Subgroups — #43273048

Order 28736.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#14267798	C₂	1	2	yes	maximal, complemented
2	#28385408	C₂	1	1	yes	maximal, characteristic, complemented
3	#28385402	C₂	1	2	yes	maximal, complemented
4	#28385394	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×D₄₄₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#14267798	—	2	2	no	—
7	#20297744	C₂²	1	1	yes	characteristic
8	C₄⋊#14267798	C₂²	1	2	yes	—
9	C₂²⋊#14267798	—	2	2	no	—
10	C₄×#14267798	C₂²	1	1	yes	characteristic
11	D₄×D₄₄₉	C₂²	1	2	yes	—
12	D₃₅₉₂	C₄	1	1	yes	characteristic, complemented
13	#20297721	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	2	no	—
17	C₂×#14267798	—	4	4	no	—
18	C₂×#14267798	D₄	1	2	yes	—
19	#16813318	—	2	1	no	—
20	C₂²×D₄₄₉	—	2	2	no	—
21	D₁₇₉₆	C₂×C₄	1	2	yes	complemented
22	C₂²⋊D₄₄₉	—	2	2	no	—
23	C₄×D₄₄₉	C₂³	1	1	yes	characteristic
24	#16813311	C₂×C₄	1	1	yes	characteristic, complemented
25	D₄×C₄₄₉	C₂×C₄	1	2	yes	complemented
26	C₈×C₄₄₉	C₂×C₄	1	1	yes	characteristic, complemented
27	C₂²×C₄₄₉	—	2	2	no	—
28	C₂×D₄₄₉	—	2	2	no	—
29	C₂×D₄₄₉	—	4	2	no	—
30	C₂×D₄₄₉	—	4	2	no	—
31	C₂×D₄₄₉	C₂×D₄	1	1	yes	characteristic
32	#14267798	—	2	2	no	—
33	#14267798	—	4	2	no	—
34	C₄×C₄₄₉	C₂²×C₄	1	1	yes	characteristic
35	Dic₄₄₉	#41	1	1	yes	characteristic
36	C₂×C₄₄₉	—	4	2	no	—
37	C₂×C₄₄₉	C₄×D₄	1	1	yes	characteristic
38	D₄₄₉	—	4	2	no	—
39	D₄₄₉	AGL(1,ℤ/8)	1	2	yes	—
40	C₄₄₉	#442	1	1	yes	characteristic, complemented, Sylow
41	#442	—	449	1	no	maximal, Sylow
42	C₂×D₈	—	449	1	no	—
43	C₄×D₄	—	449	2	no	—
44	#106	—	449	1	no	—
45	#102	—	449	2	no	—
46	#97	—	449	1	no	—
47	C₂×D₄	—	449	2	no	—
48	C₂²×C₄	—	898	2	no	—
49	D₈	—	449	2	no	—
50	D₈	—	449	1	no	—
51	D₈	#14267798	1	1	yes	characteristic, complemented
52	C₂×C₈	—	449	1	no	—
53	C₂×C₈	—	449	1	no	—
54	C₄⋊C₄	—	449	2	no	—
55	C₂²⋊C₄	—	898	2	no	—
56	C₄²	—	449	1	no	—
57	C₂³	—	898	2	no	—
58	D₄	—	898	2	no	—
59	D₄	—	449	2	no	—
60	D₄	C₂×#14267798	1	2	yes	complemented
61	C₂×C₄	—	1796	4	no	—
62	C₂×C₄	—	898	2	no	—
63	C₂×C₄	—	449	2	no	—
64	C₂×C₄	—	449	1	no	—
65	C₈	—	898	1	no	—
66	C₈	—	449	1	no	—
67	C₈	C₂×#14267798	1	1	yes	characteristic, complemented
68	C₂²	—	2	2	no	—
69	C₂²	—	1796	2	no	—
70	C₂²	—	1796	2	no	—
71	C₂²	—	898	2	no	—
72	C₂²	—	449	1	no	—
73	C₄	—	1796	2	no	—
74	C₄	—	898	2	no	—
75	C₄	—	449	1	no	—
76	C₄	C₂²×#14267798	1	1	yes	characteristic
77	C₂	—	4	2	no	—
78	C₂	—	1796	2	no	—
79	C₂	—	449	2	no	—
80	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	D₈×D₄₄₉	C₂
cosocle	C₄×D₄₄₉	C₂³
hypercenter	D₈	#14267798
hypocenter	C₄₄₉	#442
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. D₄×#14267798	C₂	semidirect
2. #28385408	C₂	semidirect
3. #28385402	C₂	semidirect
4. #28385394	C₂	semidirect
12. D₃₅₉₂	C₄	semidirect
13. #20297721	C₄	semidirect
15. D₈×C₄₄₉	C₄	semidirect
21. D₁₇₉₆	C₂×C₄	semidirect
24. #16813311	C₂×C₄	semidirect
25. D₄×C₄₄₉	C₂×C₄	semidirect
26. C₈×C₄₄₉	C₂×C₄	semidirect
40. C₄₄₉	#442	semidirect
51. D₈	#14267798	semidirect
60. D₄	C₂×#14267798	semidirect
67. C₈	C₂×#14267798	semidirect

Maximal subgroups

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

subgroup	index
D₄×#14267798	2
#28385408	2
#28385402	2
#28385394	2
D₈×D₄₄₉	2
#442	449