Subgroups — #43272920

Order 28736.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385413	C₂	1	1	yes	maximal, characteristic
2	#28385409	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₄₄₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#14267798	—	2	1	no	—
5	#20297739	—	2	1	no	—
6	Q₈×D₄₄₉	—	2	1	no	—
7	Dic₁₇₉₆	C₄	1	1	yes	characteristic, complemented
8	#20297726	—	2	1	no	—
9	C₈×D₄₄₉	C₂²	1	1	yes	characteristic
10	Q₁₆×C₄₄₉	C₄	1	1	yes	characteristic, complemented
11	C₂×#14267798	—	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	D₈	1	1	yes	characteristic
20	#14267798	—	8	1	no	—
21	C₄×C₄₄₉	—	4	1	no	—
22	C₄×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₄₄₉	—	4	1	no	—
24	Dic₄₄₉	SD₁₆	1	1	yes	characteristic
25	C₂×C₄₄₉	#102	1	1	yes	characteristic
26	D₄₄₉	SD₃₂	1	1	yes	characteristic
27	D₄₄₉	Q₃₂	1	1	yes	characteristic
28	C₄₄₉	#358	1	1	yes	characteristic, complemented, Sylow
29	#358	—	449	1	no	maximal, Sylow
30	C₂×Q₁₆	—	449	1	no	—
31	C₂×C₁₆	—	449	1	no	—
32	#107	—	449	1	no	—
33	C₂×Q₈	—	898	1	no	—
34	Q₁₆	—	898	1	no	—
35	Q₁₆	—	449	1	no	—
36	Q₁₆	#14267798	1	1	yes	characteristic, complemented
37	C₂×C₈	—	449	1	no	—
38	C₄⋊C₄	—	898	1	no	—
39	C₁₆	—	898	1	no	—
40	Q₈	—	2	1	no	—
41	Q₈	—	1796	1	no	—
42	Q₈	—	898	1	no	—
43	C₂×C₄	—	1796	1	no	—
44	C₂×C₄	—	1796	1	no	—
45	C₂×C₄	—	449	1	no	—
46	C₈	—	449	1	no	—
47	C₈	C₂×#14267798	1	1	yes	characteristic
48	C₂²	—	449	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	1796	1	no	—
51	C₄	—	3592	1	no	—
52	C₄	—	449	1	no	—
53	C₄	C₂²⋊#14267798	1	1	yes	characteristic
54	C₂	—	449	1	no	—
55	C₂	—	449	1	no	—
56	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	D₈
cosocle	C₈×D₄₄₉	C₂²
hypercenter	Q₁₆	#14267798
hypocenter	C₄₄₉	#358
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
7. Dic₁₇₉₆	C₄	semidirect
10. Q₁₆×C₄₄₉	C₄	semidirect
28. C₄₄₉	#358	semidirect
36. Q₁₆	#14267798	semidirect

Maximal subgroups

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

subgroup	index
#28385413	2
#28385409	2
Q₁₆×D₄₄₉	2
#358	449