Subgroups — #46776983

Order 33568.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30680917	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₁₀₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#30680906	C₂	1	1	yes	maximal, characteristic, complemented
4	#30680905	C₂	1	1	yes	maximal, characteristic, complemented
5	#30680903	C₂	1	1	yes	maximal, characteristic, complemented
6	#30680899	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₁₀₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₂₀₉₈	—	2	1	no	—
9	Dic₂₀₉₈	C₂²	1	1	yes	characteristic
10	D₄₁₉₆	—	2	1	no	—
11	D₄₁₉₆	C₂²	1	1	yes	characteristic
12	C₄×D₁₀₄₉	—	2	1	no	—
13	C₄×D₁₀₄₉	—	2	1	no	—
14	C₄×D₁₀₄₉	C₂²	1	1	yes	characteristic
15	#22554209	C₂²	1	1	yes	characteristic
16	Q₈×C₁₀₄₉	C₂²	1	1	yes	characteristic
17	Q₈×C₁₀₄₉	C₂²	1	1	yes	characteristic
18	C₈×C₁₀₄₉	C₂²	1	1	yes	characteristic
19	C₂×D₁₀₄₉	—	2	1	no	—
20	C₂×D₁₀₄₉	D₄	1	1	yes	characteristic
21	C₄×C₁₀₄₉	—	2	1	no	—
22	C₄×C₁₀₄₉	—	2	1	no	—
23	C₄×C₁₀₄₉	C₂³	1	1	yes	characteristic
24	Dic₁₀₄₉	—	2	1	no	—
25	Dic₁₀₄₉	D₄	1	1	yes	characteristic
26	C₂×C₁₀₄₉	C₂×D₄	1	1	yes	characteristic
27	D₁₀₄₉	—	2	1	no	—
28	D₁₀₄₉	—	4	1	no	—
29	C₁₀₄₉	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	1049	1	no	maximal, Sylow
31	#41	—	1049	1	no	—
32	C₂×Q₈	—	1049	1	no	—
33	Q₁₆	—	1049	1	no	—
34	Q₁₆	D₁₀₄₉	1	1	yes	characteristic, complemented
35	SD₁₆	—	1049	1	no	—
36	SD₁₆	—	1049	1	no	—
37	M₁₆	—	1049	1	no	—
38	Q₈	—	1049	1	no	—
39	Q₈	—	2098	1	no	—
40	Q₈	C₂×D₁₀₄₉	1	1	yes	characteristic
41	Q₈	C₂×D₁₀₄₉	1	1	yes	characteristic
42	D₄	—	1049	1	no	—
43	D₄	—	2098	1	no	—
44	C₂×C₄	—	1049	1	no	—
45	C₂×C₄	—	2098	1	no	—
46	C₂×C₄	—	2098	1	no	—
47	C₈	—	1049	1	no	—
48	C₈	C₂×D₁₀₄₉	1	1	yes	characteristic
49	C₂²	—	1049	1	no	—
50	C₂²	—	2098	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	1049	1	no	—
54	C₄	—	2098	1	no	—
55	C₄	C₂²×D₁₀₄₉	1	1	yes	characteristic
56	C₂	—	2098	1	no	—
57	C₂	—	4196	1	no	—
58	C₂	D₄×D₁₀₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₀₄₉
commutator, cosocle	C₄×C₁₀₄₉	C₂³
Frattini	C₄	C₂²×D₁₀₄₉
Fitting	Q₁₆×C₁₀₄₉	C₂
socle	C₂×C₁₀₄₉	C₂×D₄
prime radical	#30680917	C₂
hypercenter	Q₁₆	D₁₀₄₉
hypocenter	C₁₀₄₉	#137
LCS	G ▷ C₄×C₁₀₄₉ ▷ C₂×C₁₀₄₉ ▷ C₁₀₄₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₁₀₄₉	C₂	semidirect
3. #30680906	C₂	semidirect
4. #30680905	C₂	semidirect
5. #30680903	C₂	semidirect
6. #30680899	C₂	semidirect
7. Q₁₆×C₁₀₄₉	C₂	semidirect
29. C₁₀₄₉	#137	semidirect
34. Q₁₆	D₁₀₄₉	semidirect

Maximal subgroups

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

subgroup	index
#30680917	2
Q₈×D₁₀₄₉	2
#30680906	2
#30680905	2
#30680903	2
#30680899	2
Q₁₆×C₁₀₄₉	2
#137	1049