Subgroups — #43272890

Order 28736.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20297746	C₂	1	1	yes	maximal, characteristic
2	#28385419	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₄₄₉	C₂	1	1	yes	maximal, characteristic
4	#20297746	—	2	1	no	—
5	#20297746	—	2	1	no	—
6	C₂×#16813318	C₄	1	2	yes	complemented
7	C₄⋊#14267798	—	2	1	no	—
8	C₂²⋊#14267798	C₄	1	2	yes	—
9	C₄×#14267798	—	2	1	no	—
10	C₂×C₄×D₄₄₉	C₂²	1	1	yes	characteristic
11	#20297720	C₄	1	1	yes	characteristic, complemented
12	#20297719	—	2	1	no	—
13	C₈×D₄₄₉	—	2	1	no	—
14	M₁₆×C₄₄₉	C₄	1	1	yes	characteristic, complemented
15	C₂×#14267798	—	2	2	no	—
16	#16813318	—	2	2	no	—
17	C₂²×D₄₄₉	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₄₄₉	C₂×C₄	1	1	yes	characteristic
19	C₄×D₄₄₉	D₄	1	1	yes	characteristic
20	C₄×D₄₄₉	D₄	1	1	yes	characteristic
21	C₄×D₄₄₉	D₄	1	1	yes	characteristic
22	C₄×D₄₄₉	Q₈	1	1	yes	characteristic
23	#16813311	—	2	1	no	—
24	C₂×C₄×C₄₄₉	C₂×C₄	1	1	yes	characteristic
25	C₈×C₄₄₉	—	2	1	no	—
26	C₂²×C₄₄₉	C₄²	1	1	yes	characteristic
27	C₂×D₄₄₉	—	4	1	no	—
28	C₂×D₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₄₄₉	C₄⋊C₄	1	1	yes	characteristic
30	#14267798	—	4	2	no	—
31	C₄×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₄₄₉	C₄⋊C₄	1	1	yes	characteristic
33	Dic₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₄₄₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄₄₉	—	2	1	no	—
36	C₂×C₄₄₉	#95	1	1	yes	characteristic
37	D₄₄₉	—	2	1	no	—
38	D₄₄₉	—	2	1	no	—
39	C₄₄₉	#344	1	1	yes	characteristic, complemented, Sylow
40	#344	—	449	1	no	maximal, Sylow
41	C₂×M₁₆	—	449	1	no	—
42	C₂×M₁₆	—	449	1	no	—
43	#117	—	449	1	no	—
44	C₂²×C₄	—	449	1	no	—
45	M₁₆	—	898	1	no	—
46	M₁₆	—	898	1	no	—
47	M₁₆	—	898	1	no	—
48	M₁₆	—	449	1	no	—
49	M₁₆	#14267798	1	1	yes	characteristic, complemented
50	C₂×C₈	—	898	1	no	—
51	C₂×C₈	—	449	2	no	—
52	C₄⋊C₄	—	898	1	no	—
53	C₂²⋊C₄	—	449	2	no	—
54	C₄²	—	898	1	no	—
55	C₂³	—	449	1	no	—
56	C₂×C₄	—	898	2	no	—
57	C₂×C₄	—	449	1	no	—
58	C₂×C₄	—	449	1	no	—
59	C₂×C₄	—	449	1	no	—
60	C₂×C₄	—	449	1	no	—
61	C₂×C₄	—	449	1	no	—
62	C₂×C₄	C₂×#14267798	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	898	2	no	—
65	C₈	—	898	1	no	—
66	C₂²	—	1796	1	no	—
67	C₂²	—	449	1	no	—
68	C₂²	—	449	1	no	—
69	C₂²	C₄×#14267798	1	1	yes	characteristic
70	C₄	—	1796	2	no	—
71	C₄	—	449	1	no	—
72	C₄	—	449	1	no	—
73	C₄	C₂²⋊#14267798	1	1	yes	characteristic
74	C₄	C₄⋊#14267798	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	898	1	no	—
77	C₂	—	898	1	no	—
78	C₂	(C₂×#14267798)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×#14267798)⋊C₄
commutator	C₂²×C₄₄₉	C₄²
Frattini	C₂×C₄	C₂×#14267798
Fitting	M₁₆×C₄₄₉	C₄
socle	C₂×C₄₄₉	#95
prime radical	C₂²×D₄₄₉	C₂×C₄
cosocle	C₂×C₄×D₄₄₉	C₂²
hypercenter	M₁₆	#14267798
hypocenter	C₄₄₉	#344
LCS	G ▷ C₂²×C₄₄₉ ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×#16813318	C₄	semidirect
11. #20297720	C₄	semidirect
14. M₁₆×C₄₄₉	C₄	semidirect
39. C₄₄₉	#344	semidirect
49. M₁₆	#14267798	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20297746	2
#28385419	2
M₁₆×D₄₄₉	2
#344	449