Subgroups — #46776873

Order 33568.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₁₉₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₁₀₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₁₀₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₀₄₉	—	2	1	no	—
5	D₄₁₉₆	—	2	1	no	—
6	D₄₁₉₆	C₄	1	2	yes	complemented
7	C₂×Dic₁₀₄₉	—	2	1	no	—
8	C₂×C₄×C₁₀₄₉	C₂²	1	1	yes	characteristic
9	C₈×C₁₀₄₉	—	2	1	no	—
10	C₂²×C₁₀₄₉	D₄	1	1	yes	characteristic
11	C₂×D₁₀₄₉	—	2	2	no	—
12	C₂×D₁₀₄₉	—	4	1	no	—
13	C₂×D₁₀₄₉	—	4	1	no	—
14	C₄×C₁₀₄₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₁₀₄₉	D₄	1	1	yes	characteristic
16	Dic₁₀₄₉	—	4	1	no	—
17	C₂×C₁₀₄₉	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₁₀₄₉	D₈	1	1	yes	characteristic
19	C₂×C₁₀₄₉	SD₁₆	1	1	yes	characteristic
20	D₁₀₄₉	—	4	2	no	—
21	C₁₀₄₉	#102	1	1	yes	characteristic, complemented, Sylow
22	#102	—	1049	1	no	maximal, Sylow
23	C₂×D₄	—	1049	1	no	—
24	C₂×C₈	D₁₀₄₉	1	1	yes	characteristic, complemented
25	C₄⋊C₄	—	1049	1	no	—
26	C₂³	—	2098	1	no	—
27	D₄	—	1049	2	no	—
28	D₄	—	2098	1	no	—
29	C₂×C₄	—	2098	1	no	—
30	C₂×C₄	C₂×D₁₀₄₉	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₂²	—	2098	2	no	—
33	C₂²	—	4196	1	no	—
34	C₂²	—	4196	1	no	—
35	C₂²	D₄₁₉₆	1	1	yes	characteristic
36	C₄	—	4196	1	no	—
37	C₄	C₄×D₁₀₄₉	1	1	yes	characteristic
38	C₄	C₂²⋊D₁₀₄₉	1	1	yes	characteristic
39	C₂	—	4196	2	no	—
40	C₂	#30680893	1	1	yes	characteristic
41	C₂	D₈₃₉₂	1	1	yes	characteristic
42	C₂	#30680905	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₁₉₆
commutator	C₄×C₁₀₄₉	C₂×C₄
Frattini	C₂×C₄	C₂×D₁₀₄₉
Fitting	C₂×C₈×C₁₀₄₉	C₂
socle	C₂²×C₁₀₄₉	D₄
prime radical	C₂×D₄₁₉₆	C₂
cosocle	C₂×C₄×C₁₀₄₉	C₂²
hypercenter	C₂×C₈	D₁₀₄₉
hypocenter	C₁₀₄₉	#102
LCS	G ▷ C₄×C₁₀₄₉ ▷ C₂×C₁₀₄₉ ▷ C₁₀₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₄⋊Dic₁₀₄₉	C₂	semidirect
3. C₂×C₈×C₁₀₄₉	C₂	semidirect
6. D₄₁₉₆	C₄	semidirect
21. C₁₀₄₉	#102	semidirect
24. C₂×C₈	D₁₀₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄₁₉₆	2
C₄⋊Dic₁₀₄₉	2
C₂×C₈×C₁₀₄₉	2
#102	1049