Subgroups — #37526257

Order 22976.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₈₇₂	C₂	1	1	yes	maximal, characteristic
2	#26039951	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₄₃₆	—	2	1	no	—
5	D₂₈₇₂	—	2	1	no	—
6	D₂₈₇₂	C₄	1	2	yes	—
7	#19153325	—	2	1	no	—
8	C₂×C₈×C₃₅₉	C₂²	1	1	yes	characteristic
9	C₁₆×C₃₅₉	—	2	1	no	—
10	C₂²×D₃₅₉	—	4	1	no	—
11	D₁₄₃₆	—	2	2	no	—
12	D₁₄₃₆	—	4	1	no	—
13	C₃₅₉⋊C₈	—	4	1	no	—
14	C₂×C₄×C₃₅₉	D₄	1	1	yes	characteristic
15	C₈×C₃₅₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₅₉	D₄	1	1	yes	characteristic
17	C₂²×C₃₅₉	SD₁₆	1	1	yes	characteristic
18	C₂×D₃₅₉	—	4	2	no	—
19	C₂×D₃₅₉	—	8	2	no	—
20	C₄×C₃₅₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₅₉	D₈	1	1	yes	characteristic
22	C₂×C₃₅₉	—	2	1	no	—
23	C₂×C₃₅₉	#102	1	1	yes	characteristic
24	D₃₅₉	—	8	2	no	—
25	C₃₅₉	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	359	1	no	maximal, Sylow
27	C₂×D₈	—	359	1	no	—
28	M₃₂	D₃₅₉	1	1	yes	characteristic, complemented
29	#108	—	359	1	no	—
30	C₂×D₄	—	718	1	no	—
31	D₈	—	359	2	no	—
32	D₈	—	718	1	no	—
33	M₁₆	—	718	1	no	—
34	C₂×C₈	C₂×D₃₅₉	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	1436	1	no	—
37	D₄	—	1436	1	no	—
38	D₄	—	718	2	no	—
39	C₂×C₄	D₁₄₃₆	1	1	yes	characteristic
40	C₈	—	1436	1	no	—
41	C₈	C₄×D₃₅₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₃₅₉	1	1	yes	characteristic
43	C₂²	—	2872	2	no	—
44	C₂²	—	1436	2	no	—
45	C₂²	#19153330	1	1	yes	characteristic
46	C₄	(C₂×D₃₅₉)⋊C₄	1	1	yes	characteristic
47	C₄	D₂₈₇₂	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	2872	2	no	—
50	C₂	#26039937	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26039937
commutator	C₈×C₃₅₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₃₅₉
Fitting	M₃₂×C₃₅₉	C₂
socle	C₂×C₃₅₉	#102
prime radical	C₂×D₂₈₇₂	C₂
cosocle	C₂×C₈×C₃₅₉	C₂²
hypercenter	M₃₂	D₃₅₉
hypocenter	C₃₅₉	#361
LCS	G ▷ C₈×C₃₅₉ ▷ C₄×C₃₅₉ ▷ C₂×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #26039951	C₂	semidirect
3. M₃₂×C₃₅₉	C₂	semidirect
25. C₃₅₉	#361	semidirect
28. M₃₂	D₃₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₈₇₂	2
#26039951	2
M₃₂×C₃₅₉	2
#361	359