Subgroups — #43273054

Order 28736.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385427	C₂	1	2	yes	maximal, complemented
2	#28385410	C₂	1	1	yes	maximal, characteristic, complemented
3	#28385404	C₂	1	2	yes	maximal, complemented
4	#28385394	C₂	1	1	yes	maximal, characteristic, complemented
5	#28385359	C₂	1	1	yes	maximal, characteristic
6	#20297746	C₂²	1	2	yes	—
7	#20297745	—	2	2	no	—
8	#20297744	C₂²	1	1	yes	characteristic
9	C₂×#16813318	—	2	2	no	—
10	C₄×#14267798	C₂²	1	1	yes	characteristic
11	#20297735	C₂²	1	2	yes	—
12	Dic₁₇₉₆	C₄	1	1	yes	characteristic, complemented
13	#20297724	C₄	1	2	yes	complemented
14	C₈×D₄₄₉	C₂²	1	1	yes	characteristic
15	D₈×C₄₄₉	C₄	1	1	yes	characteristic, complemented
16	C₂×#14267798	—	2	1	no	—
17	#16813318	—	2	2	no	—
18	#16813318	D₄	1	2	yes	—
19	Dic₈₉₈	C₂×C₄	1	2	yes	—
20	C₂²⋊D₄₄₉	—	2	2	no	—
21	C₂×Dic₄₄₉	—	2	2	no	—
22	C₄×D₄₄₉	C₂³	1	1	yes	characteristic
23	#16813311	C₂×C₄	1	1	yes	characteristic
24	D₄×C₄₄₉	C₂×C₄	1	2	yes	—
25	C₈×C₄₄₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₄₉	—	2	2	no	—
27	C₂×D₄₄₉	#41	1	1	yes	characteristic
28	#14267798	—	4	1	no	—
29	C₄×C₄₄₉	C₂²×C₄	1	1	yes	characteristic
30	Dic₄₄₉	—	2	2	no	—
31	Dic₄₄₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄₄₉	—	4	2	no	—
33	C₂×C₄₄₉	C₄×D₄	1	1	yes	characteristic
34	D₄₄₉	—	2	1	no	—
35	C₄₄₉	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	449	1	no	maximal, Sylow
37	#135	—	449	1	no	—
38	#131	—	449	2	no	—
39	#108	—	449	1	no	—
40	#104	—	449	2	no	—
41	#97	—	449	1	no	—
42	#41	—	449	2	no	—
43	Q₁₆	—	449	1	no	—
44	SD₁₆	—	449	2	no	—
45	D₈	#14267798	1	1	yes	characteristic, complemented
46	M₁₆	—	898	2	no	—
47	M₁₆	—	449	2	no	—
48	C₂×C₈	—	898	2	no	—
49	C₂×C₈	—	449	1	no	—
50	C₂×C₈	—	449	1	no	—
51	C₄²	—	449	1	no	—
52	Q₈	—	449	2	no	—
53	D₄	—	898	2	no	—
54	D₄	C₂×#14267798	1	2	yes	—
55	C₂×C₄	—	898	1	no	—
56	C₂×C₄	—	898	2	no	—
57	C₂×C₄	—	449	1	no	—
58	C₈	—	898	2	no	—
59	C₈	—	449	2	no	—
60	C₈	—	449	1	no	—
61	C₈	C₂×#14267798	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	449	1	no	—
64	C₄	—	1796	1	no	—
65	C₄	—	898	2	no	—
66	C₄	—	449	1	no	—
67	C₄	C₂²×#14267798	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	898	1	no	—
70	C₂	D₄×#14267798	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#14267798
commutator	C₄×C₄₄₉	C₂²×C₄
Frattini	C₄	C₂²×#14267798
Fitting	D₈×C₄₄₉	C₄
socle	C₂×C₄₄₉	C₄×D₄
prime radical	#28385359	C₂
cosocle	C₄×D₄₄₉	C₂³
hypercenter	D₈	#14267798
hypocenter	C₄₄₉	#444
LCS	G ▷ C₄×C₄₄₉ ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #28385427	C₂	semidirect
2. #28385410	C₂	semidirect
3. #28385404	C₂	semidirect
4. #28385394	C₂	semidirect
12. Dic₁₇₉₆	C₄	semidirect
13. #20297724	C₄	semidirect
15. D₈×C₄₄₉	C₄	semidirect
35. C₄₄₉	#444	semidirect
45. D₈	#14267798	semidirect

Maximal subgroups

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

subgroup	index
#28385427	2
#28385410	2
#28385404	2
#28385394	2
#28385359	2
#444	449