M₁₆	—	898	1	no	—
36	C₂×C₈	—	449	1	no	—
37	C₁₆	—	898	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	1796	1	no	—
40	Q₈	—	898	1	no	—
41	C₂×C₄	—	1796	1	no	—
42	C₂×C₄	—	449	1	no	—
43	C₈	—	1796	1	no	—
44	C₈	—	449	1	no	—
45	C₈	C₂×#14267798	1	1	yes	characteristic
46	C₂²	—	449	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	1796	1	no	—
49	C₄	—	449	1	no	—
50	C₄	C₂²⋊#14267798	1	1	yes	characteristic
51	C₂	—	898	1	no	—
52	C₂	#28385402	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28385402
commutator	C₈×C₄₄₉	C₂×C₄
Frattini	C₈	C₂×#14267798
Fitting	Q₁₆×C₄₄₉	C₄
socle	C₂×C₄₄₉	#102
prime radical	C₂×D₄₄₉	SD₁₆
cosocle	C₈×D₄₄₉	C₂²
hypercenter	Q₁₆	#14267798
hypocenter	C₄₄₉	#362
LCS	G ▷ C₈×C₄₄₉ ▷ C₄×C₄₄₉ ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
26. C₄₄₉	#362	semidirect

Maximal subgroups

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

subgroup	index
#28385415	2
#28385410	2
Q₁₆×D₄₄₉	2
#362	449