Subgroups — #43272921

Order 28736.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385413	C₂	1	1	yes	maximal, characteristic, complemented
2	#28385411	C₂	1	1	yes	maximal, characteristic, complemented
3	#28385359	C₂	1	1	yes	maximal, characteristic
4	#20297746	—	2	1	no	—
5	#20297739	—	2	1	no	—
6	#20297735	—	2	1	no	—
7	Dic₁₇₉₆	C₄	1	1	yes	characteristic
8	#20297724	—	2	1	no	—
9	C₈×D₄₄₉	C₂²	1	1	yes	characteristic
10	D₈×C₄₄₉	C₄	1	1	yes	characteristic
11	#16813318	—	4	1	no	—
12	Dic₈₉₈	—	2	1	no	—
13	C₂²⋊D₄₄₉	—	4	1	no	—
14	C₂×Dic₄₄₉	—	4	1	no	—
15	C₄×D₄₄₉	D₄	1	1	yes	characteristic
16	#16813311	D₄	1	1	yes	characteristic
17	D₄×C₄₄₉	—	2	1	no	—
18	C₈×C₄₄₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄₄₉	—	4	1	no	—
20	C₂×D₄₄₉	SD₁₆	1	1	yes	characteristic
21	C₄×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₄₄₉	—	4	1	no	—
23	Dic₄₄₉	D₈	1	1	yes	characteristic
24	C₂×C₄₄₉	—	8	1	no	—
25	C₂×C₄₄₉	#102	1	1	yes	characteristic
26	D₄₄₉	—	2	1	no	—
27	C₄₄₉	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	449	1	no	maximal, Sylow
29	#135	—	449	1	no	—
30	C₂×C₁₆	—	449	1	no	—
31	#108	—	449	1	no	—
32	#41	—	898	1	no	—
33	Q₁₆	—	449	1	no	—
34	SD₁₆	—	898	1	no	—
35	D₈	#14267798	1	1	yes	characteristic
36	M₁₆	—	898	1	no	—
37	C₂×C₈	—	449	1	no	—
38	C₁₆	—	898	1	no	—
39	Q₈	—	898	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	1796	1	no	—
42	C₂×C₄	—	1796	1	no	—
43	C₂×C₄	—	449	1	no	—
44	C₈	—	1796	1	no	—
45	C₈	—	449	1	no	—
46	C₈	C₂×#14267798	1	1	yes	characteristic
47	C₂²	—	4	1	no	—
48	C₂²	—	449	1	no	—
49	C₄	—	1796	1	no	—
50	C₄	—	449	1	no	—
51	C₄	C₂²⋊#14267798	1	1	yes	characteristic
52	C₂	—	8	1	no	—
53	C₂	—	898	1	no	—
54	C₂	#28385402	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28385402
commutator	C₈×C₄₄₉	C₂×C₄
Frattini	C₈	C₂×#14267798
Fitting	D₈×C₄₄₉	C₄
socle	C₂×C₄₄₉	#102
prime radical	#28385359	C₂
cosocle	C₈×D₄₄₉	C₂²
hypercenter	D₈	#14267798
hypocenter	C₄₄₉	#359
LCS	G ▷ C₈×C₄₄₉ ▷ C₄×C₄₄₉ ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #28385413	C₂	semidirect
2. #28385411	C₂	semidirect
27. C₄₄₉	#359	semidirect

Maximal subgroups

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

subgroup	index
#28385413	2
#28385411	2
#28385359	2
#359	449