Subgroups — #39910344

Order 26176.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20267000	C₂	1	2	yes	maximal, complemented
2	C₂×#20266996	C₂	1	1	yes	maximal, characteristic
3	#20267000	—	2	2	no	—
4	#20266996	—	2	2	no	—
5	C₂×#15692550	C₄	1	1	yes	characteristic
6	C₂×#15692550	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄₀₉	C₄	1	1	yes	characteristic
8	#15692550	—	2	1	no	—
9	#15692550	D₄	1	2	yes	—
10	C₂²×D₄₀₉	C₈	1	1	yes	characteristic
11	C₂×Dic₄₀₉	C₂×C₄	1	1	yes	characteristic
12	C₄×D₄₀₉	—	2	1	no	—
13	C₄×D₄₀₉	—	2	1	no	—
14	C₂×C₄×C₄₀₉	C₈	1	1	yes	characteristic
15	C₂²×C₄₀₉	C₂×C₈	1	1	yes	characteristic
16	C₂×D₄₀₉	—	2	1	no	—
17	C₂×D₄₀₉	—	2	1	no	—
18	C₂×D₄₀₉	C₁₆	1	2	yes	complemented
19	C₄×C₄₀₉	—	2	1	no	—
20	Dic₄₀₉	C₂²⋊C₄	1	1	yes	characteristic
21	Dic₄₀₉	M₁₆	1	1	yes	characteristic
22	C₂×C₄₀₉	C₂²⋊C₈	1	1	yes	characteristic
23	C₂×C₄₀₉	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₄₀₉	M₃₂	1	1	yes	characteristic
25	D₄₀₉	—	2	2	no	—
26	C₄₀₉	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	409	1	no	maximal, Sylow
28	C₂²×C₈	—	409	1	no	—
29	C₂×C₁₆	—	409	2	no	—
30	C₂²×C₄	—	409	1	no	—
31	C₂×C₈	—	818	2	no	—
32	C₂×C₈	—	409	1	no	—
33	C₂×C₈	—	409	1	no	—
34	C₁₆	—	818	2	no	—
35	C₂³	—	409	1	no	—
36	C₂×C₄	—	818	1	no	—
37	C₂×C₄	—	818	1	no	—
38	C₂×C₄	—	409	1	no	—
39	C₂×C₄	#15692552	1	1	yes	characteristic
40	C₈	—	818	1	no	—
41	C₈	—	409	2	no	—
42	C₂²	—	818	1	no	—
43	C₂²	—	818	1	no	—
44	C₂²	—	409	2	no	—
45	C₂²	C₂×#15692552	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	409	1	no	—
48	C₄	—	409	1	no	—
49	C₂	—	818	2	no	—
50	C₂	C₂²⋊#15692552	1	1	yes	characteristic
51	C₂	#27189812	1	1	yes	characteristic
52	C₂	#27189814	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#15692552
commutator	C₂×C₄₀₉	C₂×C₁₆
Fitting	C₂×C₄×C₄₀₉	C₈
socle	C₂²×C₄₀₉	C₂×C₈
prime radical	C₂²×D₄₀₉	C₈
cosocle	C₂×#15692550	C₂²
hypercenter	C₂×C₄	#15692552
hypocenter	C₄₀₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄₀₉ ▷ C₄₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#20267000	C₂	semidirect
18. C₂×D₄₀₉	C₁₆	semidirect
26. C₄₀₉	C₂²⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20267000	2
C₂×#20266996	2
C₂²⋊C₁₆	409