Subgroups — #43273051

Order 28736.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385428	C₂	1	2	yes	maximal, complemented
2	#28385411	C₂	1	1	yes	maximal, characteristic, complemented
3	#28385405	C₂	1	2	yes	maximal, complemented
4	C₈×#14267798	C₂	1	1	yes	maximal, characteristic, complemented
5	#28385363	C₂	1	1	yes	maximal, characteristic
6	#20297746	—	2	2	no	—
7	#20297746	C₂²	1	2	yes	—
8	#20297744	—	2	2	no	—
9	#20297744	C₂²	1	1	yes	characteristic
10	C₄×#14267798	C₂²	1	1	yes	characteristic
11	#20297737	C₂²	1	2	yes	—
12	#20297723	C₄	1	2	yes	complemented
13	D₃₅₉₂	C₄	1	1	yes	characteristic, complemented
14	C₈×D₄₄₉	C₂²	1	1	yes	characteristic
15	Q₁₆×C₄₄₉	C₄	1	1	yes	characteristic, complemented
16	C₂×#14267798	—	2	1	no	—
17	#16813318	—	2	2	no	—
18	#16813318	D₄	1	1	yes	characteristic
19	#16813318	D₄	1	1	yes	characteristic
20	D₁₇₉₆	—	2	2	no	—
21	D₁₇₉₆	C₂×C₄	1	2	yes	—
22	C₄×D₄₄₉	—	2	2	no	—
23	C₄×D₄₄₉	C₂³	1	1	yes	characteristic
24	#16813311	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₄₄₉	C₂×C₄	1	2	yes	—
26	C₈×C₄₄₉	C₂×C₄	1	1	yes	characteristic
27	C₂×D₄₄₉	—	2	2	no	—
28	C₂×D₄₄₉	#41	1	1	yes	characteristic
29	#14267798	—	2	2	no	—
30	C₄×C₄₄₉	—	2	2	no	—
31	C₄×C₄₄₉	C₂²×C₄	1	1	yes	characteristic
32	Dic₄₄₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄₄₉	C₄×D₄	1	1	yes	characteristic
34	D₄₄₉	—	2	1	no	—
35	D₄₄₉	—	4	2	no	—
36	C₄₄₉	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	449	1	no	maximal, Sylow
38	#135	—	449	1	no	—
39	#131	—	449	2	no	—
40	#108	—	449	1	no	—
41	#104	—	449	2	no	—
42	C₄×C₈	—	449	1	no	—
43	#41	—	449	2	no	—
44	Q₁₆	#14267798	1	1	yes	characteristic, complemented
45	SD₁₆	—	449	2	no	—
46	D₈	—	449	1	no	—
47	M₁₆	—	898	2	no	—
48	M₁₆	—	449	2	no	—
49	C₂×C₈	—	898	2	no	—
50	C₂×C₈	—	449	1	no	—
51	C₂×C₈	—	449	1	no	—
52	C₄²	—	449	1	no	—
53	Q₈	C₂×#14267798	1	2	yes	—
54	D₄	—	898	2	no	—
55	D₄	—	449	2	no	—
56	C₂×C₄	—	898	2	no	—
57	C₂×C₄	—	898	1	no	—
58	C₂×C₄	—	449	1	no	—
59	C₈	—	898	2	no	—
60	C₈	—	449	1	no	—
61	C₈	—	449	1	no	—
62	C₈	—	449	1	no	—
63	C₈	C₂×#14267798	1	1	yes	characteristic
64	C₂²	—	898	2	no	—
65	C₂²	—	449	1	no	—
66	C₄	—	2	2	no	—
67	C₄	—	898	2	no	—
68	C₄	—	449	1	no	—
69	C₄	C₂²×#14267798	1	1	yes	characteristic
70	C₂	—	1796	2	no	—
71	C₂	—	898	1	no	—
72	C₂	D₄×#14267798	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#14267798
commutator	C₄×C₄₄₉	C₂²×C₄
Frattini	C₄	C₂²×#14267798
Fitting	Q₁₆×C₄₄₉	C₄
socle	C₂×C₄₄₉	C₄×D₄
prime radical	#28385363	C₂
cosocle	C₄×D₄₄₉	C₂³
hypercenter	Q₁₆	#14267798
hypocenter	C₄₄₉	#443
LCS	G ▷ C₄×C₄₄₉ ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #28385428	C₂	semidirect
2. #28385411	C₂	semidirect
3. #28385405	C₂	semidirect
4. C₈×#14267798	C₂	semidirect
12. #20297723	C₄	semidirect
13. D₃₅₉₂	C₄	semidirect
15. Q₁₆×C₄₄₉	C₄	semidirect
36. C₄₄₉	#443	semidirect
44. Q₁₆	#14267798	semidirect

Maximal subgroups

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

subgroup	index
#28385428	2
#28385411	2
#28385405	2
C₈×#14267798	2
#28385363	2
#443	449