Subgroups — #37526859

Order 22976.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26040021	C₂	1	1	yes	maximal, characteristic
2	#26039955	C₂	1	1	yes	maximal, characteristic, complemented
3	#26039954	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₃₅₉	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×C₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#19153341	C₄	1	1	yes	characteristic
7	#19153325	C₄	1	1	yes	characteristic
8	#19153324	C₄	1	2	yes	—
9	C₈×D₃₅₉	C₂²	1	2	yes	—
10	C₃₅₉⋊C₁₆	C₂²	1	2	yes	—
11	C₂×C₈×C₃₅₉	C₂²	1	1	yes	characteristic
12	C₁₆×C₃₅₉	C₂²	1	1	yes	characteristic
13	C₁₆×C₃₅₉	C₂²	1	1	yes	characteristic
14	Dic₇₁₈	C₈	1	1	yes	characteristic
15	D₁₄₃₆	C₈	1	1	yes	characteristic
16	C₂²⋊D₃₅₉	C₈	1	2	yes	—
17	C₄×D₃₅₉	C₂×C₄	1	2	yes	—
18	C₃₅₉⋊C₈	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₃₅₉	C₂×C₄	1	1	yes	characteristic
20	C₈×C₃₅₉	C₂×C₄	1	1	yes	characteristic
21	C₈×C₃₅₉	C₂³	1	1	yes	characteristic
22	C₂²×C₃₅₉	C₂×C₈	1	1	yes	characteristic
23	C₂×D₃₅₉	C₂×C₈	1	2	yes	—
24	C₄×C₃₅₉	C₂×C₈	1	1	yes	characteristic
25	C₄×C₃₅₉	C₂²×C₄	1	1	yes	characteristic
26	Dic₃₅₉	C₂×C₈	1	2	yes	—
27	C₂×C₃₅₉	—	2	1	no	—
28	C₂×C₃₅₉	C₂²×C₈	1	1	yes	characteristic
29	D₃₅₉	—	2	2	no	—
30	C₃₅₉	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	359	1	no	maximal, Sylow
32	#131	—	359	1	no	—
33	M₃₂	—	359	1	no	—
34	M₃₂	—	359	2	no	—
35	C₂×C₁₆	—	359	2	no	—
36	C₂×C₁₆	D₃₅₉	1	1	yes	characteristic, complemented
37	#41	—	359	1	no	—
38	M₁₆	—	359	1	no	—
39	M₁₆	—	359	2	no	—
40	C₂×C₈	—	359	2	no	—
41	C₂×C₈	C₂×D₃₅₉	1	1	yes	characteristic
42	C₁₆	—	359	2	no	—
43	C₁₆	C₂×D₃₅₉	1	1	yes	characteristic
44	C₁₆	C₂×D₃₅₉	1	1	yes	characteristic
45	Q₈	—	359	1	no	—
46	D₄	—	359	2	no	—
47	D₄	—	359	1	no	—
48	C₂×C₄	—	359	2	no	—
49	C₂×C₄	C₄×D₃₅₉	1	1	yes	characteristic
50	C₈	—	359	2	no	—
51	C₈	C₄×D₃₅₉	1	1	yes	characteristic
52	C₈	C₂²×D₃₅₉	1	1	yes	characteristic
53	C₂²	—	359	2	no	—
54	C₂²	C₈×D₃₅₉	1	1	yes	characteristic
55	C₄	—	359	2	no	—
56	C₄	C₈×D₃₅₉	1	1	yes	characteristic
57	C₄	C₂×C₄×D₃₅₉	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	718	2	no	—
60	C₂	C₂×C₈×D₃₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×D₃₅₉
commutator, socle	C₂×C₃₅₉	C₂²×C₈
Frattini	C₈	C₂²×D₃₅₉
Fitting	C₂×C₁₆×C₃₅₉	C₂
prime radical	#19153341	C₄
cosocle	C₈×C₃₅₉	C₂³
hypercenter	C₂×C₁₆	D₃₅₉
hypocenter	C₃₅₉	#504
LCS	G ▷ C₂×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #26039955	C₂	semidirect
3. #26039954	C₂	semidirect
4. C₁₆×D₃₅₉	C₂	semidirect
5. C₂×C₁₆×C₃₅₉	C₂	semidirect
30. C₃₅₉	#504	semidirect
36. C₂×C₁₆	D₃₅₉	semidirect

Maximal subgroups

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

subgroup	index
#26040021	2
#26039955	2
#26039954	2
C₁₆×D₃₅₉	2
C₂×C₁₆×C₃₅₉	2
#504	359